on patient flow in hospitals: a data-based queueing-science

Stochastic Systems

ON PATIENT FLOW IN HOSPITALS A DATA-BASEDQUEUEING-SCIENCE PERSPECTIVE

By Mor Armonylowast Shlomo Israelitdagger Avishai MandelbaumDaggerYariv N Marmorsect Yulia Tseytlinpara and Galit B Yom-Tov

NYUlowast Rambam Hospitaldagger TechnionDaggerORT Braude College amp Mayo Clinicsect IBM Researchpara Technion

Hospitals are complex systems with essential societal benefits andhuge mounting costs These costs are exacerbated by inefficiencies inhospital processes which are often manifested by congestion and longdelays in patient care Thus a queueing-network view of patient flowin hospitals is natural for studying and improving its performanceThe goal of our research is to explore patient flow data through thelens of a queueing scientist The means is exploratory data analysis(EDA) in a large Israeli hospital which reveals important featuresthat are not readily explainable by existing models

Questions raised by our EDA include Can a simple (parsimonious)queueing model usefully capture the complex operational reality ofthe Emergency Department (ED) What time scales and operationalregimes are relevant for modeling patient length of stay in the Inter-nal Wards (IWs) How do protocols of patient transfer between theED and the IWs influence patient delay workload division and fair-ness EDA also underscores the importance of an integrative view ofhospital units by for example relating ED bottlenecks to IW physi-cian protocols The significance of such questions and our relatedfindings raise the need for novel queueing models and theory whichwe present here as research opportunities

Hospital data and specifically patient flow data at the level of theindividual patient is increasingly collected but is typically confiden-tial andor proprietary We have been fortunate to partner with ahospital that allowed us to open up its data for everyone to accessThis enables reproducibility of our findings through a user-friendlyplatform that is accessible via the Technion SEELab

1 Introduction Health care systems in general and hospitals in par-ticular are major determinants of our quality of life They also require asignificant fraction of our resources and at the same time they suffer from(quoting a physician research partner) ldquoa ridiculous number of inefficienciesthus everybodymdashpatients families nurses doctors and administrators are

Keywords and phrases Queueing Models Queueing Networks Healthcare Patientflow EDA Emergency Departments Hospital wards Event logs

1imsart-ssy ver 20130306 file Short_Patientflowmaintex date January 19 2015

2 ARMONY ET AL

frustratedrdquo In (too) many instances this frustration is caused and exacer-bated by delaysmdashldquowaiting for something to happenrdquo in turn these delaysand the corresponding queues signal inefficiencies Hospitals thus present apropitious ground for research in Queueing Theory and more generally Ap-plied Probability (AP) Operations Research (OR) and Service Engineering(SE) Such research would ideally culminate in reduced congestion (crowd-ing) and its accompanying important benefits clinical financial psychologi-cal and societal For such benefits to accrue it is critical that the supportingresearch is data-based

As it happens however operational hospital data is accessible to veryfew researchers and patient-level data has in fact been publicly unavailableThe reasons span nonexistence or poor quality of data concerns for patientconfidentiality and proprietorial constraints or lack of incentives for dataowners We attempt to address these issues as follows First we presentan Exploratory Data Analysis (EDA) of a 1000-bed hospital covering 3years of patient-flow at the inter-departmental level of the individual pa-tient Through this EDA we identify and propose research opportunitiesfor AP OR and SE Then we open up our operational database and makeit universally accessible at the Technion IEampM Laboratory for Service En-terprise Engineering (SEELab) it can be either downloaded or analyzedonline with a user-friendly platform for EDA Our goal is thus to providean entry to and accelerate the learning of data-based OR of hospitals re-searchers can use it (and some already have) to reproduce our EDA whichwould serve as a trigger and a starting point for further data mining andnovel research of their own

11 Patient flow focus Of particular interest to both researchers andpractitioners is patient flow in hospitals improving it can have a signifi-cant impact on quality of care as well as on patient satisfaction restrictingattention to it adds a necessary focus to our work Indeed the medical com-munity has acknowledged the importance of patient flow management (egStandard LD31010 which the Joint Commission on Accreditation of Hos-pital Organizations (JCAHO 2004) set for patient flow leadership) Thisacknowledgment is natural given that operational measures of patient floware relatively easy to track and that they inherently serve as proxies forother quality of care measures (see Section 61) In parallel patient flow hascaught the attention of researchers in OR in general and Queueing Theory inparticular This is not surprising hospital systems being congestion-pronenaturally fit the framework of Queueing Theory which captures the tradeoffsbetween (operational) service quality and resource efficiency

imsart-ssy ver 20130306 file Short_Patientflowmaintex date January 19 2015

PATIENT FLOW IN HOSPITALS 3

Our starting point is that a queueing network encapsulates the operationaldimensions of patient flow in a hospital with the medical units being thenodes of the network patients are the customers while beds medical staffand medical equipment are the servers What are the special features ofthis queueing network To address this question we study an extensivedata set of patient flow through the lens of a queueing scientist Our studyhighlights interesting phenomena that arise in the data which leads to adiscussion of their implications on system operations and queueing modelingand culminates in the proposal of related research opportunities

However patient flow is still too broad a subject for a single study Wethus focus on the inter-ward resolution as presented in the flow chart (pro-cess map) of Figure 1 this is in contrast to intra-ward or out-of-hospitalpatient flow We further narrow the scope to the relatively isolated ED+IWnetwork as depicted in Figure 2 and elaborated on in sect121

12 Rambam Medical Center Our data originates from Rambam Med-ical Center which is a large Israeli academic hospital This hospital catersto a population of more than two million people and it serves as a tertiaryreferral center for twelve district hospitals The hospital consists of about1000 beds and 45 medical units with about 75000 patients hospitalized an-nually The data includes detailed information on patient flow throughoutthe hospital over a period of several years (2004ndash2008) at the flow levelof Figure 1 and the resolution level of individual patients Thus the dataallows one to follow the paths of individual patients throughout their stay atthe hospital including admission discharge and transfers between hospitalunits

121 The ED+IW network Traditionally hospital studies have focusedon individual units in isolation from the rest of the hospital but this ap-proach ignores interactions among units On the flip side looking at thehospital as a whole is complex and may lack necessary focus Instead and al-though our data encompasses the entire hospital we focus on a sub-networkthat consists of the main Emergency Department (ED) (adult Internal Or-thopedics Surgery and Trauma) and five Internal Wards (IWs) denotedby A through E see Figure 2 This sub-network referred to as ED+IW ismore amenable to analysis than studying the entire hospital At the sametime it is truly a system of networked units which requires an integrativeapproach for its study Moreover the ED+IW network is also not too smallAccording to our data approximately 53 of the patients entering the hos-pital remain within this sub-network and 21 of those are hospitalized inthe IWs Finally the network is fairly isolated in the sense that its interac-


4 ARMONY ET AL

One

day

at th

e Ho

spita

l 32

60

317

284

118

291

183

183

193

3744

3

54

122

23511

84

9 35

82

196

7

71

37

13

12

25

14

27

97

20

50 6

8

08

06

14

09

11 1

9

20

09

29

08

13

23

43

03 4

9

05

06

17

22

13

18

32

11

16

06 0

2

03

06

02

03

01

01

06

02

04

Dece

ased

Disa

ppea

red

Disc

harg

edTr

ansf

erre

d

Ram

bam

Au

gust

200

4 A

vera

ge D

ay

Fig 1 Patient Flow (Process Map) at inter-ward resolution (Data animationis available at SEEnimations) For example during the period over whichthe flow was calculated (August 2004) 326 patients arrived to the ED perday on average and 183 transferred from the ED to Surgery (To avoidclutter arcs with monthly flow below 4 patients were filtered out Createdby SEEGraph at the Technion SEELab)



ArrivalsEmergencyDepartment

Abandonment

Services

IW A

IW C

IW B

IW D

IW E

Dischargedpatients

Dischargedpatients

InternalWards

OtherMedical

Units

53

136

JusticeTable

Blocked at IWs

35

699

5

157

236

843

754

245 patday

161 patday

1

165

13 patday

Fig 2 The ED+IW sub-network

tions with the rest of the hospital are minimal To wit virtually all arrivalsinto the ED are from outside the hospital and 935 of the patient transfersinto the IWs are either from outside the hospital or from within the ED+IWnetwork

122 Data description Rambamrsquos 2004ndash2008 patient-level flow dataconsists of 4 compatible ldquotablesrdquo that capture hospital operations as fol-lows The first table (Visits) contains records of ED patients including theirID arrival and departure times arrival mode (eg independently or by am-bulance) cause of arrival and some demographic data The second table(Justice Table) contains details of the patients that were transferred fromthe ED to the IWs This includes information on the time of assignmentfrom the ED to an IW the identity of this IW as well as assignment can-celations and reassignment times when relevant The third table (HospitalTransfers) consists of patient-level records of arrivals to and departures fromhospital wards It also contains data on the ward responsible for each patientas sometimes due to lack of capacity patients are not treated in the wardthat is clinically most suitable for them hence there could be a distinctionbetween the physical location of a patient and the ward that is clinically


6 ARMONY ET AL

in charge of that patient The last table (Treatment) contains individualrecords of first treatment time in the IWs Altogether our data consists ofover one million records

13 ldquoApologiesrdquo to the statistician Our approach of learning from datais in the spirit of Tukeyrsquos Exploratory Data Analysis (EDA) (Tukey 1977)which gives rise to the following two ldquoapologiesrdquo Firstly the goals of thepresent study as well as its target audience and space considerations rendersecondary the role of ldquorigorousrdquo statistical analysis (eg hypothesis testingconfidence intervals model selection)

Secondly our data originates from a single Israeli hospital operating dur-ing 2004ndash2008 This casts doubts on the scope of the scientific and practicalrelevance of the present findings and rightly so Nevertheless other studiesof hospitals in Israel (Marmor (2003) Tseytlin (2009) and Section 56 of EV)and in Singapore (Shi et al 2013) together with privately-communicatedempirical research by colleagues reveal phenomena that are common acrosshospitals worldwide (eg the LOS distributions in Figure 9) Moreover ourstudy can serve as a benchmark to compare against other hospitals Fi-nally the present research has already provided the empirical foundationfor several graduate theses each culminating in one or several data-basedtheoretical papers (see sect21)

14 Paper structure The rest of the paper is organized as follows Westart with a short literature review in Section 2 We then proceed to discussthe gate to the hospitalmdashthe EDmdashin Section 3 followed by the IWs (sect4)and the ED+IW network as a whole (sect5) We start each section with back-ground information Next we highlight relevant EDA and lastly we proposecorresponding research opportunities In sect6 we offer a final commentarywhere we also provide a broader discussion of some common themes thatarise throughout the paper Finally the Appendix covers data access instruc-tions and documentation as well as EDA logistics We encourage interestedreaders to refer to EV a working paper that provides a more elaborate dis-cussion of various issues raised here and covers additional topics that arenot included here due to focus and space considerations

2 Some Hints to the Literature Patient flow in hospitals has beenstudied extensively Readers are referred to the papers in Hall (2013) andDenton (2013) which provide further leads to many other references In thepresent subsection we merely touch on published work along the threedimensions that are most relevant to our study a network view queueingmodels and data-based analysis Many additional references to recent and



ongoing research on particular issues that arise throughout the paper will becited as we go along This subsection concludes with what can be viewed asa ldquoproof of conceptrdquo a description of some existing research that the presentwork and our empirical foundation have already triggered and supported

Most research on patient flow has concentrated on the ED and how to im-prove the internal ED flows There are a few exceptions that offer a broaderview For example Cooper et al (2001) identifies a main source of ED con-gestion to be controlled variability downstream from the ED (eg operating-room schedules) In the same spirit de Bruin et al (2007) observes thatldquorefused admissions at the First Cardiac Aid are primarily caused by un-availability of beds downstream the care chainrdquo These blocked admissionscan be controlled via proper bed allocation along the care chain of Cardiacinpatients to support such allocations a queueing network model was pro-posed with parameters that were estimated from hospital data Broadeningthe view further Hall et al (2006) develops data-based descriptions of hos-pital flows starting at the highest unit-level (yearly view) down to specificsub-wards (eg imaging) The resulting flow charts are supplemented withdescriptions of various factors that cause delays in hospitals and then somemeans that hospitals employ to alleviate these delays Finally Shi et al(2012) develops data-based models that lead to managerial insights on theED-to-Ward transfer process

There has been a growing body of research that treats operational prob-lems in hospitals with Operations Research (OR) techniques BrandeauSainfort and Pierskalla (2004) is a handbook of OR methods and applica-tions in health care the part that is most relevant to this paper is its chapteron Health Care Operations Management (OM) Next Green (2008) surveysthe potential of OR in helping reduce hospital delays with an emphasis onqueueing models A recent handbook on System Scheduling is Hall (2012)mdashwhich contains additional leads on OROM and queueing perspectives ofpatient flow Of special interest is Chapter 8 where Hall describes the chal-lenging reality of bed management in hospitals Jennings and de Vericourt(2008 2011) and Green and Yankovic (2011) apply queueing models to de-termine the number of nurses needed in a medical ward Green (2004) andde Bruin et al (2009) rely on queueing models such as Erlang-C and losssystems to recommend bed allocation strategies for hospital wards LastlyGreen Kolesar and Whitt (2007) survey and develop (time-varying) queue-ing networks that help determine the number of physicians and nurses re-quired in an ED

There is also an increased awareness of the significant role that data canand often must play in patient flow research For example Kc and Terwiesch


8 ARMONY ET AL

(2009) is an empirical work in the context of ICU patient flow it has inspiredthe analytical model of Chan Yom-Tov and Escobar (2014) (see also ChanFarias and Escobar (2014) on the correlation between patient wait and ICULOS) Another example is Baron et al (2014) that does both modeling anddata analysis for patient flow in outpatient test provision centers More onpatient flow in outpatient clinics and the need for relevant data is discussedin Froehle and Magazine (2013)

21 A proof of concept The present research has provided the empiricalfoundation for several graduate theses and subsequent research papers Mar-mor (2010) studied ED architectures and staffing (see Zeltyn et al (2011)and Marmor et al (2012)) Yom-Tov (2010) focused on time-varying modelswith reentrant customers in the ED (Yom-Tov and Mandelbaum 2014) andthe IWs Tseytlin (2009) investigated the transfer process from the ED tothe IWs (Mandelbaum Momcilovic and Tseytlin 2012) Maman (2009) ex-plored over-dispersion characteristics of the arrival process into the ED (Ma-man Zeltyn and Mandelbaum 2011) and Huang (2013) developed schedul-ing controls that help ED physicians choose between newly-arriving vs in-process patients while still adhering to triage constraints (Huang Carmeliand Mandelbaum 2011)

3 Emergency Department The Emergency Department (ED) is thegate to the hospital through which virtually all non-elective patients enterPatient flow within the ED has been widely investigated both academically(Hall et al 2006 Saghafian Austin and Traub 2014 Zeltyn et al 2011)and in practice (IHI 2011 McHugh et al 2011) Here we focus on its empiri-cal macro (black box) view Specifically we highlight interesting phenomenathat relate to patient arrivals departures and occupancy counts Our EDAunderscores the importance of including time- and state-dependent effects inthe EDmdashsome of these are not readily explained by existing queueing mod-els Yet our EDA also reveals that a simple stationary model may providea good fit for patient-counts during periods when the ED is most congestedFor limited purposes therefore our EDA supports the use of simple sta-tionary models for the ED which has been prevalent in the literature (egGreen et al (2006) and de Bruin et al (2009))

31 Basic facts The main ED has 40 beds and it treats on average245 patients daily close to 60 are classified as Internal (general) patientsand the rest are Surgical Orthopedic or Multiple Trauma While there areformally 40 beds in the ED this bed capacity is highly flexible and canbe doubled and more Indeed there is effectively no upper bound on how



many patients can simultaneously reside within the EDmdasheither in beds orstretchers chairs etc The hospital has other EDs physically detached fromthe main one discussed heremdashthese are dedicated to other patient typessuch as Pediatrics or Ophthalmology Throughout the rest of our paper wefocus on the main ED and simply refer to it as the ED Furthermore withinthe ED we focus on Internal (general) patients in beds or walking theyconstitute the majority of ED patients and give rise to many operationalchallenges

During weekdays the average length of stay (ALOS) of patients in theED is 425 hours this covers the duration from entry until the decisionto discharge or hospitalize it does not include boarding time which is theduration between hospitalization decision to actual transfer We estimateboarding time to be 32 hours on average (See Section 52) In addition10 (5) of weekday patients experience LOS that is over 8 (11) hours andabout 3ndash5 leave on their own (LWBS = left without being seen by a doctorLAMA = left against medical advice or Absconded = disappeared duringthe process and are neither LWBS nor LAMA) Finally another measurethat has been gaining prominence is readmission rates It is being used as aproxy for clinical quality of care and we further discuss it in Section 611out of the 2004ndash2005 ED patients around 37 were eventually readmittedand overall 3 11 and 16 of the patients returned within 2 14 and30 days respectively

311 Research opportunities Performance metrics The ED per-formance metrics discussed above are mostly related to ED congestionHwang et al (2011) lists over 70 such measures which have given rise toprevalent crowding indices that support daily ED management (eg Bern-stein et al (2003) Hoot et al (2007)) Such indices arose from ad-hoc sta-tistical analysis that seeks to summarize (eg via regression) the state of EDcongestion Operations Research and Queueing Theory could complementthese efforts by providing a natural environment for rigorously studying anddeveloping congestion indices For instance operational regimes (Section43) and state-space collapse in heavy-traffic (Huang Carmeli and Mandel-baum (2011)) could yield rigorous state-summaries and sufficient statistics

A practical challenge is that useful metrics are often difficult or impossi-ble to measure from data For example our data does not cover time-till-first-consultation which is often part of triage protocols eg following theCanadian Triage and Acuity Scale (Canadadian-Triage) 90 of Category 3(Urgent) patients should be seen by a physician within 30 minutes of arrivalA related research challenge is to infer unobservable metrics from the mea-


10 ARMONY ET AL

surable ones Another example is patientsrsquo (im)patience (the time a patientis willing to wait before abandoning the ED) which is a natural buildingblock for ED queueing models while the overall abandonment proportion isobservable exact times till abandonment need not be To be concrete somepatients notify the system about their abandonment the others are eitherserved in which case their waiting time provides a lower bound for theirpatience or they are discovered missing when called for service which pro-vides an upper bound Statistical inference of ED (im)patience thus requiresnovel models and methods these may draw from current-status (Sun 2006)and survival analysis (Brown et al 2005)

32 EDA Time dependency and overdispersion ED hourly arrival ratesvary significantly over the daymdashsee Figure 3 where it varies by a factor ofover 5 We also observe a time-lag between the arrival rate and occupancylevels it is due to the arrival rate changing significantly during a patientLOS and it is formally explained by the time-varying version of LittlersquosLaw (Bertsimas and Mourtzinou 1997) This lag and in fact the daily shapeof the arrival rate clearly must be taken into account by staffing policies(Feldman et al 2008 Green Kolesar and Whitt 2007 Yom-Tov and Man-delbaum 2014)

Analyzing our data Maman (2009) found support for the daily arrivals tofit a time-varying Poisson process but with heterogeneity levels across daysthat render random the arrival rate itself Kim and Whitt (2014) identifiedsimilar patterns in a large Korean hospital Such overdispersion (relative toPoisson arrivals) has significant operational consequencesmdashthe higher thevariability the more pronounced is the effect (Kocaga Armony and Ward(2014) Maman (2009))

0

5

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15

20

25

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35

0

3

5

8

10

13

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Arr

ival

Rat

e

Time (60 min resolution)

Emergency Internal Medicine Unit January 2004ndashOctober 2007 All days

Patient Arrivals at Emergency Department Number of Patients in Emergency Department (average)

Fig 3 Average number of patients and arrival rate by hour of the day



321 Research opportunities Consider the time-varying shape ofthe arrival rate in Figure 3 Such temporal variability is typical of servicesystems for example call centers (Brown et al 2005) and it gives rise totwo research questions what are the main drivers of this shape and howcan a hospital affect it to benefit its patient flow

1 What drives the shape of ED arrival rates This question has not beensystematically addressed Its answer which is a prerequisite for answer-ing the second question above could start with classifying shape driversinto natural financial or behavioral An example for a natural driver isthat some time-periods are more emergency-prone than others thus thereare relatively few arrivals during 2amndash6am and multi-trauma arrival rates(not depicted here) exhibit an early evening peak (and no morning peak)mdashconceivably at the time-of-day that is most vulnerable to such emergencies

An (Israeli) example for a financial driver is that a referral letter froma Primary Care Physician (PCP) significantly reduces hospital charges forED patients consequently most ED arrivals visit their PCP first and sincePCPs start seeing patients around 8am these patients will start arrivingto the ED around 10am Interestingly emergency maternity arrivals (againnot depicted) peak at 9am indeed maternity patients do not need PCPreferrals

Behavioral drivers reflect preferences for some periods relative to otherswhich could add an explanation for the 10am peak if patients are able tochoose their time of travel they would try to avoid the morning rush-hour

2 Can a hospital affect the shape of its arrival-rates The hospital has littlecontrol over arrivals due to natural factors which can be still accommodatedby time-varying staffing (Green Kolesar and Whitt 2007 Yom-Tov andMandelbaum 2014) or ambulance diversion (Hagtvedt et al 2009) At thesame time it may be able to affect the behavioral as well as the financialdrivers of the time-varying arrival-rate Conceivably both are associatedwith the less- or non-emergency patients who enjoy (clinical) freedom inchoosing their time of arrival The shape of their arrival rate would hencefavor convenience over need (in contrast to multi-trauma) which makes ita prime candidate for change according to operational priorities Indeedhospitals have started making lsquoappointmentsrsquo to ED visits (eg Gormanand Colliver (2014)) in an effort to balance workload

A related effort is control of temporary overloading via the provision ofcongestion information for example predicted waiting time (Dong Yom-Tovand Yom-Tov 2014) The challenge here is to accurately forecast congestionwhich has become an active area of research in EDs (Plambeck et al 2014)


12 ARMONY ET AL

and elsewhere (Ibrahim and Whitt 2011 Senderovich et al 2014)Indeed many hospitals advertise their ED waiting-time and some do so

by announcing a 4-hour moving average (eg HCA North Texas) This isnot very informative as the ED state may change dramatically during 4-hour periods (see Figure 3) One could attempt to relate this uninformativegranularity to the cheap-talk literature (eg Allon Bassamboo and Gurvich(2011)) to help shape these announcements

Finally an indirect effort to affect workload shape is to identify as earlyas possibly the least- or non-emergency patients which is at the heart ofany triage system One could then possibly route the least-urgent to a fast-track and prepare in advance for those predicted to be hospitalized (Barak-Corren Israelit and Reis 2013)

33 EDA Fitting a simple model to a complex reality Figure 4 is details-heavy yet highly informative Its left part shows 24 patient-count histogramsfor internal ED patients each corresponding to a specific hour of the daywith reference (right) to mean patient count also by hour of the day (Similarshapes arise from total ED patient countmdashsee Figure 10 in EV) The fig-ure displays a clear time-of-day behavior There are two distinct bell-shapeddistributions that correspond to low occupancy (15 patients on average) dur-ing the AM (3ndash9AM) and high (30 patients) during the PM (12ndash11PM)with two transitionary periods of low-to-high (9AMndash12PM) and high-to-low (11PMndash3AM) We refer to these four periods as the four ldquooccupancyregimesrdquo Interestingly when attempting to fit a mixture of three normal dis-tributions to the ED occupancy distribution SEEStat automatically detectsthe low high and transitionary phases (See Figure 5a)

020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies

Number of patients (1 hour resolution )

Distribution of ED Internal state by hour of day (sec)January 2004-October 2007 All days

[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s


Number of Patients in Emergency Department (average)

ED Internal UnitJanuary 2004-October 2007 All days

Fig 4 Internal ED Occupancy histogram (left) and Average Census (right)by hour of the day



025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies

Number of patients (resolution 1)

ED Internal state frequency (sec)January 2004-October 2007 All days

Fitting Mixtures of DistributionsNormal (2647) location = 13 scale = 415Normal (2417) location = 20 scale = 609Normal (4936) location = 30 scale = 984

Early MorningNormal

Intermediate hoursNormal PM

Normal

Sum of three Normals

(a) Fitting a mixture of three Normal distributionsto the Empirical distribution of ED occupancy

0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies


ED Internal state frequency (sec)Time of Day [1300-2300)Total for 2005 Mondays

Empirical Normal (mu=3322 sigma=576)

(b) Fitting a Normal distribu-tion for a specific year day of theweek and time of day

Fig 5 Fitting parametric distributions to the Empirical distribution of EDoccupancy

Further EDA (Figure 5b) reveals that during peak times (PM) when con-trolling for factors such as day-of-the-week patient type and calendar yearone obtains a good fit for the empirical distribution by a ldquosteady-staterdquo nor-mal distribution with equal mean and variance Hence one might speculatethat the underlying system dynamics can be modeled by an MMinfin queuewhich has a Poisson steady-state (mean=variance) Alternatively howeverit may also be modeled by an MMN + M queue with equal rates ofservice and abandonment (LWBS LAMA or Absconded) It follows thatone cannot conclusively select a model through its empirical steady-statedistribution (Whitt 2012)

331 Research opportunities In light of the above one is led toseek the relevance-boundary of ldquoblack-boxrdquo ED models they may supportoperational decisions that depend only on total patient count but not on in-ternal dynamics (nor may these decisions alter internal dynamics) or theycan model ED sojourn times within a larger hospital model If in additionand following Whitt (2012) a birth-death steady-state model is found ap-propriate for the ldquoblack-boxrdquo then model reversibility could accommodateapplications that change total count for example ambulance diversion whentotal count exceeds a certain threshold which then truncates the count tothis threshold (and the steady-state distribution is truncated correspond-ingly see Chapter 1 in Kelly (1979)) On the other hand such black-boxmodels cannot support ED staffing (eg Yom-Tov and Mandelbaum (2014)


14 ARMONY ET AL

acknowledges some internal network dynamics) or ambulance diversion thatdepends on the number of boarding patients

In contrast to the macro level of our black-box model one could considera detailed model (such as simulation (Zeltyn et al 2011)) which acknowl-edges explicitly micro-events at the level of individual patients and providers(physicians nurses) The macro- and micro-models are two extreme casesof model granularity with a range of levels in between (Huang Carmeliand Mandelbaum 2011 Marmor et al 2012 Yom-Tov and Mandelbaum2014) The granularity level to be used depends on the target applicationdata availability and analytical techniques Choosing the ldquorightrdquo level foran ORqueueing model has been mostly an art which calls for systemizingthis choice process It could start with Whitt (2012) and Dong and Whitt(2014) that fit birth-death models and continue with statistical techniquesfor model selection (eg Burnham and Anderson (2002))

34 EDA State dependency In addition to time-dependent effects weobserve that the Internal ED displays some intriguing state-dependent be-havior Specifically Figure 6 depicts service (or departure) rates as a func-tion of the Internal patient count L the graph on the left displays thetotal service rate and the one on the right shows the service rate per pa-tient These graphs cannot arise from commonly-used (birth-death) queue-

0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r

Number of Patients (L)

ED Internal state January 2004-October 2007All days 24 hours of day

01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



Fig 6 Service rate and service rate per patient as a function of number ofpatients

ing models such as MMN (for which the total departure rate is linearlyincreasing up to a certain point and then it is constant) or MMinfin (forwhich a constant service rate per patient is expected) In contrast the per-patient service rate has an interval (11 le L le 20) where it is increasing inL which is between two intervals of service-rate decrease (The noise at theextremes L le 3 and L ge 55 is due to small sample sizes) Note that Batt



and Terwiesch (2012) and Kc and Terwiesch (2009) also found evidence fora state-dependent service rate

Identifying the key factors that cause this particular state-dependenceof the service rate per patient requires further exploration of the data Westart with explaining the apparent ldquospeeduprdquo effect (10 le L le 25) fol-lowed by discussion of the slowdown effect in sect341 As it turns out thissupposed speedup is actually an artifact of biased sampling due to patient-heterogeneity and time-variability (Marmor et al 2013) To see this wefurther investigate the departure rate per patient as a function of the pa-tient count at four different time-of-day intervals (corresponding roughlyto the four occupancy regimes identified in Figure 4) For each of these weobserve in Figure 7 either a constant service rate or a slowdown thereofbut no speedup

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L


ED Internal state January 2004-October 2007 All days

0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L


ED Internal stateJanuary 2004-October 2007 All days

0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259

Fig 7 Service rate per patient as a function of L by occupancy regime

Now the rate-per-patient in Figure 6 is a weighted average of the fourgraphs of Figure 7 But these weights are not constant as a function of thepatient count as seen in Figure 8 Moreover the service rate as a functionof patient count varies at different times of the day It follows that whatappears to be a speedup (increasing graph) is merely a weighted average ofnon-increasing graphs with state-dependent weights

341 Research opportunities As opposed to speedup slowdown inservice rate (L ge 25) appears to be real Identifying the key factors thatcause this slowdown requires further research We propose some plausible


16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L



Total - 24 hours of day 1200 to 21590300 to 0859 0900 to 11592200 to 0259

00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259

Fig 8 Service rate as a function of 10 le L le 20 (left) and Relative frequency(weight) of occupancy regime per L (right)

explanations next

bull Multiple resource types with limited capacity As the number of occu-pied beds increases the overall load on medical staff and equipmentincreases as well Assuming a fixed processing capacity the service rateper bed must then slow downbull Psychological Medical staff could become emotionally overwhelmed

to a point that exacerbates slowdown (Sullivan and Baghat 1992)bull Choking Service slowdown may also be attributed to so-called re-

source ldquochokingrdquo medical staff becomes increasingly occupied withcaring for boarding ED patients (who create work while they waitand moreover their condition could actually deteriorate) that mightend up taking capacity away from the to-be-released patients therebyldquochokingrdquo their throughput (see Figure 13 in Section 53) The chokingphenomenon is well known in other environments such as transporta-tion (Chen Jia and Varaiya 2001) and telecommunications (Gerla andKleinrock 1980) where it is also referred to as throughput degrada-tionbull Time dependency and patient heterogeneity Finally similar to the

speedup effect slowdown may also be attributed to the combinationof time dependent arrivals and heterogenous patient mix

In light of the above one would like to identify the dominant factor thatcauses service-rate to slow down Consequently it is important to explorewhat can be done to alleviate this slowdown

4 Internal Wards Internal Wards (IWs) often referred to as Gen-eral Internal Wards or Internal Medicine Wards are the ldquoclinical heartrdquo of ahospital Yet relative to EDs Operating Rooms and Intensive Care Units



IWs have received less attention in the Operations literature this is hardlyjustified IWs and other medical wards offer a rich environment in needof OROM research which our EDA can only tap It has revealed multipletime-scales of LOS intriguing phenomena of scale diseconomies and coexist-ing operational-regimes of multiple resource types (beds physicians) Thesecharacteristics are attributed to IW inflow design capacity management andoperational policies (eg discharge procedures physician rounds)

41 Basic facts Rambam hospital has five Internal Wards consisting ofabout 170 beds that cater to around 1000 patients per month Wards Athrough D are identical from a clinical perspective the patients treated inthese wards share the same array of clinical conditions Ward E is differentin that it admits only patients of less severe conditions Table 1 summarizesthe operational profiles of the IWs For example bed capacity ranges from24 to 45 beds and Average LOS (ALOS) from 37 to 6 days

Table 1Internal wards operational profile

Ward A Ward B Ward C Ward D Ward E

Average LOS (days) 60 39 49 51 37(STD) (79) (54) (101) (66) (33)

Mean occupancy level 977 944 867 969 1032

Mean patients per month 2063 1935 2097 2165 1787

Standard (maximal) 45 (52) 30 (35) 44 (46) 42 (44) 24capacity ( beds)

Mean patients per bed 458 645 477 516 744per month

Readmission rate 106 112 118 90 64(within 1 month)

Data refer to period May 1 2006ndashOctober 30 2007 (excluding the months1-32007 when Ward B was in charge of an additional 20-bed sub-ward)

IWs B and E are by far the smallest (least number of beds) and theldquofastestrdquo (shortest ALOS highest throughput) The short ALOS in IW Eis to be expected as it treats the clinically simplest cases In contrast theldquospeedrdquo of IW B is not as intuitive because this ward is assigned the samepatient mix as IWs AC and D

A shorter ALOS could reflect a more efficient clinical treatment or al-ternatively a less conservative discharge policy Either must not arise fromclinically premature discharges of patients which would hurt patients clin-ical quality of care To get a grasp on that quality we use its operational(accessible hence common) proxy namely patient readmission rate (propor-


18 ARMONY ET AL

tion of patients who are re-hospitalized within a pre-specified period of timeone month in our case) In Table 1 we observe that the readmission rate ofIW B is comparable to the other comparable wards (A-D) Moreover patientsurveys by Elkin and Rozenberg (2007) indicated that satisfaction levels donot differ significantly across wards We conclude that IW B appears to beoperationally superior yet clinically comparable to the other wards Thisfact may be attributed to the smaller size of IW B which we return to inSection 433

42 EDA LOSmdasha story of multiple time scales Next we examine thedistribution of LOS in the IWs While it is to be expected that clinicalconditions affect patients LOS the influence of operational and managerialprotocols is less obvious It turns out that some of this influence can beuncovered by examining the LOS distribution at the appropriate time scale

Figure 9 shows the LOS distribution in IW A in two time scales daysand hours At a daily resolution the Log-Normal distribution turns out to fitthe data well When considering an hourly resolution however a completelydifferent distribution shape is observed there are peaks that are periodically24 hours apart which correspond to a mixture of daily distributions (Wefound that a normal mixture fits quite well as depicted by the 7 normalmixture-components over the range of 0ndash150 hours in the right diagram ofFigure 9)

0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es

Time (1 day resolution)

Patient length of stay in Ward (days) Internal Medicine A

January 2004-October 2007 All days

Empirical Lognormal (mu=138 sigma=083)

Empirical N = 8934 mean = 57 std = 63Lognormal mean = 56 std = 56

00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es

Time (1 hour resolution)

Patient length of stay in Ward (hours)Internal Medicine A

January 2004-October 2007 all daysFitting Mixtures of Distributions

Empirical Total Normal Normal NormalNormal Normal Normal Normal

Fig 9 LOS distribution of IW A in two time-scales daily and hourly

These two graphs reveal the impact of two operational protocols Thedaily time scale represents physician decisions made every morning onwhether to discharge a patient on that same day or to extend hospitalizationby at least one more day The second decision is the hour-of-day at which thepatient is actually discharged This latter decision is made according to the



following discharge process It starts with the physician who writes the dis-charge letters (after finishing the morning rounds) then nurses take care ofpaperwork instructing patients on how to continue medical treatment afterdischarge and then arranging for transportation (if needed) The dischargeprocedure is performed over ldquobatchesrdquo of patients and hence takes a fewhours The result is a relatively low variance of the discharge time as mostpatients are released between 3pm and 4pmmdashsee Figure 10 which provides

36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es


Internal Medicine AJanuary 2004-October 2007 Sundays

Patient Arrivals to Ward (by ward_department)Patient Discharges from Ward (by ward_department) TotalNumber of Patients in Ward (average) (by ward_department)

Fig 10 Arrivals departures and average number of patients in Internalwards by hour of day

an explanation for the observed peaks in the hourly LOS distribution thatare spaced 24 hours apart The variation around these peaks is determinedby the arrival process patients are admitted into the IWs almost exclusivelyover a 12-hour period (10amndash10pm) (Figure 10) Similar observations in aSingapore hospital led Shi et al (2012) to model an inpatient ward as a 2-time-scale system and to consequently propose flow-stabilization as a meansof reducing delays

We also observed two periods of unusual increase in arrival rate one be-tween 3pmndash5pm and a second towards midnight The first is due to thephenomenon discussed abovemdashpatients discharge peaks at 3pmndash4pm andthis enables higher transfer rates from the ED to the IWs The influence ofsuch transfers on ED congestion is discussed in Section 56 One plausibleexplanation for the second peak that occurs towards midnight lies withinthe ED shift schedule ED physicians who work the night shift (which startsat midnight) are typically less experienced and in many cases are not autho-rized to approve patient hospitalization As a result towards the end of theevening shift the more experienced physicians ldquoclear off the tablerdquo in the


20 ARMONY ET AL

ED by making hospitalization decisions for many of the relevant patientssome of these end up being transferred to the IW later that night

Who is the Server in an IW queueing model Operational time-resolutionsspecifically dayshours and hoursminutes for IWs correspond to the timescale by which service durations are naturally measured which in turn iden-tifies a corresponding notion of ldquoa serverrdquo For example IW LOS resolutionin days corresponds to conceptualizing beds as servers which is relevant indetermining ward capacity This is the setup in de Bruin et al (2009) andBekker and de Bruin (2010) who assume (hyper-) exponential LOS (Log-Normal service durations are yet to be accommodated by queueing models)Another IW resolution is hours which is appropriate with servers beingnurses physicians or special IW equipment in that case the service timesare measured in minutes or parts of an hour

421 Research opportunities Workload characterization pro-tocol mining flow control and why Log-Normal Offered Load orWorkload The offered load is the skeleton around which capacity (staffingin the case of personnel) is dimensioned (Green Kolesar and Whitt 2007)Consider nurses as an example Their time-varying offered load results fromboth routine and special care and it varies during the day for at least tworeasons (Mandelbaum Momcilovic and Tseytlin 2012) (a) routine care de-pends linearly on patient count which varies over a day (Figure 10) and (b)admission and discharge of patients require additional work beyond routineand it is more frequent during some hours than others (Figure 10) Combin-ing both of these time variations it is clear that staffing levels must (andactually do) vary during the day hence the importance of observing andunderstanding the system in hourly resolution As mentioned above someefforts to develop queueing models for nurse staffing in medical wards havebeen carried out by Jennings and de Vericourt (2011) Green and Yankovic(2011) and Yom-Tov (2010) However these works neither explain or incor-porate the LOS distribution observed in our data nor do they distinguishbetween routine admission and discharge workload Even such a distinc-tion might not be rich enough indeed the hospital environment calls for abroader view of workload which we discuss in Section 554

LOS and Protocols LOS or Delay distributions encapsulate important op-erational characteristics and can hence be used to suggest measure or trackimprovements Consider for example the hourly effect of IW LOS (Figure9) which is due to IW discharge protocols It calls for an effort in the direc-tion of smoothing IW discharge rates over the day (Shi et al 2012) Takingan example from elsewhere at the hospital consider the differences in shape



of LOS distribution between two Maternity wards (sect421 in EV) which re-sult from differing patient mix it suggests the redesign of routing protocolstowards a more balanced workload (Plonski et al 2013) Queueing modelsare natural for analyzing the interplay between LOS distributions and oper-ational protocols This leads to open data-based questions in two directionsfirst incorporating protocols (eg patient priorities resource scheduling)in queueing models and validating the theoretical LOS distribution againstdata (performance) second and conversely mining protocols from data Wenow give two examples one for each of the two directions

Flow Control How will changes in the IW discharge process influence thesystem For example would the balancing of discharges more uniformlyover the day benefit the entire hospital How would such a change influencedelays of patients waiting to be transferred into the IW from the ED Thisconnection between ED boarding and ward discharges was explored by Shiet al (2012) We return to it in Section 56

Why Log-Normal A long-standing challenge is to explain the prevalenceof Log-Normal as a distribution of service durations (eg IW LOS in dayshere or durations of telephone calls in Brown et al (2005)) Is Log-normalitydue to service protocols Is it perhaps an inherent attribute of customer ser-vice requirements Note that Log-Normal has an intrinsic structure that isboth multiplicativemdashits logarithm is a central limit and additivemdashit is in-finitely divisible being an integral against a Gamma process (Thorin 1977)Can these properties help one explain the empirical Log-Normal service timedistribution

43 EDA Operational regimes and diseconomies of scale An asymp-totic theory of many-server queues has developed and matured in recentyears (Gans Koole and Mandelbaum (2003) can serve as a starting point)This theory which has highlighted three main operational regimes EfficiencyDriven (ED) Quality Driven (QD) and Quality amp Efficiency Driven (QED)The ED-regime prioritizes resource efficiency servers are highly utilized(close to 100) which results in long waits for service In fact waitingdurations in the ED-regime are at least in the order of service times In theQD-regime the emphasis is on the operational quality of service customershardly wait for service which requires that servers be amply staffed and thusavailable to serve Finally the QED-regime carefully balances service qual-ity and server efficiency thus aiming at high levels of both and achieving itin systems that are large enough Under the QED-regime server utilizationcould exceed 90 while at the same time possibly half of the customersare served without delay and those delayed wait one order of magnitude


22 ARMONY ET AL

less than their service duration Under some circumstances (eg Erlang-Cmodel) the QED-regime exhibits economies of scale in the sense that asthe system grows operational performance improves

Many-server queueing theory is based on asymptotic analysis as the num-ber of servers grows indefinitely Nevertheless QED theory has been foundvaluable also for small systems (few servers) that are not exceedingly over-loaded This robustness to system size is due to fast rates of convergence(Janssen van Leeuwaarden and Zwart 2011) and significantly it rendersQED theory relevant to healthcare systems (Jennings and de Vericourt2011 Yom-Tov and Mandelbaum 2014) One should mention that prior tothe era of many-server theory asymptotic queueing theory was mostly con-cerned with relatively small systemsmdashthat is few servers that are too over-loaded for QED to be applicable (eg hours waiting time for service times ofminutes) This regime is nowadays referred to as conventional heavy-traffic(Chen and Yao 2001) and at our level of discussion it will be convenientto incorporate it into the ED-regime

In the following subsection we seek to identify the operational regimethat best fits the IWs We then investigate (sect433) how ward performancedepends on its size We shall argue that although IW beds plausibly operatein the QED-regime there is nevertheless evidence for diseconomies of scale

431 In what regime do IWs operate Can QED- and ED-regimes co-exist We start by identifying the operational regimes that are relevant tothe IWs These units have multiple types of servers (beds nurses physiciansmedical equipment) that must be all considered Here we focus on beds andphysicians

We argue that IW beds operate (as servers) in the QED-regime To sup-port this statement we first note that our system of IWs has many (10rsquos)bedsservers Next we consider three of its performance measures (a) bedoccupancy levels (b) fraction of patients that are hospitalized in non-IWswhile still being under the medical care of IW physicians (patients who wereblocked from being treated in IWs due to bed scarcity) (c) ratio betweenwaiting time for a bed (server) and LOS (service time)

Considering data from the year 2008 we find that 354 of the ED pa-tients were blocked the occupancy level of IW beds was 931 and patientswaited hours (boarding) for service that lasted days (hospitalization) Suchoperational performance is QEDmdashsingle digit blocking probability 90+utilization and waiting duration that is an order of magnitude less than ser-vice Preliminary formal analysis carried out in Section 431 of EV demon-strates that QED performance of a loss model (Erlang-B as in de Bruin et al



(2009)) usefully fits these operational performance measures of the IWsTurning to physicians as servers we argue that they operate in the ED-

regime (conventional heavy traffic) This is based on the following observa-tion from 4pm to 8am the following morning there is a single physician onduty in each IW and this physician admits the majority of new patientsof the day Therefore patients that are admitted to an IW (only if there isan available bed) must wait until both a nurse and the physician becomeavailable The admission process by the physician lasts approximately 30minutes and waiting time for physicians is plausibly hours (it takes an av-erage of 32 hours to transfer a patient from the ED to the IWs see Section52) Performance of physicians is therefore Efficiency Driven

432 Research opportunities We identified two operational regimesthe QED- and ED-regime that coexist within the ED+IW What queue-ing models and operational regimes can valuably capture this reality Notethat such models must accommodate three time scales minutes for physi-cian treatment hours for transfer delays and days for hospitalization LOSSome questions that naturally arise are the following How do the regimesinfluence each other Can we assume that the ldquobottleneckrdquo of the systemis the Efficiency Driven resource (physicians) Thus can one conclude thatadding IW physicians is necessary for reducing transfer delays while addingIW beds would have only a marginal impact on these delays How would achange of IW physician priority influence the system say giving higher pri-ority to incoming patients (from the ED) over the already hospitalized (inthe IWs) Does the fact that the IW physicians operate in the ED-regimeeliminate the economies of scale that one typically expects to find in QEDsystems Empirical observations that will now be presented suggest thatthis might indeed be the case

433 Diseconomies of scale (or how ward size affects LOS) Our data(Table 1) exhibits what appears to be a form of diseconomies of scale asmaller ward (IW B) has a relative workload that is comparable to the largerwards yet it enjoys a higher turnover rate per bed and a shorter ALOSwith no apparent negative influence on the quality of medical care Thephenomenon is reinforced by observing changes in LOS of IW B when thenumber of beds in that ward changes Figure 11 presents changes in ALOSand the average patient count in IWs B and D over the years During 2007the ALOS of Ward B significantly increased This was due to a temporarycapacity increase over a period of two months during which IW B wasmade responsible for 20 additional beds We observe that although the sameoperational methods were used they seem to work better in a smaller ward


24 ARMONY ET AL

In concert with the latter observation we note a reduction in ALOS of IWD mainly from 2007 when ward size decreased as a result of a renovationOne is thus led to conjecture that there are some drawbacks in operatinglarge medical unitsmdasheg larger wards are more challenging to manage atleast under existing conditions

90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year

Number of Patients and Average Length of Stay in Wards (by physical location)

January 2004-October 2007 All day

Number of Patients in Ward Internal Medicine B Number of Patients in Ward Internal Medicine D ALOS in Ward (hours) Internal Medicine B ALOS in Ward (hours) Internal Medicine D

Fig 11 Average LOS and number of patients in Internal wards B and D byyear

Indeed several factors could limit the blessings of scale economies

bull Staffing policy It is customary in this hospital to assign an IW nurseto a fixed set of beds then nominate one experienced nurse to be afloater for solving emerging problems and help as needed This settinggives little operational advantage to large units if at all the largerthe unit the less a single floater can help each nurse The tradeoffthat is raised is between personal care (dedicated servers hence carecontinuity) vs operational efficiency (pooling) This tradeoff has beenaddressed in call centers (Aksin Karaesmen and Ormeci 2007 JouiniDallery and Aksin 2009) and in outpatient medical care (Balasubra-manian Muriel and Wang 2012 Balasubramanian et al 2010) butinpatient healthcare will surely add its own idiosyncracies Anothernatural tradeoff that arises is whether the floater should indeed be anexperienced nurse or is it better to let more junior nurses be floatersso that they can learn from this broader experiencebull Centralized medical responsibility Ward physicians share the respon-

sibility over all patients Every morning the senior physicians resi-dents interns and medical students examine every patient case to-gether (physician rounds) and discuss courses of treatment This isessential as Rambam is a teaching hospital and one of its central mis-



sions is the education and training of doctors Naturally the larger theunit the longer its morning round and consequently less capacity isavailable for other tasks (eg admissions and discharges)

434 Research opportunities In Section 432 of EV we provide ad-ditional plausible explanations for the observed diseconomies of scale Thisphenomenon is important to model carefully and understand as it can sig-nificantly affect decisions on unit sizing and operational strategy Whilequeueing theorists are well equipped to address the operational dimensionsof such decisions they must collaborate with researchers from other dis-ciplines such as organizational behavior for a comprehensive treatmentThis has been recently illustrated in Song Tucker and Murrell (2015) thatexplores diseconomies of scale in the ED They showed that when work isassigned to physicians early on they develop an enhanced sense of owner-ship and tend to work faster thereby negating positive effects of poolingSuch schemes of work assignment are discussed in sect54 (see Figure 15)

Now suppose one takes size differences among wards as a given fact (egdue to space constraints that cannot be relaxed) Then the following questionarises What protocol should be used to route patients from the ED to thewards in order to fairly and efficiently distribute workload among themThis challenge is directly related to the process of transferring patients fromthe ED to the IWs which is the topic of the next section

5 The ED+IW Network After discussing the ED and IWs sepa-rately in this section we discuss the ED+IW network as a whole We startwith the ldquoED-to-IWrdquo process of transferring patients from the ED to theIWs this is the ldquogluerdquo that connects the ED to the IWs We discuss delaysin the transfer process (Sections 52-54) and fairness in this process towardsboth patients and medical staff (Section 55) We conclude in Section 56with an integrative view of the interplay between the three components EDIWs and ED-to-IW

51 ED-to-IW transfer process Basic facts The ldquoED-to-IWrdquo processcovers patient transfers from the ED to the IWs We view this process in thecontext of flow or routing control Routing in hospitals differs from routingin other service systems for various reasons including incentive schemescustomersrsquo (patientsrsquo) limited control (or even helplessness) and the timingof the routing decision Thus although the transfer process involves routing-related issues similar to those that have been looked at extensively in thequeueing literature our data indicate that unusual system characteristics


26 ARMONY ET AL

significantly affect delays and fairness features in a hospital setting whichcreates many research opportunities

A patient whom an ED physician decides to hospitalize in an IW is as-signed to one of five wards according to a certain routing policy (describedmomentarily) If that ward is full its staff may ask for reassignment withthe approval of the hospitalrsquos Head Nurse Once the assigned ward is setthe ward staff prepares for this patientrsquos arrival In order for the transferto commence a bed and medical staff must be available and the bed andequipment must be prepared for the specific patient (including potentialrearrangement of current IW patients) Up to that point the boarding pa-tient waits in the ED and is under its care and responsibility If none of theIWs is able to admit the patient within a reasonable time the patient isldquoblockedrdquo namely transferred to a non-internal ward Then the latter un-dertakes nursing responsibilities while medical treatment is still provided byan IW physician

An integral component of the transfer process is a routing policy or pa-tient assignment algorithm As described in Section 42 Wards AndashD providesimilar medical services while Ward E treats only the less severe patientsThe similarity between Wards AndashD requires a systematic assignment schemeof patients to these wards Rambam hospital determines the assignment viaa round-robin (cyclical) order among each patient type (ventilated specialcare and regular) while accounting for ward size (eg if Ward X has twiceas many beds as Ward Y then Ward X gets two assignments per one as-signment of Y) This scheme is implemented by a computer software calledldquoThe Justice Tablerdquo As the name suggests the algorithm was designed bythe hospital to ensure fair distribution of patients among wards so that staffworkload will be balanced It is worth noting that a survey among 5 addi-tional hospitals in Israel (EV Section 56) revealed that a cyclical routingpolicy is very common still some hospitals apply alternative assignmentschemes for example random assignment by patient ID Interestingly onlyone of the surveyed hospitals uses an assignment that takes into accountreal-time bed occupancy

52 Delays in transfer As is customary elsewhere the operational goalof Rambam hospital is to admit ED boarding patients to the IWs withinfour hours from decision of hospitalization However the delays are oftensignificantly longer The waiting-time histogram in Wards AndashD for the years2006ndash2008 is depicted in Figure 12 We observe significant delays while theaverage delay was 32 hours 25 of the patients were delayed for more than4 hours



$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032

Patient AVG delay delayType (STD) le 4 h gt 10 h

Regular 300 77 2(253)

Special 333 74 5Care (316)

Ventilated 839 41 41(659)

All Types 322 75 4(298)

Fig 12 Transfer time by patient type in hours

Data refer to period 506ndash1008 (excluding the months 1ndash307 when Ward Bwas in charge of an additional sub-ward)

An interesting phenomenon is observed when analyzing transfer delaysby patient type We note that on average ventilated patients wait muchlonger (84 hours) than regular and special care patients (average of 3 and33 hours respectively)mdashsee Figure 12 In particular the delay distributionof these ventilated patients is bi-modal with 41 of such patients delayedby more than 10 hours Ventilated patients must have the highest priorityin transfer but in reality many do not benefit from it

How come so many of the ventilated patients experience such long delaysWe observe that the shorter delays of the ventilated patients (le 4 hours)have a pattern that resembles that of the other two patient types The longerdelays are harder to decipher Possible explanations include (a) Ventilatedpatients are hospitalized in a sub-ward inside the IW (AndashD) often referredto as Transitional (intensive) Care Unit (TCU) (Armony Chan and Zhu2013) Each such TCU has only 4ndash5 beds The average occupancy rate ofthe TCUs at Rambam is 986 the combination of high occupancy with asmall number of beds results in long waits during overloaded periods (b)Ventilated patients require a highly qualified staff to transfer them to theward Coordinating such transfers takes longer

521 Research opportunities Delays in transfer add opportunitiesto those arising from protocol mining as discussed at the end of sect421relevant here is the specific challenge of deciphering a routing protocol fromdata such as in Figure 12 In addition one would like to be able to analyzeand optimize patient-flow protocols in queueing models specifically herefork-join networks (representing synchronization between staff beds andmedical equipment) with heterogeneous customers Such models under the


28 ARMONY ET AL

FCFS discipline were approximated in Nguyen (1994) Their control wasdiscussed in Atar Mandelbaum and Zviran (2012) and Leite and Fragoso(2013)

The discussion above also raises again the tradeoff between the benefitsof pooling and of continuity-of-care (see discussion of diseconomies of scalein sect433) The fact that Rambam chose to distribute TCU beds amongfour IWs instead of having one larger TCU definitely increases waitingtime for a TCU bed Nevertheless it is also advantageous from the quality-of-care perspective to have the TCU beds be part of an IW since whenpatientsrsquo condition improves they are transferred from the TCU in the IWto a regular room in the same IW while continuing treatment by the samemedical staff (physicians and nurses) This continuity-of-care reduces thenumber of hand-offs which are prone to loss of information and medicalerrors The tradeoff between pooling and continuity-of-care is an interestingchallenge to navigate using OR methods

53 Influence of transfer delays on the ED Patients awaiting transfer(boarding patients) overload the ED beds remain occupied while new pa-tients continue to arrive and the ED staff remains responsible for theseboarding patients Therefore the ED in fact takes care of two types of pa-tients boarding patients (awaiting hospitalization) and in-process patients(under evaluation or treatment in the ED) Both types suffer from delays inthe transfer process

Boarding patients may experience significant discomfort while waitingthe ED is noisy it is not private and often does not serve hot meals Inaddition ED patients do not enjoy the best professional medical treatmentfor their particular condition and do not have dedicated attention as inthe wards Moreover longer ED stays are associated with higher risk forhospital-acquired infections (nosocomial infections) Such delays may in-crease both hospital LOS and mortality rates similarly to risks of delaysin ICU transfer (eg Chalfin et al (2007) Long and Mathews (2012) Maa(2011)) Hence the longer patients wait in the ED the higher the likelihoodfor clinical deterioration and the lower is their satisfaction

In-process ED patients may suffer from delays in treatment as additionalworkload imposed by boarding patients on ED staff can be significant Figure13 shows our estimates of the fraction of time that ED physicians spentcaring for the boarding patients assuming (consistently with the Rambamexperience) that every such patient requires an average of 15 minutes ofphysicianrsquos time every 15 minutes We observe that boarding patients takeup to 11 of physician time in the ED This extra workload for the ED



staff that occurs at times when their workload is already high results inldquowastedrdquo capacity and throughput degradation as discussed in Section 34

0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s


HomeHospital Number of Patients in ED-to-Ward transfer (average) (by physical location)

Department of Internal Medicine January 2004-October 2007 All days

Number of Patients in ED-to-Ward transfer Fraction of Physician Load

Fig 13 Number of patients in ED-to-IW transfer (AndashE) and the fraction oftime that ED physicians devote to these patients

To summarize by improving patient flow from the ED to the IWs inparticular reducing boarding times hospitals can improve the service andtreatment provided to both transfer and in-process patients In turn reduc-ing the workload in the ED would improve response to arriving patients andcould in fact save lives

531 Research opportunities The delays in transfer give rise to thefollowing research questions

1 Modeling transfer queue Boarding patients may be viewed as cus-tomers waiting in queue to be served in the IW Traditionally inQueueing Theory it has been assumed that customers receive ser-vice only once they reach a server and not while waiting in queueIn contrast here a waiting patient is ldquoservedrdquo by both the ED andthe IW In the ED clinical treatment is provided according to regula-tions boarding patients must be examined at least every 15 minutesIn the ward ldquoservicerdquo actually starts prior to the physical arrival of thepatient when the ward staff once informed about a to-be-admittedpatient starts preparing for the arrival of this specific patient Theabove has implications on modeling the ED-to-IW process and it af-fects staffing work scheduling etc A natural modeling framework herecould be queueing networks with signals (Chao Miyazawa and Pinedo1999)


30 ARMONY ET AL

2 Emergency Department architecture As described ED staff attends totwo types of patients boarding and in-process Each type has its ownservice requirements leading to differing service distributions and dif-fering distribution of time between successive treatments While board-ing patients receive periodic service according to a nearly-deterministicschedule (unless complications arise) in-process schedule is random innature Incorporating such a mix of distributions in queueing modelsand theory is a challenge of great interestThe above distribution mix may also impact the choice of ED ar-chitecture one may consider two options (a) treating boarding andin-process patients together in the same physical location as is doneat Rambam or (b) move the boarding patients to a transitional unit(sometimes called ldquodelay roomrdquo or ldquoobservation roomrdquo) where theywait for transfer this is done for example in a Singapore hospital thatwe were in contact with Note that using option (b) implies having ded-icated staff equipment and space for this unit The following questionthen arises Under what conditions is each of these ED architecturesmore appropriateInterestingly the Singapore architecture is even more complicated than(b) above as the responsibility for the boarding patients is handed overto IW physicians after a two-hour ED boarding time This providesthe IW medical staff with an incentive to transfer the patients to theward as soon as possible where they can be comfortably treatedIn EV Section 56 we further discuss how different architectures arerelated to incentive schemes and in turn influence delay times

54 Causes of delay In order to understand the causes of long delays inthe ED-to-IW transfer we interviewed hospital staff conducted a time-and-motion study and further explored our data We learned that delays arecaused not only by bed unavailability patients often wait even when thereare available beds Indeed our data shows that the fraction of patients whohad an available bed in their designated ward upon their assignment timewas 43 48 76 55 for Wards AndashD respectively (which is consis-tent with our assertion in sect431 that IW beds operate in the QED-regime)However as Figure 12 shows the probability to be admitted to the wardsimmediately (or within a short time) after hospitalization decision was muchsmaller In fact over the same period of time only 49 of the patients wereadmitted to an IW within 30 minutes from their assignment to this wardOur findings identify 13 plausible causes for delay which are summarized inthe Cause-and-Effect (Fishbone) diagram depicted in Figure 14 We elabo-



Delays in ED-IW transfers

ED-IW synchronization Work methods

Staff availability Equipment availability

Communicationproblems

Not consideringward occupancies

Allowing skipping

Delayed IWdischarges

Nursesavailability

Doctorsavailability

Stretcher bearersavailability

Nurse-in-chargeavailability

Beds availability

Medical equipmentavailability

Interference intothe Justice Table

Timing of routingdecisions

Incentive mechanism

Fig 14 ED-to-IW delaysmdashCause and effect diagram

rate here on two that have some interesting modeling aspects and presentrelated research opportunities 1) The timing of the routing decision whichis associated with the question of using Input-queued vs Output-queued sys-tem when routing patients from the ED to the IWs And 2) the influenceon transfer delays of information availability during routing

541 Research opportunities

1 Timing of routing decision Input-queued vs Output-queued systemRecall that preparation for a transfer of a particular patient startsin the designated ward prior to the actual transfer This forces thehospital to adopt an output-queued scheme (Stolyar 2005) where eachpatient is first assigned to an IW and then waits until the ward is ableto admit This is in contrast to a scheme where patients are placedin a ldquocommonrdquo queue then routed to an IW only once at the headof the line and a bed in any of the IWs becomes available The latteris referred to as an input-queued scheme Figure 15 depicts the twoschemesOutput-queued schemes are inherently less efficient than their input-queued counterparts because the routing decision is made at an earliertime with less information Moreover the output-queued scheme isinequitable towards patients because FCFS is often violatedThe problem of customer routing in input-queued schemes has receivedconsiderable attention in the queueing literature (eg Armony (2005)Atar and Shwartz (2008) Gurvich and Whitt (2010) Mandelbaum and


32 ARMONY ET AL

Fig 15 Output- vs Input-queued scheme

Stolyar (2004)) Similar issues in output-queued systems have beengenerally overlooked Exceptions include Stolyar (2005) and Tezcan(2008) who establish that the two systems have asymptotically simi-lar performance in both the conventional and the QED heavy-trafficregimes This implies that inefficiencies which arise in our ED-to-IWprocess due to the use of an output-queued scheme become negligiblein heavily-loaded systems More generally insights gained from study-ing the input-queued systems as in the above references may carryover to the output-queued systems But how well does that insighttranslate to an environment such as a medical unit

2 Not considering ward occupancies The role of information availabilityin routing An additional important aspect of routing schemes whichdirectly affects patient delays is the availability of information on thesystem state at the moment of the routing decision On the one handhospitals may base the routing on no information namely use a staticrouting policy like round robin (surprisingly our experience suggeststhat this is a prevalent policy) On the other extreme a full informationpolicy that takes into account current occupancy levels and projectedfuture dismissals and transfers is feasible if the information system isaccurate and accommodating enough (See Chapter 8 in Hall (2012))Continuously-available accurate information is costly however andthis cost-benefit tradeoff is yet to be explored

55 Fairness in the ED-to-IW process Transfer policies may have rami-fications on fairness towards customers (patients) and towards servers (med-ical and nursing staff) We investigate both aspects next



551 Fairness towards patients In Section 54 we pointed out thatoutput-queued schemes lead to diminished patient fairness as FCFS order isoften violated (For references on the significance of FCFS in customer jus-tice perception see Mandelbaum Momcilovic and Tseytlin (2012)) Indeedour Rambam data indicate that 45 of the ED-to-IW transfer patients wereldquoovertakenrdquo by another patient (see Table 2) Moreover more than a thirdof those were overtaken by at least three other patients Although this fig-ure includes overtaking between patient types which may be due to clinicalpriorities within each patient type there were significant FCFS violationsas well Specifically 31 were actually overtaken by at least one patient oftheir type most of them not within the same ward thus these violationsare conceivably due to the output-queued scheme

Table 2Percentage of FCFS violations per type within each IW

IW Type Regular Special care Ventilated Total

Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781

Total within wards 691 680 067 680

Total in ED-to-IW 31 31 5

While output-queues are inherently inefficient and unfair they are un-likely to change in Rambam hospital due to the practicalclinical consid-erations described above as well as psychological consideration (eg earlyward assignment reduces uncertainty which in turn reduces anxiety for pa-tients and their families) The use of output-queues in the ED-to-IW processillustrates some idiosyncrasies of flow control in healthcare

552 Research opportunities A natural question is how to best main-tain patient fairness in the output-queued scheme What routing policies willkeep the order close to FCFS Is FCFS asymptotically maintained in heavy-traffic

What other fairness criteria should be considered Assuming that patientshave preferences (clinical or prior experiences) for a specific ward fairnessmay be defined with respect to the number of patients who are not assignedto their top priority Related to this is the work of Thompson et al (2009)that looks into minimizing the cost that reflects the number of ldquonon-idealrdquoward assignments we propose to also look at the equity between patientsin this context One may alternatively consider achieving equity in terms of


34 ARMONY ET AL

blocking probability (recall the discussion in sect431) or patient delay

553 Fairness towards staff In Section 54 we discussed the implica-tions of the routing policy on delays in the ED-to-IW process in additionrouting also has a significant impact on wardsrsquo workload High workloadtends to cause personnel burnout especially if work allocation is perceivedas unjust (references can be found in Armony and Ward (2010)) Rambamhospital takes fairness into consideration as is implied from the name ldquoJus-tice Tablerdquo However is the patient allocation to the wards indeed fair

There are many candidates for defining server ldquofairnessrdquo One naturalmeasure is equity in the occupancy level Since the number of nurses anddoctors is typically proportional to the number of beds equal occupancylevels imply that each nursedoctor treats the same number of patients onaverage But does this imply that their workload is evenly distributed

As mentioned in sect421 staff workload in hospitals is not spread uniformlyover a patientrsquos stay as patients admissionsdischarges tend to be workintensive and treatment during the first days of a patientrsquos hospitalizationrequire much more time and effort from the staff than in the following days(Elkin and Rozenberg 2007) Thus one may consider an alternative fairnesscriterion balancing the incoming load or the ldquofluxrdquomdashnumber of admittedpatients per bed per time unit among the wards In Table 1 we observe thatWard B has a high average occupancy rate In addition as it is both thesmallest and the ldquofastestrdquo (shortest ALOS) ward then (by Littlersquos law) ithas the highest flux among comparable IWs AndashD The workload of WardB staff is hence the highest We conclude that the most efficient ward issubject to the highest loadmdashthat is patient allocation appears to be unfairtowards ward staff

Our data has already motivated some work on fair routing Analytical re-sults for input-queued systems were derived in Mandelbaum Momcilovic andTseytlin (2012) where both occupancy level and flux are taken into accountwith respect to fairness Tseytlin and Zviran (2008) propose a simulation-supported algorithm that balances a weighted function of occupancy andflux to achieve both fairness and short delays in output-queued systems

554 Research opportunities In the context of output-queued sys-tems a more rigorous analytical study is needed to formalize the conclusionsof Tseytlin and Zviran (2008) Specifically how to combine the occupancyand flux criteria into a single effective workload measure which would bebalanced across wards Even in the context of input-queued systems it is ourview that Armony and Ward (2010) Mandelbaum Momcilovic and Tseytlin(2012) and Ward and Armony (2013) have just taken the first steps towards



staff fairness as they do not fully account for the dynamic nature of work-load in healthcare As patients progress in their hospital stay their medicalneeds change (mostly reduce) and the accuracy in which one can predicttheir LOS increases This information could be very useful in successfullybalancing workload

The underlying definition of operational fairness in our discussion thusfar proposed equal workload division across medical staff A prerequisitefor solving the ldquofairness problemrdquo is then to define and calculate workloadappropriately However we argue that such calculations must include notonly direct time per resource but also emotional and cognitive efforts as wellas other relevant factors For example 1-minute of a standard chore doesnot compare with a 1-minute life-saving challenge (Plonski et al 2013)Thus the mix of medical conditions and patient severity should also beincluded in workload calculation For the latter it is not straightforward todetermine whether wards would be inclined to admit the less severe patients(who add less workload and potentially less emotional stress) as opposedto the more severe patients who would challenge the medical staff thusproviding them with further learning and research opportunities the latteris especially relevant in teaching hospitals such as Rambam

56 A system view In this Section we underscore the importance oflooking at this network of ED IWs and ED-to-IWs as a whole as thesethree components are clearly interdependent For concreteness we focus onhow the discharge policy in the IW affects ED-to-IW transfer times whichin turn affect ED workload We thereby argue that an integrative systemview is appropriate

It is natural to expect that the higher the occupancy in the IWs thelonger the boarding times due to limited IW resources The left diagram inFigure 16 displays the average boarding time alongside the average numberof patients per wardmdashin IWs AndashD by day of the week We observe that asexpected the two measures have a similar weekly pattern The right diagramin Figure 16 shows delays in the transfer process and the average number ofpatients in the IWs as they vary throughout the day The correlation hereis not as apparent as in the daily resolution other factors such as the IWdischarge process also play a role

We observe that the longest delays are experienced by patients assignedto the IWs in early morning (6amndash8am)mdashthese patients need to wait onaverage 5 hours or more This is due to a combination of two reasons First asthe night progresses most of the IW beds become occupied (see Figure 10)Hence many of the patients arriving in the morning are unlikely to encounter


36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)

Internal Medicine A-D (by physical location)Total for May 2006 - December 2006

April 2007 - October 2007

Average Boarding Time (hours)Number of Patients in Ward (average)

35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)


Internal Medicine A-D (by physical location)Total for May 2006 - December 2006 April 2007 - October 2007 All days


Fig 16 ED-to-IW boarding times and number of patients in IW

an available bed while new beds will only become available towards 3pmA second reason stems from the working procedures of physicians withinthe IW As discussed in Section 54 (see Figure 14) an available physicianis required to complete a transfer But most of the IW physicians performtheir morning rounds at this time and cannot admit new patients We notea consistent decline in the transfer delay up until noon Patients assigned tothe IWs during these times are admitted into the IWs between 1pmndash3pmThis is about the time when the physiciansrsquo morning rounds are completestaff and beds are starting to become available Indeed there is a sharpdecline in the number of IW patients around 3pmndash4pm when most of theIWs discharges are complete

Further data analysis reveals that patients who are admitted to the IWsbefore 8am experience a significantly shorter LOS Figure 17 shows that earlyhospitalization may reduce ALOS by more than 1 day A correlation betweenhospitalization time and LOS was also reported by Earnest Chen and Seow(2006) they observed that patients who are admitted in afternoonnighthours have ALOS that is longer than patients admitted in the morningIn contrast we differentiate between early- and late-morning admissionsRegardless in both cases the plausible explanation for the difference inALOS is the same If patients are admitted to the ward early enough thefirst day of treatment is more effective as tests medical procedures andtreatments start earlier and hence LOS is reduced Thus we argue that itis important to shorten the ED-to-IW transfer process and improve the IWadmission process so that the first day of hospitalization is not ldquowastedrdquo

In Section 53 we discussed how boarding times impact physician work-load in the ED and hence may influence quality of care there Thus weobserve a chain of events in which the discharge policy in the IWs impacts



0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans

Ward Admission Time (60 min resolution)

Hospitalization LOS (days) vs first ward admission time (by physical location)

January 2004 - October 2007 Weekdays

Total Internal Medicine A Internal Medicine BInternal Medicine C Internal Medicine D

Fig 17 ALOS in IWs A through D as a function of ward admission-time

the delays in transfer which in turn affects workload in the ED In partic-ular a system-view perspective is called for

561 Research opportunities Our discussion suggests that daily rou-tines (schedules) in the IWs have a significant impact on boarding times andthereby on ED workload At the same time these routines also affect IWLOS The question arises as to if and how one might wish to change dailyroutines in view of these effects The question fits well within a queueingcontext The present daily routine at Rambam may be viewed as a priorityscheme where currently-hospitalized IW patients enjoy priority during morn-ing physiciansrsquo rounds these patients become low-priority as dischargedpatients obtain priority in the afternoon then followed by newly-admittedpatients Is it possible to positively affect overall system performance by al-tering these priorities (eg prioritizing newly-admitted and to-be dischargedpatient in the morning) More broadly the challenge falls within the un-charted territory of designing priority schemes for time-varying queueingnetworks

Our discussion here brings us back to the broader issuemdashthat is the needfor a system view in order to understand and relieve delays in patient flowConsider for example the boarding patients in EDs (Figure 16) or in ICUs(Long and Mathews 2012) Long boarding times are often due to scarceresources or synchronization gaps (Zaied 2011) which are rooted in partsof the system that differ from those where the delays are manifested Forexample scarce resources in the IWs exacerbate ED delays and tardy pro-cessing of MRI results can prolong ICU LOS It follows that a system viewis required for the analysis of patient flow in hospitals

When analyzing ED+IWs flows (sect5) the wards operate naturally on a


38 ARMONY ET AL

time-scale of days while the ED time scale is hours Wards thus serve as arandom environment for the ED (Ramakrishnan Sier and Taylor 2005) Fig-ure 9 (sect42) reveals that the hourly scale is also of interest for IWs Theseempirical observations arise in a service system (hospital) that evolves inmultiple time scales which are all natural and relevant for measuring andmodeling its performance The mathematical manifestation of such scalesis asymptotic analysis that highlights what matters at each scale while av-eraging out details that are deemed insignificant (eg Mandelbaum Mom-cilovic and Tseytlin (2012) Shi et al (2012) Gurvich and Perry (2012) andZacharias and Armony (2013))

6 Discussion and Concluding Remarks We have described re-search opportunities that arose from EDA of operational patient flow dataWe now discuss the relationship between operational performance measuresand overall hospital performance and conclude with comments on data-based OR research

61 Operational measures as surrogates to overall hospital performanceHospital performance is measured across a variety of dimensions clinicalfinancial operational psychological (patient satisfaction) and societal Themost important measures are clearly clinical but practically operationalperformance is the easiest to quantify measure track and react upon inreal time Moreover operational performance is tightly coupled with theother dimensions (eg rate of readmissions with quality of clinical care orLOS and LWBS with financial performance) which explains its choice as aldquolanguagerdquo that captures overall hospital performance

Operational performance measures are often associated with patient flowAmong these we discussed LWBS (Section 3) and ldquoblockingrdquo (where pa-tients end up being hospitalized in a ward different from that which is med-ically best for them - Section 431) boarding (transfer) time from the EDto the appropriate medical unit and measures related to LOS in the EDor IWs such as merely averages (or medians) or fractions staying beyonda desired threshold Other measures that have not been mentioned requireintra-ward data which is beyond our data granularity Examples includethe time until triage or until a patient is first seen by an ED physician (Zel-tyn et al 2011) the number of visits to a physician during an ED sojourn(Huang Carmeli and Mandelbaum 2011) and the time-ingredients of anED visit (treatment and waitingmdashfor a resource for synchronization or fora treatment to take its effect see Zaied (2011) and Atar Mandelbaum andZviran (2012))



611 Readmissions As already indicated in Sections 31 and 41 ourdata supports the analysis of readmissions (Mandelbaum et al 2013) Wenow elaborate on this operational measure of performance since policy mak-ers are increasingly focusing on it as part of efforts to extend quality of caremeasures from within-hospital processes to after-hospital short-term out-comes (Medicare USA 2013) As mentioned the likelihood of readmissionto the hospital within a relatively short time is a natural indirect measurefor quality of care (similarly to first-call-resolution rates in call centers)Consequently readmission rates are accounted for when profiling hospitalsrsquoquality and determining reimbursements for their services

We argue that one should consider readmissions judiciously as some ofthem could be due to factors outside hospital control or they may be an inte-gral part of the treatment regimen For example returns within a few monthsto chemotherapy are typically planned and are unrelated to poor quality Butthere are also unplanned chemotherapy returns after 1ndash2 weeks which arisefrom complications after treatment To properly incorporate readmissions ina queueing model (such as in Yom-Tov and Mandelbaum (2014)) one shoulddistinguish between these two readmission types by for example model-ing planned (unplanned) readmissions as deterministic (stochastic) returnsAlso note that readmissions should be measured in their natural time-scaleFor example readmission to an ED should be measured in a time scale ofdays-weeks while readmissions to an IW have a natural time-scale of weeks-months

612 Capacity and cost of care Of utter importance to hospital man-agers and policy makers is hospital costing Kaplan and Porter (2011) arguethat the mapping of patient process flow and the association of its ac-tivities with their supporting resources should constitute the first step inunderstanding the cost of care This is consistent with promoting a queueing-network view for understanding and calculating cost of care Indeed Kaplanand Porter (2011) further submit that most hospital costs are mistakenlyjudged as fixed while they ought to be viewed as variable costs it followsthat the corresponding resource levels are in fact flexible an observationthat renders controllable most resources in a hospital

This viewpoint naturally connects with the distinction between static anddynamic capacity in queueing systems which we now explain Capacity ofa hospital or a ward is commonly expressed in terms of the number of beds(or rooms or physical space) However it is also necessary to associate witha ward its processing capacity which is determined by its human and equip-ment resources nurses physicians support personnel and medical appara-


40 ARMONY ET AL

tus One thus distinguishes between static capacity (eg beds) and dynamic(processing) capacity of a resource (Note that bed capacity plays the dualrole of static capacitymdashcapping the number of patients that can be simul-taneously hospitalized and dynamic capacitymdashserving as a proxy for theprocessing capacity of medical personnel) This distinction connects backto costs in the sense that static capacity is thought of as fixed over therelevant horizon hence its cost is fixed processing capacity on the otherhand is considered variable in that its level (and hence also cost) is flexible(controllable)

62 Some concluding comments on data-based researchmdasha great oppor-tunity but no less of a challenge The goal of the present work has beentwo-fold first to encourage and strengthen through data and its EDA thenatural link between queueing theory and its application to patient flow inhealthcare and second to facilitate data-based learning for researchers whoseek to reinforce this important link

While theory has been the comfort zone of Operations Research (OR) andApplied Probability (AP) the situation dramatically differs when data isbrought into the picture Fundamental changes are therefore essentialmdashbothwithin our ORAP community as well as our potential healthcare partnerschanges in accessibility to healthcare data in education (eg concerningthe necessity of data-based OR research importance and need to publishEDA benefits of research reproducibility) and in funding priorities (egfor developing and sustaining the infrastructure that is a prerequisite for aresearch such as the one reported here)

However we are cautiously optimistic Indeed comprehensive data collec-tion is becoming increasingly feasible systematic and cheaper for examplevia Real-time Location Systems (RTLS) which will ultimately integratewith Personal-Health and Financial Records This will enable partnershipsbetween researchers and healthcare providersmdashpartnerships that are basedon multidisciplinary (clinical operational financial psychological) track-ing of complete care-paths that start possibly at onset of symptoms (ratherthan hospital entrance) and at resolution levels of the individual patientand provider The process of data-based OR research in hospitals is thusonly beginning1

1Complete operational coverage within the hospital is already feasible SEELab isnow continuously getting RTLS data from a large day-hospital which is collected through900 sensors spread over 7 floors it covers around 700 patients and 300 providers daily at3-second resolution and it amounts to more than 1GB of raw data per week



REFERENCES

Aksin O Z Karaesmen F and Ormeci E L (2007) A Review of Workforce Cross-Training in Call Centers from an Operations Management Perspective In WorkforceCross Training Handbook (D Nembhard ed) CRC Press 433

Allon G Bassamboo A and Gurvich I (2011) ldquoWe Will Be Right with YourdquoManaging Customer Expectations with Vague Promises and Cheap Talk OperationsResearch 59 1382ndash1394 321

Armony M (2005) Dynamic Routing in Large-Scale Service Systems with Heteroge-neous Servers Queueing Systems 51 287ndash329 1

Armony M Chan C W and Zhu B (2013) Critical Care in Hospitals When toIntroduce a Step Down Unit Working paper Columbia University 52

Armony M and Ward A (2010) Fair Dynamic Routing in Large-ScaleHeterogeneous-Server Systems Operations Research 58 624ndash637 553 554

Armony M Israelit S Mandelbaum A Marmor Y N Tseytlin Y andYom-Tov G B (2013) Patient Flow in Hospitals A Data-Based Queueing-SciencePerspective An Extended Version (EV) 13 14 33 421 431 434 51 2

Atar R Mandelbaum A and Zviran A (2012) Control of Fork-Join Networks inHeavy Traffic Allerton Conference 521 61

Atar R and Shwartz A (2008) Efficient Routing in Heavy Traffic under PartialSampling of Service Times Mathematics of Operations Research 33 899ndash909 1

Balasubramanian H Muriel A and Wang L (2012) The Impact of Flexibilityand Capacity Allocation on the Performance of Primary Care Practices Flexible Servicesand Manufacturing Journal 24 422ndash447 433

Balasubramanian H Banerjee R Denton B Naessens J Wood D andStahl J (2010) Improving Clinical Access and Continuity Using Physician PanelRSSedesign Journal of General Internal Medicine 25 1109ndash1115 433

Barak-Corren Y Israelit S and Reis B Y (2013) Progressive Prediction ofHospitalization in The Emergency Department Uncovering Hidden Patterns to ImprovePatient Flow Working paper 321

Baron O Berman O Krass D and Wang J (2014) Using Strategic Idlenessto Improve Customer Service Experience in Service Networks Operations Research 62123ndash140 2

Batt R J and Terwiesch C (2012) Doctors Under Load An Empirical Study ofState Dependent Service Times in Emergency Care Working paper 34

Bekker R and de Bruin A M (2010) Time-Dependent Analysis for Refused Ad-missions in Clinical Wards Annals of Operations Research 178 45ndash65 42

Bernstein S L Verghese V Leung W Lunney A T and Perez I (2003)Development and Validation of a New Index to Measure Emergency Department Crowd-ing Academic Emergency Medicine 10 938ndash942 311

Bertsimas D and Mourtzinou G (1997) Transient Laws of Non-stationary Queue-ing Systems and their Applications Queueing Systems 25 115ndash155 32

Brandeau M L Sainfort F and Pierskalla W P eds (2004) OperationsResearch and Health Care A Handbook of Methods and Applications Kluwer AcademicPublishers London 2

Brown L Gans N Mandelbaum A Sakov A Shen H Zeltyn S andZhao L (2005) Statistical Analysis of a Telephone Call Center A Queueing-Science


42 ARMONY ET AL

Perspective Journal of the American Statistical Association 100 36ndash50 311 321421

Burnham K P and Anderson D R (2002) Model Selection and Multimodal Infer-ence a Practical Information-Theoretic Approach 2nd Edition Springer 331

Canadadian-Triage Admission of Paitents to over-capacity inpatient bedsAppendix A httpwwwcalgaryhealthregioncapolicydocs1451Admission_

over-capacity_AppendixApdf 311

Chalfin D B Trzeciak S Likourezos A Baumann B M andDellinger R P (2007) Impact of Delayed Transfer of Critically Ill Patients fromthe Emergency Department to the Intensive Care Unit Critical Care Medicine 35 1477ndash1483 53

Chan C Farias V and Escobar G (2014) The Impact of Delays on Service Timesin the Intensive Care Unit Working paper 2

Chan C Yom-Tov G B and Escobar G (2014) When to use Speedup An Ex-amination of Service Systems with Returns Operations Research 62 462ndash482 2

Chao X Miyazawa M and Pinedo M (1999) Queueing Networks CustomersSignals and Product Form Solutions Wiley 1

Chen C Jia Z and Varaiya P (2001) Causes and Cures of Highway CongestionControl Systems IEEE 21 26ndash33 341

Chen H and Yao D D (2001) Fundamentals of Queuing Networks PerformanceAsymptotics and Optimization Springer 43

Cooper A B Litvak E Long M C and McManus M L (2001) EmergencyDepartment Diversion Causes and Solutions Academic Emergency Medicine 8 1108ndash1110 2

de Bruin A M van Rossum A C Visser M C and Koole G M (2007)Modeling the Emergency Cardiac In-Patient Flow An Application of Queuing TheoryHealth Care Management Science 10 125ndash137 2

de Bruin A M Bekker R van Zanten L and Koole G M (2009) Dimension-ing Hospital Wards using the Erlang Loss Model Annals of Operations Research 17823ndash43 2 3 42 431

Denton B T ed (2013) Handbook of Healthcare Operations Management Methodsand Applications Springer 2

Dong J and Whitt W (2014) On Fitted Birth-and-Death Queue Models Workingpaper Columbia University 331

Dong J Yom-Tov E and Yom-Tov G B (2014) Hospital Network Synchroniza-tion Through Waiting Time Announcements Working paper 321

Earnest A Chen M and Seow E (2006) Exploring if Day and Time of Admissionis Associated with Average Length of Stay among Inpatients from a Tertiary Hospital inSingapore An Analytic Study Based on Routine Admission Data BMC Health ServicesResearch 6 6 56

Elkin K and Rozenberg N (2007) Patients Flow from the Emergency Departmentto the Internal Wards IEampM project Technion (In Hebrew) 41 553

Feldman Z Mandelbaum A Massey W A and Whitt W (2008) Staffingof Time-Varying Queues to Achieve Time-Stable Performance Management Science 54324ndash338 32

Froehle C M and Magazine M J (2013) Improving scheduling and flow in com-plex outpatient clinics In Handbook of Healthcare Operations Management Methods andApplications (B T Denton ed) 9 229ndash307 Springer 2



Gans N Koole G and Mandelbaum A (2003) Telephone Call Centers TutorialReview and Research Prospects Manufactoring Services and Operations Management5 79ndash141 43

Gerla M and Kleinrock L (1980) Flow Control A Comparative Survey IEEETransactions on Communcations 28 553ndash574 341

Gorman A and Colliver V (2014) The Latest In Medical Convenience ER Ap-pointments Chronicle for Kaiser Health News http kaiserhealthnews org news

the-latest-in-medical-convenience-er-appointments 321

Green L (2004) Capacity Planning and Management in Hospitals In Operations Re-search and Health Care A Handbook of Methods and Applications (M L BrandeauF Sainfort and W P Pierskalla eds) 14ndash41 Kluwer Academic Publishers London 2

Green L V (2008) Using Operations Research to Reduce Delays for Healthcare InTutorials in Operations Research (Z-L Chen and S Raghavan eds) 1ndash16 INFORMS2

Green L V Kolesar P J and Whitt W (2007) Coping with Time-VaryingDemand When Setting Staffing Requirements for a Service System Production and Op-erations Management 16 13ndash39 2 32 321 421

Green L and Yankovic N (2011) Identifying Good Nursing Levels A QueuingApproach Operations Research 59 942ndash955 2 421

Green L Soares J Giglio J F and Green R A (2006) Using Queuing The-ory to Increase the Effectiveness of Emergency Department Provider Staffing AcademicEmergency Medicine 13 61ndash68 3

Gurvich I and Perry O (2012) Overflow Networks Approximations and Implica-tions to Call-Center Outsourcing Operations Research 60 996ndash1009 561

Gurvich I and Whitt W (2010) Service-Level Differentiation in Many-Server ServiceSystems via Queue-Ratio Routing Operations Research 58 316ndash328 1

Hagtvedt R Ferguson M Griffin P Jones G T and Keskinocak P (2009)Cooperative Strategies To Reduce Ambulance Diversion Proceedings of the 2009 WinterSimulation Conference 266 1085ndash1090 321

Hall R W ed (2012) Handbook of Healthcare System Scheduling Springer 2 2

Hall R W ed (2013) Patient Flow Reducing Delay in Healthcare Delivery Springer2nd edition 2

Hall R Belson D Murali P and Dessouky M (2006) Modeling Patient FlowsThrough the Healthcare System In Patient Flow Reducing Delay in Healthcare Delivery(R W Hall ed) 1 1ndash45 Springer 2 3

HCA North Texas Hospitals are Moving at the Speed of LifemdashReal Time De-lays Announcement Web-page of Emergency Departments in North Texas USAFASTERTXCOM httphcanorthtexascom 321

Hoot N R Zhou C Jones I and Aronsky D (2007) Measuring and ForecastingEmergency Department Crowding in Real Time Annals of Emergency Medicine 49 747ndash755 311

Huang J (2013) Patient Flow Management in Emergency Departments PhD thesisNational University of Singapore (NUS) 21

Huang J Carmeli B and Mandelbaum A (2011) Control of Patient Flow inEmergency Departments Multiclass Queues with Feedback and Deadlines Working pa-per 21 311 331 61


44 ARMONY ET AL

Hwang U McCarthy M L Aronsky D Asplin B Crane P WCraven C K Epstein S K Fee C Handel D A Pines J M Rath-lev N K Schafermeyer R W Zwemer F L and Bernstein S L (2011)Measures of Crowding in the Emergency Department A Systematic Review AcademicEmergency Medicine 18 527ndash538 311

Ibrahim R and Whitt W (2011) Wait-Time Predictors for Customer Service Sys-tems with Time-Varying Demand and Capacity Operations Research 59 1106ndash1118321

IHI (2011) Patient First Efficient Patient Flow Management Impact on theED Institute for Healthcare Improvement httpwwwihiorgknowledgePages

ImprovementStoriesPatientFirstEfficientPatientFlowManagementEDaspx 3

Janssen A J E M van Leeuwaarden J S H and Zwart B (2011) RefiningSquare-Root Safety Staffing by Expanding Erlang C Operations Research 56 1512ndash152243

JCAHO (2004) JCAHO Requirement New Leadership Standard on Managing PatientFlow for Hospitals Joint Commission Perspectives 24 13ndash14 11

Jennings O B and de Vericourt F (2008) Dimensioning Large-Scale MembershipServices Operations Research 56 173ndash187 2

Jennings O B and de Vericourt F (2011) Nurse Staffing in Medical Units AQueueing Perspective Operations Research 59 1320ndash1331 2 421 43

Jouini O Dallery Y and Aksin O Z (2009) Queueing Models for Full-FlexibleMulti-class Call Centers with Real-Time Anticipated Delays International Journal ofProduction Economics 120 389ndash399 433

Kaplan R S and Porter M E (2011) How to Solve the Cost Crisis in Health CareHarvard Business Review 89 46ndash64 612

Kc D and Terwiesch C (2009) Impact of Workload on Service Time and PatientSafety An Econometric Analysis of Hospital Operations Management Science 55 1486ndash1498 2 34

Kelly F P (1979) Markov Processes and Reversibility Wiley 331

Kim S H and Whitt W (2014) Are Call Center and Hospital Arrivals Well Modeledby Nonhomogeneous Poisson Processes Forthcoming at MampSOM 32

Kocaga A L Armony M and Ward A R (2014) Staffing Call Centers withUncertain Arrival Rates and Co-sourcing Working paper 32

Leite S C and Fragoso M D (2013) Diffusion Approximation for SignalingStochastic Networks Stochastic Processes and their Applications 123 2957ndash2982 521

Long E F and Mathews K M (2012) ldquoPatients Without Patiencerdquo A PriorityQueuing Simulation Model of the Intensive Care Unit Working paper 53 561

Maa J (2011) The Waits that Matter The New England Journal of Medicine 3642279ndash2281 53

Maman S (2009) Uncertainty in the Demand for Service The Case of Call Centersand Emergency Departments Masterrsquos thesis TechnionmdashIsrael Institute of Technology21 32

Maman S Zeltyn S and Mandelbaum A (2011) Uncertainty in the Demand forService The Case of Call Centers and Emergency Departments Working paper 21

Mandelbaum A Momcilovic P and Tseytlin Y (2012) On Fair Routing FromEmergency Departments to Hospital Wards QED Queues with Heterogeneous ServersManagement Science 58 1273ndash1291 21 421 551 553 554 561



Mandelbaum A and Stolyar S (2004) Scheduling Flexible Servers with ConvexDelay Costs Heavy-Traffic Optimality of the Generalized cmicro-Rule Operations Research52 836ndash855 1

Mandelbaum A Trofimov V Gavako I and Nadjhahrov E (2013) Home-Hospital (Rambam) Readmission Analysis httpseeserveriemtechnionacil

databasesDocsHomeHospital_visits_returnpdf 611

Marmor Y N (2003) Developing a Simulation Tool for Analyzing Emergency De-partment Performance Masterrsquos thesis TechnionmdashIsrael Institute of Technology 13

Marmor Y N (2010) Emergency-Departments Simulation in Support of Service-Engineering Staffing Design and Real-Time Tracking PhD thesis TechnionmdashIsraelInstitute of Technology 21

Marmor Y N Golany B Israelit S and Mandelbaum A (2012) Design-ing Patient Flow in Emergency Departments IIE Transactions on Healthcare SystemsEngineering 2 233ndash247 21 331

Marmor Y N Rohleder T Cook D Huschka T and Thompson J (2013)Recovery Bed Planning in Cardiovascular Surgery a Simulation Case Study Health CareManagement Science 16 314ndash327 34

McHugh M Van Dyke K McClelland M and Moss D (2011) Improv-ing Patient Flow and Reducing Emergency Department Crowding Agency for Health-care Research and Quality httpwwwahrqgovresearchfindingsfinal-reportsptflowindexhtml 3

Medicare USA (2013) Hospital Compare 30-Day Death and Readmission MeasuresData httpwwwmedicaregovHospitalCompareDataRCD30-day-measuresaspx611

Nadjhahrov E Trofimov V Gavako I and Mandelbaum A (2013) Home-Hospital (Rambam) EDA via SEEStat 30 to Reproduce ldquoOn Patients Flow inHospitalsrdquo httpietechnionacilLabsServengfilesHHDreproducing_flow_paperpdf 62 62

Nestler S (2011) Reproducible (Operations) Research A Primer on ReproducibleResearch and Why the OR Community Should Care About it ORMS Today 38 62

Nguyen V (1994) The Trouble with Diversity Fork-Join Networks with HeterogeneousCustomer Population The Annals of Applied Probability 1ndash25 521

Plambeck E Bayati M Ang E Kwasnick S and Aratow M (2014) Fore-casting Emergency Department Wait Times Working Paper 321

Plonski O Efrat D Dorban A David N Gologorsky M Zaied I Man-delbaum A and Rafaeli A (2013) Fairness in Patient Routing Maternity Ward inRambam Hospital Technical report 421 554

Ramakrishnan M Sier D and Taylor P G (2005) A Two-Time-Scale Model forHospital Patient Flow IMA Journal of Management Mathematics 16 197ndash215 561

Rambam Rambam Health Care Campus Haifa Israel httpwwwrambamorgilHome+2

RambamData Rambam Hospital Data Repositories Technion SEELab http

seeserveriemtechnionacildatabases 62 62

Saghafian S Austin G and Traub S J (2014) Operations Research Contri-butions to Emergency Department Patient Flow Optimization Review and ResearchProspects Working paper 3

SEELab SEE Lab TechnionmdashIsrael Institute of Technology httpietechnion

acilLabsServeng 1 1 62 62


46 ARMONY ET AL

SEEServer Server of the Center for Service Enterprise Engineering http

seeserveriemtechnionacilsee-terminal 62

SEEStat SEEStat Documentation TechnionmdashIsrael Institute of Technology httpietechnionacilLabsServeng 62 62

Senderovich A Weidlich M Gal A and Mandelbaum A (2014) Queue Miningfor Delay Prediction in Multi-Class Service Processes Working paper 321

Shi P Chou M C Dai J G Ding D and Sim J (2012) Models and Insightsfor Hospital Inpatient Operations Time-Dependent ED Boarding Time ManagementScience 24 13ndash14 2 42 421 561

Shi P Dai J G Ding D Ang J Chou M Jin X and Sim J (2013) PatientFlow from Emergency Department to Inpatient Wards Empirical Observations from aSingaporean Hospital Working paper 13

Song H Tucker A L and Murrell K L (2015) The Diseconomies of QueuePooling An Empirical Investigation of Emergency Department Length of Stay Forth-coming in Management Science 434

Stolyar S (2005) Optimal Routing in Output-Queued Flexible Server Systems Prob-ability in the Engineering and Informational Sciences 19 141ndash189 1 1

Sullivan S E and Baghat R S (1992) Organizational Stress Job Satisfactionand Job Performance Where Do We Go from Here Journal of Management 18 353ndash375 341

Sun J (2006) The Statistical Analysis of Interval-Censored Failure Time DataSpringer 311

Tezcan T (2008) Optimal Control of Distributed Parallel Server Systems under theHalfin and Whitt Regime Math of Operations Research 33 51ndash90 1

Thompson S Nunez M Garfinkel R and Dean M D (2009) Efficient Short-Term Allocation and Reallocation of Patients to Floors of a Hospital During DemandSurges Operations Research 57 261ndash273 552

Thorin O (1977) On the Infinite Divisibility of the Lognormal Distribution Scandi-navian Actuarial Journal 1977 121ndash148 421

Tseytlin Y (2009) Queueing Systems with Heterogeneous Servers On Fair Routingof Patients in Emergency Departments Masterrsquos thesis TechnionmdashIsrael Institute ofTechnology 13 21

Tseytlin Y and Zviran A (2008) Simulation of Patients Routing from an Emer-gency Department to Internal Wards in Rambam Hospital OR Graduate project IEampMTechnion 553 554

Tukey J W (1977) Exploratory Data Analysis Addison Wesley 13

Ward A and Armony M (2013) Blind Fair Routing in Large-Scale Service Systemswith Heterogeneous Customers and Servers Operations Research 61 228ndash243 554

Whitt W (2012) Fitting Birth-and-Death Queueing Models to Data Statistics andProbability Letters 82 998ndash1004 33 331

Yom-Tov G B (2010) Queues in Hospitals Queueing Networks with ReEnteringCustomers in the QED Regime PhD thesis TechnionmdashIsrael Institute of Technology21 421

Yom-Tov G B and Mandelbaum A (2014) Erlang-R A Time-Varying Queue withReentrant Customers in Support of Healthcare Staffing MampSOM 16 283ndash299 21 32321 331 43 611



Zacharias C and Armony M (2013) Joint Panel Sizing and Appointment Schedulingin Outpatient Care Working paper 561

Zaied I (2011) The Offered Load in Fork-Join Networks Calculations and Applica-tions to Service Engineering of Emergency Department Masterrsquos thesis TechnionmdashIsraelInstitute of Technology 561 61

Zeltyn S Marmor Y N Mandelbaum A Carmeli B Greenshpan OMesika Y Wasserkrug S Vortman P Schwartz D Moskovitch KTzafrir S Basis F Shtub A and Lauterman T (2011) Simulation-Based Mod-els of Emergency Departments Real-Time Control Operations Planning and ScenarioAnalysis Transactions on Modeling and Computer Simulation (TOMACS) 21 21 3331 61

Acknowledgements We dedicate our paper to the memory of the lateDavid Sinreich As a professor at the Technion IEampM Faculty David was apioneer and an example-to-follow in recognizing the necessity and impor-tance of data- and simulation-based research in healthcare

Our research and its seed financial backing started within the OCR(Open Collaborative Research) Project funded by IBM and led jointly byIBM Haifa Research (headed by Oded Cohn) Rambam Hospital (CEO RafiBeyar) and Technion IEampM Faculty (past dean Boaz Golany) Indeed itwas Beyar who invited us at the outset to ldquouserdquo the healthcare campus asour research laboratory this invitation has given rise to the present workand many offsprings

Data analysis maintenance of data repositories and continuous adviceand support have been provided by the Technion SEE Laboratory and itsaffiliates Valery Trofimov Igor Gavako Ella Nadjharov Shimrit MamanKatya Kutsy Nitzan Carmeli and Arik Senderovic

Financially the research of YM GY and YT was supported by graduatefellowships from Technionrsquos Graduate School and the Israel National Insti-tute for Health Services and Health Policy Research The joint research ofMA and AM was funded by BSF (Bi-national Science Foundation) Grants20051752008480 AM was partially supported by ISF Grant 135708 andby the Technion funds for promotion of research and sponsored researchMA was partially funded by the Lady Davis Fellowship as a visitor at theTechnion IEampM faculty

Some of AMrsquos research was funded by and carried out while visitingSAMSI NSF STOR UNC IOMS Stern NYU and Statistics Wharton UPennndash the hospitality of all these institutions is truly appreciated

Our paper greatly benefited from feedback by colleagues and a thoroughand insightful refereeing process Ward Whitt discovered a flaw in our empir-ical analysis that led to the rewriting of the ED section Jim Dai read care-fully the first version and provided significant and helpful editorial feedback


48 ARMONY ET AL

We are very grateful to Peter Glynn founding editor-in-chief of StochasticSystems for his encouragement and support throughout He was joined byan anonymous AE to lead and guide us safely through the revision process

Last but certainly not least a project such as this one requires a collab-orative effort by many individuals Their list which is too long to acknowl-edge here must have at its top our host Rambam hospital its managementnursing staff and physicians made as good a partner as one could hope for

Appendix A model for ORAP data-based research The tra-ditional still prevalent model for data-based ORAP research has been onewhere an individual researcher or a small group obtains and analyzes datafor the sake of an isolated research project Our experience is that such amodel cannot address todayrsquos empirical needs For example hospital datais typically large complex contaminated and incomplete which calls for aprofessional and inevitably time-consuming treatment Next using data in asingle project or a few for that matter is wasteful This calls for data-reuseand sharing across student generations or research groups which requires in-frastructure documentation maintenance and coordination The challengeis exacerbated by healthcare data being confidential and proprietary whichprevents reproducibility and slows down progress (Nestler 2011)

A feasible model An alternative model is a research laboratory fundedby and serving a small community of researchers with access to its databeing as broad as possible A working example is the Technion SEELabwhere readers can access RambamData Little effort will be then required toreproduce our present EDA and going beyond it In fact most of our figureswere created by SEEStatmdasha SEELab-developed user-friendly platform foronline (real-time) EDAmdashand readers can recreate this process by followingNadjhahrov et al (2013)

SEELab To elaborate some SEELab is a data-based research labora-tory residing at the IEampM Faculty of the Technion in Haifa Israel (SEEstands for ldquoService Enterprise Engineeringrdquo) SEELab maintains a reposi-tory for transaction-level operational data (log-files) from large service oper-ations This data is collected and cleaned thus preparing it for research andteaching Currently SEELab databases include transaction-level multi-yeardata from 4 call centers an internet academic website 8 emergency depart-ments (mainly arrivals data) a large ambulatory hospital (RTLS-based)and 4 years of data from the Rambam Hospitalmdashthe latter is the empiricalfoundation for the present research



The EDA environment of SEELab is SEEStatmdasha software platform thatenables real-time statistical analysis of service data at seconds-to-monthstime resolutions SEEStat was used to create most of our figures It imple-ments many statistical algorithms parametric distribution fitting and selec-tion fitting of distribution mixtures survival analysis and moremdashwith allalgorithms interacting seamlessly with all the databases SEEStat also inter-acts with SEEGraph a pilot-environment for structure-mining on-demandcreation display and animation of data-based process maps (eg Figure 1and the animation of its underlying data (SEEnimations))

Working Online with SEEStat Three SEELab databases are pub-licly accessible at SEEServer the SEELab server two from call centers andone from the Rambam hospital The Rambam data is described in sect12 andour analysis of it greatly benefitted from our call-center experiences

The connection protocol to SEEStat for any research or teaching pur-pose is simply as follows go to the SEELab webpagehttpietechnionacilLabsServengthen proceed either via the link SEEStat Online or directly throughhttpseeserveriemtechnionacilsee-terminal and complete theregistration procedure Within a day or so you will receive a confirma-tion of your registration plus a password that allows you access to SEE-Stat SEELabrsquos EDA environment and via SEEStat to the above-mentioneddatabases Note that your confirmation email includes two attachments atrouble-shooting document and a self-taught tutorial that is based on callcenter data and the Rambam hospital data We propose that you print outthe tutorial connect to SEEStat and then let the tutorial guide you hands-on through SEEStat basicsmdashthis should take no more than 15 hours

Reproducing our EDA and beyond Rambam data is publicly availableeither for downloading (RambamData) or through SEEStat as describedabove The download link includes data documentation To facilitate re-producibility the document Nadjhahrov et al (2013) provides a detaileddescription of the creation process of our EDA which includes all figures(except for Figure 12) in the present paper

Mor ArmonyStern School of Business NYU44 West 4th StreetNew York NY 10012E-mail marmonysternnyuedu

Shlomo IsraelitDirector Emergency Trauma DepartmentRambam Health Care Campus (RHCC)6 HarsquoAliya StreetHaifa Israel 31096E-mail s israelitrambamhealthgovil


50 ARMONY ET AL

Avishai MandelbaumFaculty of Industrial Engineering and ManagementTechnionmdashIsrael Institute of TechnologyTechnion city Haifa Israel 32000E-mail avimietechnionacil

Yariv N MarmorDepartment of Industrial Engineering and ManagementORT Braude CollegeKarmiel IsraelHealth Care Policy and Research DepartmentMayo Clinic200 First Street SWRochester MN USA 55905E-mail myarivbraudeacil

Yulia TseytlinIBM Haifa Research LabHaifa University CampusMount Carmel Haifa Israel 31905E-mail yuliatsegmailcom

Galit B Yom-TovFaculty of Industrial Engineering and ManagementTechnionmdashIsrael Institute of TechnologyTechnion city Haifa Israel 32000E-mail galitytxtechnionacil


Introduction

Patient flow focus

Rambam Medical Center

The ED+IW network

Data description

``Apologies to the statistician

Paper structure

Some Hints to the Literature

A proof of concept

Emergency Department

Basic facts

Research opportunities Performance metrics

EDA Time dependency and overdispersion

Research opportunities

EDA Fitting a simple model to a complex reality


EDA State dependency


Internal Wards

Basic facts

EDA LOSmdasha story of multiple time scales

Research opportunities Workload characterization protocol mining flow control and why Log-Normal

EDA Operational regimes and diseconomies of scale

In what regime do IWs operate Can QED- and ED-regimes co-exist


Diseconomies of scale (or how ward size affects LOS)


The ED+IW Network

ED-to-IW transfer process Basic facts

Delays in transfer


Influence of transfer delays on the ED


Causes of delay


Fairness in the ED-to-IW process

Fairness towards patients


Fairness towards staff


A system view


Discussion and Concluding Remarks

Operational measures as surrogates to overall hospital performance

Readmissions

Capacity and cost of care

Some concluding comments on data-based researchmdasha great opportunity but no less of a challenge

References

Acknowledgements

Appendix A model for ORAP data-based research

SEELab

Working Online with SEEStat

Authors addresses

2 ARMONY ET AL

frustratedrdquo In (too) many instances this frustration is caused and exacer-bated by delaysmdashldquowaiting for something to happenrdquo in turn these delaysand the corresponding queues signal inefficiencies Hospitals thus present apropitious ground for research in Queueing Theory and more generally Ap-plied Probability (AP) Operations Research (OR) and Service Engineering(SE) Such research would ideally culminate in reduced congestion (crowd-ing) and its accompanying important benefits clinical financial psychologi-cal and societal For such benefits to accrue it is critical that the supportingresearch is data-based

As it happens however operational hospital data is accessible to veryfew researchers and patient-level data has in fact been publicly unavailableThe reasons span nonexistence or poor quality of data concerns for patientconfidentiality and proprietorial constraints or lack of incentives for dataowners We attempt to address these issues as follows First we presentan Exploratory Data Analysis (EDA) of a 1000-bed hospital covering 3years of patient-flow at the inter-departmental level of the individual pa-tient Through this EDA we identify and propose research opportunitiesfor AP OR and SE Then we open up our operational database and makeit universally accessible at the Technion IEampM Laboratory for Service En-terprise Engineering (SEELab) it can be either downloaded or analyzedonline with a user-friendly platform for EDA Our goal is thus to providean entry to and accelerate the learning of data-based OR of hospitals re-searchers can use it (and some already have) to reproduce our EDA whichwould serve as a trigger and a starting point for further data mining andnovel research of their own

11 Patient flow focus Of particular interest to both researchers andpractitioners is patient flow in hospitals improving it can have a signifi-cant impact on quality of care as well as on patient satisfaction restrictingattention to it adds a necessary focus to our work Indeed the medical com-munity has acknowledged the importance of patient flow management (egStandard LD31010 which the Joint Commission on Accreditation of Hos-pital Organizations (JCAHO 2004) set for patient flow leadership) Thisacknowledgment is natural given that operational measures of patient floware relatively easy to track and that they inherently serve as proxies forother quality of care measures (see Section 61) In parallel patient flow hascaught the attention of researchers in OR in general and Queueing Theory inparticular This is not surprising hospital systems being congestion-pronenaturally fit the framework of Queueing Theory which captures the tradeoffsbetween (operational) service quality and resource efficiency








4 ARMONY ET AL

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day

at th

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spita

l 32

60

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291

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3744

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23511

84

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ay





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IW A

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InternalWards

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53

136

JusticeTable

Blocked at IWs

35

699

5

157

236

843

754

245 patday

161 patday

1

165

13 patday





6 ARMONY ET AL













8 ARMONY ET AL












10 ARMONY ET AL




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0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

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ival

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[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

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0 2 4 6 8 10 12 14 16 18 20 22Aver

age

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14 ARMONY ET AL




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s pe

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1200-2159

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2200-0259





16 ARMONY ET AL

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rate

s pe

r hou

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01

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18 ARMONY ET AL




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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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tive

frequ

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11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

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tive

frequ

enci

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20 ARMONY ET AL












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24 ARMONY ET AL


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26 ARMONY ET AL







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-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



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28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



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32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

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35

36

37

38

39

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00051015202530354045

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ber o

f Pat

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ours

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3

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5

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200

400

600

800

100

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000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL






































Rambam Rambam Health Care Campus Haifa Israel httpwwwrambamorgilHome+Page 12







46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







4 ARMONY ET AL

One

day

at th

e Ho

spita

l 32

60

317

284

118

291

183

183

193

3744

3

54

122

23511

84

9 35

82

196

7

71

37

13

12

25

14

27

97

20

50 6

8

08

06

14

09

11 1

9

20

09

29

08

13

23

43

03 4

9

05

06

17

22

13

18

32

11

16

06 0

2

03

06

02

03

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01

06

02

04

Dece

ased

Disa

ppea

red

Disc

harg

edTr

ansf

erre

d

Ram

bam

Au

gust

200

4 A

vera

ge D

ay





Abandonment

Services

IW A

IW C

IW B

IW D

IW E

Dischargedpatients

Dischargedpatients

InternalWards

OtherMedical

Units

53

136

JusticeTable

Blocked at IWs

35

699

5

157

236

843

754

245 patday

161 patday

1

165

13 patday





6 ARMONY ET AL













8 ARMONY ET AL












10 ARMONY ET AL




0

5

10

15

20

25

30

35

0

3

5

8

10

13

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Arr

ival

Rat

e














12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses



Abandonment

Services

IW A

IW C

IW B

IW D

IW E

Dischargedpatients

Dischargedpatients

InternalWards

OtherMedical

Units

53

136

JusticeTable

Blocked at IWs

35

699

5

157

236

843

754

245 patday

161 patday

1

165

13 patday





6 ARMONY ET AL













8 ARMONY ET AL












10 ARMONY ET AL




0

5

10

15

20

25

30

35

0

3

5

8

10

13

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Arr

ival

Rat

e














12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

6 ARMONY ET AL













8 ARMONY ET AL












10 ARMONY ET AL




0

5

10

15

20

25

30

35

0

3

5

8

10

13

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Arr

ival

Rat

e














12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







8 ARMONY ET AL












10 ARMONY ET AL




0

5

10

15

20

25

30

35

0

3

5

8

10

13

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Arr

ival

Rat

e














12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







10 ARMONY ET AL




0

5

10

15

20

25

30

35

0

3

5

8

10

13

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Arr

ival

Rat

e














12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses









12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

12 ARMONY ET AL





020406080

100120140160180200220240260280300320340

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies



[0000 - 0100)[0100 - 0200)[0200 - 0300)[0300 - 0400)[0400 - 0500)[0500 - 0600)[0600 - 0700)[0700 - 0800)[0800 - 0900)[0900 - 1000)[1000 - 1100)[1100 - 1200)[1200 - 1300)[1300 - 1400)[1400 - 1500)[1500 - 1600)[1600 - 1700)[1700 - 1800)[1800 - 1900)[1900 - 2000)[2000 - 2100)[2100 - 2200)[2200 - 2300)[2300 - 2400)

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20 22Aver

age

num

ber o

f pat

ient

s







025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL






































Rambam Rambam Health Care Campus Haifa Israel httpwwwrambamorgilHome+







46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses


025050075010001250150017502000225025002750300032503500

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Freq

uenc

ies




Early MorningNormal


Normal



0

500

1000

1500

2000

2500

10 15 20 25 30 35 40 45 50 55

Freq

uenc

ies









14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

14 ARMONY ET AL




0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r



01

02

02

03

03

04

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L









005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses




005

015

025

035

045

055

0 5 10 15 20 25 30 35 40

Rate

s pe

r hou

r L



0300-0859

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50

Rate

s pe

r hou

r L



0900-1159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



1200-2159

005

015

025

035

045

055

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Rate

s pe

r hou

r L



2200-0259





16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

16 ARMONY ET AL

006

016

026

036

10 12 14 16 18 20Serv

ice

rate

s pe

r hou

r L




00

01

02

03

04

05

06

07

10 12 14 16 18 20

Rela

tive

Freq

uenc

y



1200-2159 0300-08590900-1159 2200-0259


explanations next























18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses
















18 ARMONY ET AL




0123456789

10111213141516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Rela

tive

frequ

enci

es






00

01

02

03

04

05

06

07

08

09

10

11

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Rela

tive

frequ

enci

es










36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses



36

37

38

39

40

41

42

43

00

02

04

06

08

10

12

14

16

18

20

22

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Num

ber o

f Pat

ient

s

Aver

age

num

ber o

f cas

es








20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

20 ARMONY ET AL












22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







22 ARMONY ET AL














24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







24 ARMONY ET AL


90

100

110

120

130

140

150

160

20

25

30

35

40

45

50

2004 2005 2006 2007 2008 Ave

rage

leng

th o

f sta

y (A

LOS)

Ave

rage

num

ber o

f pat

ient

s

Year
















26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

37

38

39

0

1

2

3

4

5

6

000

200

400

600

800

100

0

120

0

140

0

160

0

180

0

200

0

220

0

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses








26 ARMONY ET AL







$

$

amp

amp$

amp ( $ ) + amp($)+

$amp()+

-(

0amp1(23456(

-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

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014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

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00051015202530354045

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ient

s

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e (h

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0

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0

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ient

s

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ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses


$

$

amp

amp$

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-012304

567132839

lt239

=gt032


Regular 300 77 2(253)



All Types 322 75 4(298)







28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

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00051015202530354045

Num

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s

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y tim

e (h

ours

)




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ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

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7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

28 ARMONY ET AL









0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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39

0

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0

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0

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Num

ber o

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ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses



0

002

004

006

008

01

012

014

00 05 10 15 20 25 30 35 40 45 50

0000 0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200

Frac

tion

of L

oad

Num

ber o

f Pat

ient

s










30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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ient

s

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y tim

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ours

)










0

1

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4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

30 ARMONY ET AL










Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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0

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ber o

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ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







Allowing skipping


Nursesavailability

Doctorsavailability



Beds availability




Incentive mechanism






32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

32 ARMONY ET AL










Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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0

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ient

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y tim

e (h

ours

)










0

1

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4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses





Ward A 757 733 000 737

Ward B 386 572 000 484

Ward C 709 662 000 680

Ward D 818 748 270 781







34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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39

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Dela

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e (h

ours

)










0

1

2

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4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

34 ARMONY ET AL















36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

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39

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ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses








36 ARMONY ET AL

34

35

36

37

38

39

40

00051015202530354045

Num

ber o

f Pat

ient

s

Dela

y tim

e (h

ours

)




35

36

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38

39

0

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000

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ber o

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ient

s

Dela

y tim

e (h

ours

)










0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses


0

1

2

3

4

5

6

7

8

9

000 200 400 600 800 1000 1200 1400 1600 1800 2000 2200LO

S M

eans











38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

38 ARMONY ET AL












40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses







40 ARMONY ET AL








REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses


REFERENCES




















42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

42 ARMONY ET AL











































44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses






















44 ARMONY ET AL













































46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses
























46 ARMONY ET AL

































48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses












48 ARMONY ET AL















50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses









50 ARMONY ET AL






Introduction

Patient flow focus


The ED+IW network

Data description


Paper structure


A proof of concept


Basic facts








Internal Wards

Basic facts








The ED+IW Network


Delays in transfer




Causes of delay







A system view




Readmissions



References

Acknowledgements


SEELab


Authors addresses

on patient flow in hospitals: a data-based queueing-science

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