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Waiting Time In a Multi-Server Cutoff-Priority Queue, and Its Application to an Urban Ambulance Service

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  • I. D. S. Taylor

    (Ontario Ministry of Energy, Toronto, Canada)

  • J. G. C. Templeton

    (University of Toronto, Toronto, Canada)

Abstract

We consider a priority queue in steady state with N servers, two classes of customers, and a cutoff service discipline. Low priority arrivals are “cut off” (refused immediate service) and placed in a queue whenever N 1 or more servers are busy, in order to keep N − N 1 servers free for high priority arrivals. A Poisson arrival process for each class, and a common exponential service rate, are assumed. Two models are considered: one where high priority customers queue for service and one where they are lost if all servers are busy at an arrival epoch. Results are obtained for the probability of n servers busy, the expected low priority waiting time, and (in the case where high priority customers do not queue) the complete low priority waiting time distribution. The results are applied to determine the number of ambulances required in an urban fleet which serves both emergency calls and low priority patient transfers.

Suggested Citation

  • I. D. S. Taylor & J. G. C. Templeton, 1980. "Waiting Time In a Multi-Server Cutoff-Priority Queue, and Its Application to an Urban Ambulance Service," Operations Research, INFORMS, vol. 28(5), pages 1168-1188, October.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:5:p:1168-1188
    DOI: 10.1287/opre.28.5.1168
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    Cited by:

    1. Iannoni, Ana Paula & Chiyoshi, Fernando & Morabito, Reinaldo, 2015. "A spatially distributed queuing model considering dispatching policies with server reservation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 49-66.
    2. Marcos Singer & Patricio Donoso & Natalia Jadue, 2004. "Evaluacion De Las Oportunidades De Mejoramiento De La Logistica Directa De Emergencia," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 7(2), pages 179-209.
    3. Pazour, Jennifer A. & Roy, Debjit, 2012. "Minimizing Customer Waiting Costs for Rental Vehicle Providers using Threshold Reservation Policies," IIMA Working Papers WP2012-12-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    4. Diwakar Gupta & Lei Wang, 2008. "Revenue Management for a Primary-Care Clinic in the Presence of Patient Choice," Operations Research, INFORMS, vol. 56(3), pages 576-592, June.
    5. Soovin Yoon & Laura A. Albert, 2018. "An expected coverage model with a cutoff priority queue," Health Care Management Science, Springer, vol. 21(4), pages 517-533, December.
    6. Yoon, Soovin & Albert, Laura A., 2021. "Dynamic dispatch policies for emergency response with multiple types of vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    7. Krishnamoorthy, A. & Babu, S. & Narayanan, Viswanath C., 2009. "The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service," European Journal of Operational Research, Elsevier, vol. 195(1), pages 174-185, May.
    8. Wang, Qinan, 2004. "Modeling and analysis of high risk patient queues," European Journal of Operational Research, Elsevier, vol. 155(2), pages 502-515, June.
    9. de Souza, Regiane Máximo & Morabito, Reinaldo & Chiyoshi, Fernando Y. & Iannoni, Ana Paula, 2015. "Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil," European Journal of Operational Research, Elsevier, vol. 242(1), pages 274-285.

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