queueing models of patient flow in hospitals: what does...

Queueing Models of Patient Flow in Hospitals:What Does the Data Tell Us?

Mor Armony

Joint work with: Avi Mandelbaum, Yariv Marmor,Yulia Tseytlin and Galit Yom-Tov

NYU, Technion, Mayo, IBM, Columbia

November 2010

Mor Armony INFORMS 2010

Patient Flow in Hospitals as a Queueing Network

Questions:How to model arrivals, departures and transitions?Who are the servers?What are the service and arrival rates?What are the relevant performance measures?

Our data:Anonymous Israeli hospital with 1000 beds and 45 medicalunits75,000 patients are admitted annuallyYears data collected: 2004 - 2008Individual patient level data, time stamps (admission,transfers and discharge)Our focus: ED, IW and transfers ED –> IW


Arrival rates into ED

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Hour

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Average number of patients per hour (Jan 2005, weekdays)


ED: Distribution of the number of occupied beds

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0.5%

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0 10 20 30 40 50 60 70 80 90 100L (Number of Occupied Beds)

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ED: Hourly distribution of the number of occupied beds

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H(0) H(1) H(2)H(3) H(4) H(5)H(6) H(7) H(8)H(9) H(10) H(11)H(12) H(13) H(14)H(15) H(16) H(17)H(18) H(19) H(20)H(21) H(22) H(23)


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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 21 22 23Hour of the Day

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Average number of beds per hour of the day


ED: Number of occupied beds as an Mt/M/∞queueing model

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EmpiricTheoretic


ED: Number of occupied beds as Birth & Death model

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ED: Arrival and departure rates

Observation: Both arrival and departure rates are statedependent.Consistent with Diwas and Terwiesch (2008)

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LMor Armony INFORMS 2010

Internal Wards: Capacities and ALOS

Ward A Ward B Ward C Ward D Ward EStandard capacity(# beds) 45 30 44 42 24Maximal capacity(# beds) 52 35 46 44 27ALOS(days) 6.368 4.474 5.358 5.562 4.11


Routing: ED to IW

Single line system is more efficientReality requires multiple linesPatients require care even when in queuePush versus PullJustice table is meant to ensure fairness


Fairness and Dis-economies of Scale

Ward A Ward B Ward C Ward DALOS (days) 6.368 4.474 5.358 5.562Mean Occupancy Rate 97.8% 94.4% 86.8% 91.1%Mean # Patients per Month 205.5 187.6 210.0 209.6Standard capacity 45 30 44 42Mean # Patients per Bedper Month 4.57 6.25 4.77 4.77Return Rate (within 3 months) 16.4% 17.4% 19.2% 17.6%

* Data refer to period 1/05/06 - 30/10/08 (excluding the months1-3/07)


Fork-Join networks revisited

ED physician

IW nurse, Help force

Stretcher Bearer

IW nurse in charge

General NurseReceptionist

ED nurse in charge

IW physician

Hospitaliza-tion

decision

Patient allocation request

Transferal time

decision

Patient’s status

updating

Coordination with the IW

Running the Justice Table

Request skipping?

Approve skipping?

Initial measurements

collection

Patient’s transferal

Availability check

Bed preparation

Initial medical check

Yes

No

YesNo

Resource Queue - Synchronization Queue -

Availability check

Ventilated patient

- Ending point of simultaneous processes

Transferal time

decision

“Walking patient” Ward E

Ward E

Ward E

Zviran (2008): Diffusion limits and controlZaied (2010): Offered load


Operational Regime of IW

Beds: QED regime.Prediction: Erlang-B in QED:N ' R + β

√R ⇒ P(block) ' 1√

Nφ(β)Φ(β) and

ρ ' 1− β+φ(β)/Φ(β)√N

.For our data, the QED regime predicts: P(block) ' 2.9%and ρ ' 91.7%.Actual numbers: P(block) = 3.54% and ρ = 93.1%.

Doctors: ED regime.Average handling time for patient admission: 30 minutes.Average wait for admission (once a bed is ready): 2.5hours.


Operational performance measures

Focus: Quality of CarePatient surveysRate of returnMortality rates


Conclusions

Hospital as a queueing networkArrival and departure rates are state dependentPush versus Pull in routingFairness: Occupancy + FluxEconomies and dis-economies of scaleFork-Join networksQED and ED regime co-exist in a single system.Operational measures should be in line with quality of caremeasures


queueing models of patient flow in hospitals: what does...

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