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Iterative Algorithms for Bulk Arrival, Bulk Service Queues with Poisson and Non-Poisson Arrivals

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  • Warren B. Powell

    (Princeton University, Princeton, New Jersey)

Abstract

Iterative numerical procedures are investigated for the study of queue lengths and waiting times in bulk arrival, bulk service queues. For queues with compound Poisson arrivals, the procedure uses the imbedded Markov chain to study a variety of vehicle dispatching strategies. The technique is easy to implement, numerically stable and, for most problems that arise in transportation, computationally faster than other approaches that have been proposed. For queues with non-Poisson arrivals, an iterative scheme is devised for calculating a discretized form of the waiting time distribution using the concept of unfinished work. Numerical experiments with different discretization strategies indicate that a high level of accuracy can be attained at a very moderate cost.

Suggested Citation

  • Warren B. Powell, 1986. "Iterative Algorithms for Bulk Arrival, Bulk Service Queues with Poisson and Non-Poisson Arrivals," Transportation Science, INFORMS, vol. 20(2), pages 65-79, May.
    • Handle: RePEc:inm:ortrsc:v:20:y:1986:i:2:p:65-79
    DOI: 10.1287/trsc.20.2.65
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    Cited by:

    1. Warren B. Powell, 1987. "Waiting‐time distributions for bulk arrival, bulk service queues with vehicle‐holding and cancellation strategies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 207-227, April.
    2. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "Acceptance and Dispatching Policies for a Distribution Problem," Transportation Science, INFORMS, vol. 32(2), pages 127-141, May.
    3. Hugo P. Simão & Warren B. Powell, 1988. "Waiting time distributions for transient bulk queues with general vehicle dispatching strategies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 285-306, April.
    4. 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.

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