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Waiting‐time distributions for bulk arrival, bulk service queues with vehicle‐holding and cancellation strategies

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  • Warren B. Powell

Abstract

Procedures are developed for numerically calculating the waiting‐time distribution for bulk arrival, bulk service queues operated under a vehicle‐cancellation or a vehicle‐holding strategy, as well as for queues where vehicles depart regardless of the length of the queue. Experiments indicate that the mean and variance of the calculated distribution agree very closely with analytical expressions obtained from transforms. The results can be used to study the service reliability of different dispatching strategies. Alternatively, the results may be used to evaluate simpler approximations for the higher moments.

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  • 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.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:2:p:207-227
    DOI: 10.1002/1520-6750(198704)34:23.0.CO;2-C
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    References listed on IDEAS

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    1. Warren B. Powell & Pierre Humblet, 1986. "The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure," Operations Research, INFORMS, vol. 34(2), pages 267-275, April.
    2. Marcel F. Neuts & R. Nadarajan, 1982. "A Multiserver Queue with Thresholds for the Acceptance of Customers into Service," Operations Research, INFORMS, vol. 30(5), pages 948-960, October.
    3. W. K. Grassmann & M. L. Chaudhry, 1982. "A new method to solve steady state queueing equations," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(3), pages 461-473, September.
    4. J. Medhi, 1975. "Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule," Management Science, INFORMS, vol. 21(7), pages 777-782, March.
    5. Warren B. Powell, 1985. "Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 19(4), pages 352-377, November.
    6. 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.
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