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The single server retrial queue with finite population: a BSDE approach

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Abstract

This paper uses the block-structured state-dependent event (BSDE) approach to generalize the scalar version of the single server retrial queue with finite population. The simple scalar version only involves exponential random variables, which make the underlying Markov chain tractable. However, this is a drawback in applications where the exponentiality is not a realistic assumption and the flows are correlated. The BSDE approach provides a versatile tool to deal with a non-exponential model with correlated flows, but keeping tractable the dimensionality of the block-structured Markov chain. We focus on the investigation of the limiting distribution of the system state and the waiting time. The theory is illustrated by numerical experiments, which demonstrate that the proposed BSDE approach can be applied efficiently.

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Acknowledgments

The authors are grateful to the two referees for their constructive comments and suggestions. This work was supported by the Government of Spain (Ministry of Science and Innovation) and the European Commission through project MTM 2008-01121.

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Authors and Affiliations

  1. Faculty of Mathematics, Department of Statistics and Operations Research, Complutense University of Madrid, 28040, Madrid, Spain

    J. R. Artalejo

  2. School of Statistics, Complutense University of Madrid, 28040, Madrid, Spain

    M. J. Lopez-Herrero

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  1. J. R. Artalejo
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  2. M. J. Lopez-Herrero
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Correspondence to J. R. Artalejo.

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Artalejo, J.R., Lopez-Herrero, M.J. The single server retrial queue with finite population: a BSDE approach. Oper Res Int J 12, 109–131 (2012). https://doi.org/10.1007/s12351-011-0104-8

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  • DOI: https://doi.org/10.1007/s12351-011-0104-8

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