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Approximate, Closed Form Moment Formulas for Bulk Arrival, Bulk Service Queues

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  • Warren B. Powell

    (Princeton University, Princeton, New Jersey)

Abstract

Traditional analysis of bulk queues has relied on classical transform methods, which requires the determination of the complex zeroes of a given function, or iterative numerical techniques. In this research, transform results are used to help find approximate closed form expressions for the mean and variance of the length of the queue at departure instants. The moments of the length of the queue in continuous time and of the waiting time distribution are derived in closed form as a function of the new formulas. An approximate method for fitting a distribution for the length of the queue is provided and used to calculate the probability a customer will leave on a given outbound vehicle. Finally, approximate queueing and delay formulas are developed for bulk queues operating under a vehicle cancellation policy.

Suggested Citation

  • Warren B. Powell, 1986. "Approximate, Closed Form Moment Formulas for Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 20(1), pages 13-23, February.
    • Handle: RePEc:inm:ortrsc:v:20:y:1986:i:1:p:13-23
    DOI: 10.1287/trsc.20.1.13
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    Cited by:

    1. Hall, Randolph W. & Sabnani, Vikas C., 2002. "Control of vehicle dispatching on a cyclic route serving trucking terminals," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(3), pages 257-276, March.
    2. E. Codina & A. Marín & F. López, 2013. "A model for setting services on auxiliary bus lines under congestion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 48-83, April.
    3. Justus Arne Schwarz & Martin Epp, 2016. "Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6251-6264, October.
    4. Seok Ho Chang & Dae Won Choi, 2006. "Modeling and Performance Analysis of a Finite-Buffer Queue with Batch Arrivals, Batch Services, and Setup Times: The M X /G Y /1/K + B Queue with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 218-228, May.

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