1. Lecturer: Yariv Marmor, Industrial Engineering, Technion
ORSIS 10/5/2009
Queues in Hospitals: Empirical Analysis of Patients Flows through the Emergency Department
Lecturer: Yariv Marmor, Industrial Engineering, Technion
Joint work with Yulia Tseytlin, Galit Yom-Tov and Avishai Mandelbaum
This talk is based on a PhD thesis that started under the supervision of David Sinreich (ז"ל) and is now guided by Avishai Mandelbaum.
Research has been partially conducted within the OCR research project of Technion+IBM+Rambam, under the funding of IBM
25 November 2018

2. Hospital Overview Yulia Galit
Services
IW1
Yulia
Emergency Department
Patient discharge
Arrivals
IW5
MU1
Patient discharge
Patients abandon
MUn
Galit
Joint project with Mandelbaum A., Yom-Tov G., and Tseytlin Y. :
Analyze ED, IW, and their interfaces, using simulation, empirical and theoretical models.
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3. Addressing the Following Questions:
Given an ED environment, identify a suitable ED architecture (DEA / simulation / mathematics).
Explain the difference in IW-LOS distributions, when plotted in resolutions of days vs. hours (+implication).
Why is the distribution of ED lengths of stay (LOS) LogNormal? (no clear answer, yet)
How to measure offered-load (congestion) in EDs? How to use it in support of staffing decisions (on-line, off-line)?
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4. Given an ED Environment, Identify a Suitable ED Architecture: Data
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5. Given an ED Environment, Identify a Suitable ED Architecture: Arrivals rate to the ED* (from Non Homogeneous Poisson process)
*Via SEEStat
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6. Given an ED Environment, Identify a Suitable ED Architecture: Parameters
Outputs (Yjo):
Average length of stay.
Net patients throughput.
Number of patients waiting for a bed.
Controllable inputs (Xio):
Manpower (70% of total costs).
Number of beds in the ED.
Number of hospitalizations.
Uncontrollable inputs (Zko):
Number of children / elderly.
Number of patients with injury.
Number of patients arriving by ambulance.
Number of patients referred by physician
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7. Given an ED Environment, Identify a Suitable ED Architecture: Mathematical Model (DEA)
Efficiency
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8. Given an ED Environment, Identify a Suitable ED Architecture: Comparison (DEA)
=> Best operating models: Fast Track (priority models)
Triage (routing control)
(Ongoing research)
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9. Why is the Distribution of ED Lengths of Stay (LOS) LogNormal?
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10. Why is the Distribution of ED Lengths of Stay (LOS) LogNormal: Phase Type Approximation
Each phase is exponential
Phase Type
Total LOS is LogNormal
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11. Explain the Difference in IW-LOS Distributions, When Plotted in Resolutions of Days vs. Hours
1 day resolution
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12. Explain the Difference in IW-LOS Distributions, When Plotted in Resolutions of Days vs. Hours
2 hour resolution
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13. Explain the Difference in IW-LOS Distributions, When Plotted in Resolutions of Days vs. Hours (implication): Arrival / Departure Rate
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14. How to Measure Offered-Load (Congestion) in the ED: Offered-Load Model in Mt/G/∞
Nurse
Arrivals Dr
X-Ray
Lab
Exit ∞
i – index of node.
=> Find the nominal resource level needed
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15. How to Measure Offered-Load (Congestion) in the ED: Staffing Rule
a is the fraction of patients that start service within T time units (Quality of Service)
(We have used a=0.1, and T=30 minutes for the first patient-physician encounter)
h(bt) is the Halfin-Whitt function (Halfin & Whitt 1981)
Staffing rule (Halfin & Whitt 1981; Borst, Mandelbaum, & Reiman 2004) :
25 November 2018

16. How to Measure Offered-Load (Congestion) in the ED: Results for On-Line Staffing Decisions
Comparison of the predicted for each hour in the rest of the shift:
Current: The current staffing rule.
RCCP (Rough Cut Capacity Planning): Efficiency driven staffing rule.
OL: Offered-Load staffing rule.
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17. Question ?
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