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The MAP/M/N retrial queueing system with time-phased batch arrivals

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Abstract

We consider a retrial queueing system with batch arrival of customers. Unlike standard batch arrival, where a whole batch enters the system simultaneously, we assume that customers of a batch (session) arrive one by one in exponentially distributed time intervals. Service time is exponentially distributed. The batch arrival flow is MAP. The number of customers in a session is geometrically distributed. The number of sessions that can enter the system simultaneously is a control parameter. We analyze the joint probability distribution of the number of sessions and customers in the system using the techniques of multidimensional asymptotically quasi-Toeplitz Markov chains.

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References

  1. Kist, A.A., Lloyd-Smith, B., and Harris, R.J., A Simple IP Flow Blocking Model, in Proc. 19th Int. Teletraffic Congress (ITC’19), Beijing, China, 2005, pp. 355–364.

  2. Lee, M.H., Dudin, S., and Klimenok, V., Queueing Model with Time-Phased Batch Arrivals, Managing Traffic Performance in Converged Networks: Proc. 20th Int. Teletraffic Congress (ITC’20), Ottawa, Canada, 2007, Mason, L., Drwięga, T., and Yan, J., Eds., Lect. Notes Comp. Sci., vol. 4516, Berlin: Springer, 2007, pp. 719–730.

    Google Scholar 

  3. Kim, C.S., Dudin, S., and Klimenok, V., The MAP/PH/1/N Queue with Flows of Customers as a Model for Traffic Control in Telecommunication Networks, Perform. Eval., 2009, vol. 66, no. 9–10, pp. 564–579.

    Article  Google Scholar 

  4. Artalejo, J.R., Accessible Bibliography on Retrial Queues, Math. Comput. Model., 1999, vol. 30, no. 3–4, pp. 1–6.

    Article  Google Scholar 

  5. Artalejo, J.R., A Classified Bibliography of Research on Retrial Queues: Progress in 1990–1999, Proc. 1st Int. Workshopon Retrial Queues (WRQ’98), Complutense Univ. of Madrid, Spain, 1998, Artalejo, J.R., Ed., Top, 1999, vol. 7, no. 2, pp. 187–211.

  6. Gómez-Corral, A., A Bibliographical Guide to the Analysis of Retrial Queues through Matrix Analytic Techniques, Ann. Oper. Res., 2006, vol. 141, pp. 163–191.

    Article  MATH  MathSciNet  Google Scholar 

  7. Falin, G.I. and Templeton, J.G.C., Retrial Queues, London: Chapman & Hall, 1997.

    MATH  Google Scholar 

  8. Artalejo, J.R. and Gómez-Corral, A., Retrial Queueing Systems: A Computational Approach, Berlin: Springer, 2008.

    MATH  Google Scholar 

  9. Dudin, S. and Babitsky, A., Retrial Queueing Model with Time-Phased Batch Arrivals, Selected Lectures on Multiple Access and Queueing Systems: Int. Workshop on Multiple Access Communications (MACOM-2008), St.-Petersburg, Russia, 2008, Vishnevsky, V., Vinel, A., Koucheryavy, E., and Staehle, D., Eds., pp. 100–107.

  10. Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Baltimore: Johns Hopkins Univ. Press, 1981.

    MATH  Google Scholar 

  11. Klimenok, V.I. and Dudin, A.N., Multi-Dimensional Asymptotically Quasi-Toeplitz Markov Chains and Their Application in Queueing Theory, Queueing Syst., 2006, vol. 54, no. 4, pp. 245–259.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Belarusian State University, Minsk, Russia

    S. A. Dudin

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  1. S. A. Dudin
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Correspondence to S. A. Dudin.

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Original Russian Text © S.A. Dudin, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 3, pp. 85–97.

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Dudin, S.A. The MAP/M/N retrial queueing system with time-phased batch arrivals. Probl Inf Transm 45, 270–281 (2009). https://doi.org/10.1134/S0032946009030089

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  • DOI: https://doi.org/10.1134/S0032946009030089

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