Emilio Luque Computer Architecture & Operating Systems Department

University Autonoma of Barcelona (UAB)

Emergency Departments (ED)

are complex and

quite dynamic systems.

ED’s are overcrowded and work

with limited budget.

Patients must be

addressed with the best

quality.

Simulation:What if? Optimization:

The best solution for?

Supported by the MICINN Spain, under contract TIN2007-64974 and

the MINECO (MICINN) Spain, under contract TIN2011-24384

Emilio Luque

CAOS – HPC4EAS

Manel Taboada GIMBERNAT

Eduardo Cabrera

CAOS – HPC4EAS

Francisco Epelde

PARC TAULÍ

Ma. Luisa Iglesias

PARC TAULÍ

Optimization

Simulation

Variables Values Observability

Symptoms (patients) Healthy, Cardiac/respiratory arrest, severe/moderate

trauma, headache, vomiting, diarrhea E/I

Communication skills Low, Medium, High E

Level of experience (doctors)

Resident (1 to 5); Junior (5-10); Senior (10 - 15) and Consultant (over 15 years)

E/I

Level of experience

(triage nurses)

Low, Medium, High E/I

Level of experience (emergency nurses)

Low, Medium, High E/I

Level of experience (admissions)

Low, Medium, High E/I

Current state

/ Output Input

Next state /

Output

…. …. ….

Sx / Ox Ia (p1) Sy / Oy

Sx / Ox Ia (p2) Sz / Oz

Sx / Ox Ia (p3) Sx / Ox

…. …. ….

STATE Variables Values Observability

Name/identifier <id> Unique per agent I

Personal details

Gender, Medical history (cardiology, pulmonology,

neurological,…); Allergies (yes-no);

Treatments that received (classified into therapeutic groups:

bronchodilators, vasodilators, etc.);

Origin (national or immigrant)

I

Location Entrance, Admissions, Waiting Room, Triage, Treatment

Zone. E

Action

Idle, Requesting information from <id>, Giving information

to <id>, Searching, Moving to <location> , Waiting for

ambulance.

E

Physical condition Healthy; Hemodynamic-Constant; Barthel Index (degree of

dependence). E/I/N

1) Active Agents

Patients

Companions of patients

Admission personnel

Sanitarian technicians

Nurses (Triage, Emergency)

Doctors (Emergency,

Specialists)

2) Passive Agents

Information system

Loudspeaker system

Pneumatic pipes

Tests services

1 to 1(One-to-One) 1 to n (Multicast) 1 to Zone: individuals in Zone

(Area- Restricted Broadcast)

The Environment

The model should include the spatial topographical design from the ED

Arrival/dismissal

by own means

Arrival/dismissal

by ambulance

Agents interactions

ED functionality

Agents

A

N

D

Arrival/dismissal

by own means

Arrival/dismissalb

y ambulance

What if?

ED Simulator

Patients:

How many arrive to the service

How many leave the service

Times of staying in each area

Patients arrival:

Could arrive every 3 min. , but with different probabilities:

20% (4 pat/hr), 40% (9 pat/hr),

60% (13 pat/hr) , 80% (17 pat/hr)

Staff Number Junior Senior

Admission 1-2 2 min. 1 min. 15 sec.

Triage Nurse 1-3 8 min. 5 min.

Doctor 1-4 20 min. 15 min.

Configuration of the ED Staff

Input

Output

Given any objective (index) function f :

minimize Maximize

• Find the best/optimum solution from all the possible solutions.

AxA

Ax

xf

Af

oset;constraint

tosubject

min/max

:

xfxf o xfxf o

Axo

Is it always the "best solution" (the optimum) the most interesting for us?

Methodology

Parameter configuration:

A

N

D

Simulator: 2nd version

A, N, D = > 3D + P => 4D

~ 400 patients daily

Discrete

Methodology: Computational complexity

• Search space

– # Dimensions = Patients,

staff (D, N, A, …), T, B, …

– Each dimension=> range of possible values

– # Points = # simulations (indexes)(time)

COMBINATORIAL!

A

N

D

Multidimensional

A

N

D

P

A

N

D

P

T A

N

D

P

B

T

ABM

SIMULATOR PARAMETERS

I

N

D

E

X +

constraints

DSS

14 D, 9 N, 9 A = 1,134 cases

Patient

Arrival

20% (4 pat/hr)

40% (9 pat/hr)

60% (13 pat/hr)

80% (17 pat/hr) 25,000 ticks => 1 day

1,134 cases * 4 = 4,536 cases

Staff Time (ticks)

Senior Junior

Doctors 260 350

Nurses 90 130

Admission personnel 20 35

Quantity

1 - 4

1 - 3

1 - 3

Cost (€)

Senior Junior

1000 500

500 350

200 150

Quality Index:

Minimize patient “Length of Stay” (LoS) Constraint: Cost <= 3500 €

4,536 total cases => 2,408 cases under limit

Cost constraint <= 3500 € Average patient “LoS”

4 p/hr 9 p/hr

13 p/hr 17 p/hr

Optimum

Time

(ticks)

€ #

Staff

D N A

428 3,200 5 2 S 2 S 1 S

428 2,900 5 2 S 1 S 2 S

428 2,850 5 2 S 1 S 1 S, 1 J

Patient

Arrival

20% (4 pat/hr)

40% (9 pat/hr)

60% (13 pat/hr)

80% (17 pat/hr)

4 p/hr 9 p/hr

13 p/hr 17 p/hr

Optimum

Time

(ticks)

€ # Staff D N A

3,266 3,350 7 1 S, 3 J 2 J 1 J

Cost constraint <= 3500 € Average patient “LoS”

4 p/hr 9 p/hr

13 p/hr 17 p/hr

Cost constraint <= 3500 € Average patient “LoS”

4 p/hr 9 p/hr

13 p/hr 17 p/hr

Cost constraint <= 3500 € Average patient “LoS”

Optimal

vs

Suboptimal