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Waiting time distributions for transient bulk queues with general vehicle dispatching strategies

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  • Hugo P. Simão
  • Warren B. Powell

Abstract

A numerical approach is presented for determining the waiting time distribution in a transient bulk‐arrival, bulk‐service queue. Vehicle departures from the queue are governed by a general dispatch strategy that includes holding with a variable release function and vehicle cancellations. The waiting time distribution of a customer (in a group) arriving at a given point in time is calculated by simulating the process in discrete time and determining at each step the probability the customer has left the system. The dispatch strategies require knowing the total length of the queue as well as the position a customer holds in the queue. An exact approach is compared to an accurate approximation which is 50 to 100 times faster. Comparisons are made with other approaches in the context of steady‐state systems.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:2:p:285-306
    DOI: 10.1002/1520-6750(198804)35:23.0.CO;2-V
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    References listed on IDEAS

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    1. Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis I," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 297-304, June.
    2. Eugene M. Klimko & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis II," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 305-319, June.
    3. 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.
    4. David Heimann & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis IV," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(4), pages 753-766, December.
    5. Marcel F. Neuts & Eugene Klimko, 1973. "The single server queue in discrete time‐numerical analysis III," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(3), pages 557-567, September.
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