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Introduction Transfer Conclusions
Queues in Hospitals: Empirical Study
Mor Armony
Joint work with: Avi Mandelbaum, Yariv Marmor,Yulia Tseytlin and Galit Yom-Tov
NYU, Technion, Mayo, IBM, Columbia
November 2011
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Patient Flow in Hospitals as a Queueing Network
Network features:Customers: PatientsServers: Beds, equipments, medical staffStations: Medical units
Research Questions:Special features of this networkImplications on queueing modeling and theory
Methodology:Exploratory Data Analysis (EDA)
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Our data
Data description: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)Acknowledgement: Anonymous Hospital and
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
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Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Our focus
Subnetwork including: ED, IW and ED → IWSubstantial size:
53% patients entering the hospital stay within thissubnetwork.21% of those, are hospitalized in an IW
Nearly isolated:ED Arrival are all external93% of IW arrivals are either external or from within thesubnetwork.
Relatively simple:One EDFive IWs (A-E)IW A-D identical in scope capabilities
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
A Queueing Network View
Arrivals EmergencyDepartment
Abandonment
Services
IW A
IW C
IW B
IW D
IW E
Dischargedpatients
Dischargedpatients
InternalDepartment
OtherMedical
Units
53%
13.6%
"JusticeTable"
Blocked at IWs3.5%
69.9%
16.5%
5%
15.7%
1%
23.6%
84.3%
75.4%
245 pat./day
161 pat./day
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Transfer Process
AssignmentBed
available?
Staff available
?
Bed ready? Transfer
Bed available in
another ward?
Delay Delay Delay
Yes, but later
No No
Yes Yes Yes
NoYes
Assignment to non-IW
No
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Transfer waiting times
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Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Why are delays problematic?
Patients do not receive proper care.They are exposed to other diseases.ED overcrowding.Impose extra load on ED medical staff.
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Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Average Transfer Delays per Patient Type
Patient Type Average Standard % delayed up % Delayed moreDelay (hrs) Deviation to 4 hours than 10 hours
Regular 3.00 2.53 77% 2%Special Care 3.33 3.16 74% 5%Ventilated 8.39 6.59 41% 41%All Types 3.22 2.98 75% 4%
Ventilated patients should have lowest delay, but experience thehighest!
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Transfer waiting times by patient type
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Patients need to wait for a bed, equipment, and medical staff.Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Delays in transfer: Cause and effect diagram
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
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Routing: Input versus output queues
Single line system is more efficientReality requires multiple linesPatients require care even when in queuePush versus PullFairness towards patients?
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
(Un)fairness towards patients
IW \ Type Regular Special care Ventilated TotalWard A 7.57% 7.33% 0.00% 7.37%Ward B 3.86% 5.72% 0.00% 4.84%Ward C 7.09% 6.62% 0.00% 6.80%Ward D 8.18% 7.48% 2.70% 7.81%Total within wards 6.91% 6.80% 0.67% 6.80%Total in ED-to-IW 31% 31% 5%
Percentage of FCFS violations per type within each IW
Mor Armony INFORMS 2011
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Introduction Transfer Conclusions
Internal Wards operational measuresWard A Ward B Ward C Ward D
ALOS (days) 6.5 4.5 5.4 5.7Mean occupancy 97.8% 94.4% 86.8% 91.1%Mean # patientsper month 205.5 187.6 210.0 209.6Standardcapacity (# beds) 45 30 44 42Mean # patientsper bed per month 4.58 6.38 4.89 4.86Return rate(within 3 months) 16.4% 17.4% 19.2% 17.6%
How does one explain these differences in performance?Is this work allocation fair?How is fairness defined?See Mandelbaum, Momcilovic, & Tseytlin (2010) andTseytlin & Zviran (2008)
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Introduction Transfer Conclusions
Unfairness towards wards: Patient mix
IW\Type Regular Special-care Ventilated TotalWard A 2,316 (50.3%) 2,206 (47.9%) 83 (1.8%) 4,605 (25.2%)Ward B 1,676 (43.0%) 2,135 (54.7%) 90 (2.3%) 3,901 (21.4%)Ward C 2,310 (49.9%) 2,232 (48.2%) 88 (1.9%) 4,630 (25.4%)Ward D 2,737 (53.5%) 2,291 (44.8%) 89 (1.7%) 5,117 (28.0%)Total 9,039 (49.5%) 8,864 (48.6%) 350 (1.9%) 18,253
Justice Table allocation to IWs by patient type.
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Introduction Transfer Conclusions
Conclusions
Patient flow in hospitals as a queueing networkInput versus Output queuesPush versus Pull in routingFairness towards customers (definition?)Customers served while in queueFairness: Occupancy + Flux
Mor Armony INFORMS 2011