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Optimal Hysteretic Control for the BMAP/G/ 1 System with Single and Group Service Modes

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  • Alexander Dudin
  • Srinivas Chakravarthy

Abstract

In this paper, we consider a single server queuing model with an infinite buffer in which customers arrive according to a batch Markovian arrival process (BMAP). The services are offered in two modes. In mode 1, the customers are served one at a time and in mode 2 customers are served in groups of varying sizes. Various costs for holding, service and switching are imposed. For a given hysteretic strategy, we derive an expression for the cost function from which an optimal hysteretic control can be obtained. Illustrative numerical examples are presented. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Alexander Dudin & Srinivas Chakravarthy, 2002. "Optimal Hysteretic Control for the BMAP/G/ 1 System with Single and Group Service Modes," Annals of Operations Research, Springer, vol. 112(1), pages 153-169, April.
    • Handle: RePEc:spr:annopr:v:112:y:2002:i:1:p:153-169:10.1023/a:1020985106453
    DOI: 10.1023/A:1020985106453
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    Cited by:

    1. K. Sikdar & S. K. Samanta, 2016. "Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 553-583, September.
    2. Jewgeni H. Dshalalow & Ahmed Merie & Ryan T. White, 2020. "Fluctuation Analysis in Parallel Queues with Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 295-327, March.
    3. Che Kim & Valentina Klimenok & Alexander Birukov & Alexander Dudin, 2006. "Optimal multi-threshold control by the BMAP/SM/1 retrial system," Annals of Operations Research, Springer, vol. 141(1), pages 193-210, January.

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