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Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

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  • Dieter Claeys
  • Koenraad Laevens
  • Joris Walraevens
  • Herwig Bruneel

Abstract

Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation—i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay. Copyright Springer-Verlag 2010

Suggested Citation

  • Dieter Claeys & Koenraad Laevens & Joris Walraevens & Herwig Bruneel, 2010. "Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 1-23, August.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:1:p:1-23
    DOI: 10.1007/s00186-009-0297-2
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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. Yi, Xeung W. & Kim, Nam K. & Yoon, Bong K. & Chae, Kyung C., 2007. "Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue," European Journal of Operational Research, Elsevier, vol. 181(2), pages 787-792, September.
    3. Bruneel, Herwig & Steyaert, Bart & Desmet, Emmanuel & Petit, Guido H., 1994. "Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues," European Journal of Operational Research, Elsevier, vol. 76(3), pages 563-572, August.
    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.
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    Cited by:

    1. H. Bruneel & W. Rogiest & J. Walraevens & S. Wittevrongel, 2015. "Analysis of a discrete-time queue with general independent arrivals, general service demands and fixed service capacity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 285-315, December.

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