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A Stochastic Service Network Model with Application to Hospital Facilities

Author

Listed:
  • John C. Hershey

    (University of Pennsylvania, Philadelphia, Pennsylvania)

  • Elliott N. Weiss

    (Cornell University, Ithaca, New York)

  • Morris A. Cohen

    (University of Pennsylvania, Philadelphia, Pennsylvania)

Abstract

This paper presents a methodology for estimating expected utilization and service level for a class of capacity constrained service network facilities operating in a stochastic environment. A semi-Markov process describes the flows of customers (patients) through a network of service units. We model the case where one of the units has finite capacity and no queues are allowed to form. We show that the expected level of utilization and service can be computed from a simple linear relationship based on (a) the equilibrium arrival rates at each unit which are associated with the case of infinite capacity, (b) mean holding times for each unit, and (c) the probability that the finite capacity unit is at full capacity. We use Erlang's loss formula to calculate the probability of full capacity, show this calculation to be exact for two cases, and recommend its use as an approximation in the general case. We test the accuracy of the approximation on a set of published data. In the discussion, we present a technique for analyzing collected patient flow data using the results of this methodology.

Suggested Citation

  • John C. Hershey & Elliott N. Weiss & Morris A. Cohen, 1981. "A Stochastic Service Network Model with Application to Hospital Facilities," Operations Research, INFORMS, vol. 29(1), pages 1-22, February.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:1:p:1-22
    DOI: 10.1287/opre.29.1.1
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    Citations

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    Cited by:

    1. Hideaki Takagi & Yuta Kanai & Kazuo Misue, 2017. "Queueing network model for obstetric patient flow in a hospital," Health Care Management Science, Springer, vol. 20(3), pages 433-451, September.
    2. Peter Hulshof & Richard Boucherie & Erwin Hans & Johann Hurink, 2013. "Tactical resource allocation and elective patient admission planning in care processes," Health Care Management Science, Springer, vol. 16(2), pages 152-166, June.
    3. Lixiang Jiang & Ronald Giachetti, 2008. "A queueing network model to analyze the impact of parallelization of care on patient cycle time," Health Care Management Science, Springer, vol. 11(3), pages 248-261, September.
    4. Natalia Yankovic & Linda V. Green, 2011. "Identifying Good Nursing Levels: A Queuing Approach," Operations Research, INFORMS, vol. 59(4), pages 942-955, August.
    5. Yuta Kanai & Hideaki Takagi, 2021. "Markov chain analysis for the neonatal inpatient flow in a hospital," Health Care Management Science, Springer, vol. 24(1), pages 92-116, March.
    6. Golmohammadi, Davood & Zhao, Lingyu & Dreyfus, David, 2023. "Using machine learning techniques to reduce uncertainty for outpatient appointment scheduling practices in outpatient clinics," Omega, Elsevier, vol. 120(C).
    7. Cote, Murray J., 1999. "Patient flow and resource utilization in an outpatient clinic," Socio-Economic Planning Sciences, Elsevier, vol. 33(3), pages 231-245, September.
    8. Lapierre, Sophie D. & Goldsman, David & Cochran, Roger & DuBow, Janice, 1999. "Bed allocation techniques based on census data," Socio-Economic Planning Sciences, Elsevier, vol. 33(1), pages 25-38, March.
    9. Peter Williams & Guangfu Tai & Yiming Lei, 2010. "Simulation based analysis of patient arrival to health care systems and evaluation of an operations improvement scheme," Annals of Operations Research, Springer, vol. 178(1), pages 263-279, July.
    10. Saied Samiedaluie & Vedat Verter, 2019. "The impact of specialization of hospitals on patient access to care; a queuing analysis with an application to a neurological hospital," Health Care Management Science, Springer, vol. 22(4), pages 709-726, December.
    11. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.

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