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A Multiserver Retrial Queueing System with Batch Markov Arrival Process

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Abstract

A sufficient condition for a BMAP/M/N system to have a stationary state probability distribution and an algorithm for computing this distribution are investigated.

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REFERENCES

  1. Combèe, M., Queueing Models with Dependence Structures, Amsterdam: CWI, 1994.

    Google Scholar 

  2. Lucantoni, D.M., New Results on the Single-Server Queue with a Batch Markovian Arrival Process, Commun. Statist. Stoch. Models, 1991, vol. 7, pp. 1-46.

    Google Scholar 

  3. Neuts, M. and Lucantoni, D., Some Steady-State Distribution for the MAP/SM/1 Queue, Commun. Statist. Stoch. Models, 1994, vol. 10, pp. 575-598.

    Google Scholar 

  4. Bocharov, P.P., Pechinkin, A.V., and Phong, N.K., Steady-State Probabilities of the BMAP/G/1/r Retrial System with Preemptive Service of Primary Calls, Avtom. Telemekh., 2000, no. 8, pp. 68-78.

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

    Google Scholar 

  6. Pechinkin, A.V., A Queueing System with Markov Arrival Process and Random Choice of Customers from Queue for Service, Avtom. Telemekh., 2000, no. 9, pp. 90-96.

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

    Google Scholar 

  8. Kulkarni, V.G. and Liang, H.M., Retrial Queues Revisited, in: Frontiers in Queueing: Models and Applications in Science and Engineering, Boca Raton: CRC Press, 1997, pp. 19-34.

    Google Scholar 

  9. Artalejo, J.R., Accessible Bibliography on Retrial Queues, Math. Comput. Model, 1999, vol. 30, pp. 223-233.

    Google Scholar 

  10. Diamond, J.E. and Alfa, A.S., The MAP/PH/1 Retrial Queue, Commun. Statist. Stoch. Models, 1998, vol. 14, pp. 1151-1177.

    Google Scholar 

  11. Choi, B.D. and Chang, Y., MAP 1 , MAP 2 /M/C Retrial Queue with Retrial Group of Finite Capacity and Geometric Loss, Math. Comput. Model, 1999, vol. 30, pp. 99-114.

    Google Scholar 

  12. Dudin, A.N. and Klimenok, V.I., Queueing System BMAP/G/1 with Repeated Calls, Math. Comput. Model, 1999, vol. 30, pp. 115-128.

    Google Scholar 

  13. Dudin, A.N. and Klimenok, V.I., A Retrial BMAP/SM/1 System with Linear Repeated Requests, Queueing Systems, 2000, vol. 34, pp. 47-66.

    Google Scholar 

  14. Dudin, A.N. and Klimenok, V.I., BMAP/SM/1 Model with Markov Modulated Retrials, TOP, 1999, vol. 7, pp. 267-278.

    Google Scholar 

  15. Dudin, A.N. and Klimenok, V.I., Sistemy massovogo obsluzhivaniya s korrelirovannymi potokami (Queue Systems with Correlated Inputs), Minsk: Belaruss. Gos. Univ., 2000.

    Google Scholar 

  16. Stepanov, S.N., Chislennye metody rascheta sistem s povtornymi vyzovami (Numerical Methods of Computing Retrial Systems), Moscow: Nauka, 1983.

    Google Scholar 

  17. Neuts, M. and Rao, B., Numerical Investigation of a Multiserver Retrial Model, Queueing Systems, 1990, vol. 7, pp. 169-189.

    Google Scholar 

  18. Diamond, J.E. and Alfa, A.S., Matrix Analytic Methods for a Multiserver Retrial Queue with Buffer, TOP, 1999, vol. 7, pp. 249-266.

    Google Scholar 

  19. Lucantoni, D.M. and Ramaswami, V., An Efficient Algorithm for Solving Nonlinear Matrix Equations arising in Phase-Type Queues, Commun. Statist. Stoch. Models, 1985, vol. 1, pp. 29-51.

    Google Scholar 

  20. Dudin, A.N. and Klimenok, V.I., Multidimensional Quasitoeplitz Markov Chains, J. Appl. Math. Stoch. Anal., 1999, vol. 12, pp. 393-415.

    Google Scholar 

  21. Neuts, M., Structured Stochastic Matrices of M/G/1 Type and Their Applications, New York: Marcel Dekker, 1989.

    Google Scholar 

  22. Gail, H., Hantler, S., and Taylor B., Spectral Analysis of M/G/1 and G/M/1 Type Markov Chains, Adv. Appl. Probab., 1996, vol. 28, pp. 114-165.

    Google Scholar 

  23. Klimenok, V.I., A Condition for the Existence of a Steady-State in Queue Systems with Markov Arrivals and Retrials, Vesti Natsion. Akad. Nauk Belaruss., 2000, no. 3, pp. 128-132.

  24. Bellman, R.E., Introduction to Matrix Analysis, New York: McGraw Hill, 1960. Translated under the title Vvedenie v teoriyu matrits, Moscow: Nauka, 1969.

    Google Scholar 

  25. Dudin, A.N. and Klimenok, V.I., A Queueing System Operating in a Markov Synchronized Random Medium: Computation of Its Characteristics, Avtom. Telemekh., 1997, no. 1, pp. 74-84.

  26. Kemeni, J., Shell, J., and Knapp, A., Denumerable Markov Chains, New York: Van Nostrand, 1966.

    Google Scholar 

  27. Dudin, A.N., Klimenok, V.I., Klimenok, I.A., et al., Software “SIRIUS+” for Evaluation and Optimization of Queues with BMAP-input, in: Matrix-Analytic Methods in Stochastic Models, New Jersey: Notable Publications, 2000, pp. 115-133.

    Google Scholar 

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  1. Belarussian State University, Minsk, Belarus

    V. I. Klimenok

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Klimenok, V.I. A Multiserver Retrial Queueing System with Batch Markov Arrival Process. Automation and Remote Control 62, 1312–1322 (2001). https://doi.org/10.1023/A:1010209729624

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