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A single-server finite-capacity queueing system with Markov flow and discrete-time service

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Concepts of a discrete Markov flow and discrete-time Markov service are defined. A single-server finite-capacity queueing system with Markov flow and discrete-time service is studied. An algorithm for computing the stationary state probability distribution of the system is designed. The main performance characteristics, such as the stationary loss probability and mean waiting time for service, are determined.

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  1. Ramaswami, V. and Wang, J.L., Discrete-Time Queueing Analysis of ATM Systems with Phase-Type Distributed Talk Spurts Traffic Sources, IEEE Global Telecom. Conf., 1996, no. 1, pp. 623–628.

  2. Rubin, I. and Tsai, Z.-H., Message Delay Analysis of Multiclass Priority TDMA, FDMA, and Discrete-Time Queueing Systems, IEEE Trans. Inform. Theory, 1989, vol. 35, pp. 637–647.

    Google Scholar 

  3. McKinnon, M., Perros, H., and Rouskas, G., Performance Analysis of Broadcast WDM Networks under IP Traffic, Performance Evaluation, 1999, nos. 36–37, pp. 333–358.

  4. Saito, H., Performance Evaluation and Dimensioning for AAL2 CLAD, Proc. IEEE INFOCOM, 1999, no. 1, pp. 153–160.

  5. Blondia, C., A Discrete-Time Batch Markovian Arrival Process as B-ISDN Traffic Model, Belgian J. Oper. Res., Statist. Comput. Sci., 1993, vol. 32(3, 4), pp. 3–23.

    Google Scholar 

  6. Lucantoni, D., New Results for the Single-Server Queue with a Batch Markovian Arrival Process, Stochastic Models, 1991, vol. 7, pp. 1–46.

    Google Scholar 

  7. Neuts, M., A Versatile Markovian Arrival Process, J. Appl. Prob., 1979, vol. 16, pp. 764–779.

    Google Scholar 

  8. Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.

    Google Scholar 

  9. Basharin, G.P. and Efimushkin, V.A., A Discrete-Time Single-Server System with Customers of Several Types, Probl. Peredachi Inf., 1984, vol. 20, no. 1, pp. 95–104.

    Google Scholar 

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

    Google Scholar 

  11. Bocharov, P.P. and Litvin, V.G., Analysis Methods for Queueing Systems with Phase-Type Distributions, Avtom. Telemekh., 1986, no. 5, pp. 5–23.

  12. Bocharov, P.P., Stationary Distribution of a Finite Queue with Recurrent Flow and Markov Service, Avtom. Telemekh., 1996, no. 9, pp. 66–78.

  13. Bocharov, P.P., D’Apice, C., Pechinkin, A.V., and Salerno, S., Queueing Theory, Boston: VSP, 2004.

    Google Scholar 

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Translated from Avtomatika i Telemekhanika, No. 2, 2005, pp. 73–91.

Original Russian Text Copyright © 2005 by Bocharov, Viskova.

This work was supported in part by the Russian Foundation for Basic Research, project no. 02-07-90147.

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Bocharov, P.P., Viskova, E.V. A single-server finite-capacity queueing system with Markov flow and discrete-time service. Autom Remote Control 66, 233–248 (2005).

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