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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belorussia

    Alexander Dudin

  2. Department of Industrial and Manufacturing Engineering and Business, Kettering University, Flint, MI, USA

    Srinivas Chakravarthy

Authors
  1. Alexander Dudin
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  2. Srinivas Chakravarthy
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Dudin, A., Chakravarthy, S. Optimal Hysteretic Control for the BMAP/G/ 1 System with Single and Group Service Modes. Annals of Operations Research 112, 153–169 (2002). https://doi.org/10.1023/A:1020985106453

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