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On periodic phenomena and stationary distribution of queueing system M/G/1 with group arrivals and batch service

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Abstract

In this paper several models of queueing system M/G/1 with group arrivals and batch service are considered, and the following fundamental questions are considered: (1) what is the structure of the phase space of the imbedded Markov chain? (2) what are the necessary and sufficient conditions causing the imbedded Markov chain to be reducible or irreducible, and periodic or aperiodic? (3) what are the necessary and sufficient conditions of the existence of stationary distribution? The generating function of stationary distribution is obtained.

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References

  1. Bailey, N. T. J., On Queueing Processes with Bulk Service,J. Roy. Statist. Soc., Ser. B,16 (1954), 80–87.

    Google Scholar 

  2. Downton, F., Waiting Times in Bulk Service Queues,J. Roy. Statist Soc., Ser. B,17 (1955), 256–261.

    Google Scholar 

  3. Takács, L., Introduction to the Theory of Queues, Oxford University Press, New York, 1962.

    Google Scholar 

  4. Miller, R. G., A Contribution to the Theory of Bulk Queues,J. Roy. Statist. Soc., Ser. B,21 (1959), 320–337.

    Google Scholar 

  5. Cohen, J. W., The Single Server Queue, North-Holland Publishing Company-Amsterdam-New York-Oxford, Revised Edition, 1982.

  6. Sahbazov, A. A., A Service Problem with Unusual Demand, (Russian) Dokl. Akad. Nauk, SSSR,145 (1962), 289–292.

    Google Scholar 

  7. Teghem, J., Loris-Teghem, J., Lambotte, J. P., Modèles D'Attente M/G/1 et GI/M/1 à Arrivées et Services en Gpoupes, Springer-Verlag, Berlin-Heidelberg-New York, 1969.

    Google Scholar 

  8. Pedro Vit Cimas, On the Equivalence of Certain Markov Chains,J. Appl. Prob.,13 (1976), 357–360.

    Google Scholar 

  9. Pakes, A. G., Some Conditions for Ergodicity and Recurrence of Markov Chains,Operat. Res.,17 (1969), 1058–1061.

    Google Scholar 

  10. Chaudhry, M. L., Templeton, J. G. C., A First Course in Bulk Queues, A Wiley-Interscience Publication, John Wiley & Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1983.

    Google Scholar 

  11. Zhang Fuji, The Stationary Distribution of a Queueing System with Batch Arrivals,Knowledge Practice Math.,2 (1979), (in Chinese) (Math. Rev. 81. a. 60116).

  12. Wang Shasheng, Tu Fengsheng, Extension of Vandermonde Determinant and Its Applications to Theory of Control (Chinese),Acta Mathematica Scientia, Vol. 4, No. 3, (1984).

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Authors and Affiliations

  1. Xingjiang University, China

    Zhang Fuji

  2. Lanzhou University, China

    Chen Yongyi

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  1. Zhang Fuji
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  2. Chen Yongyi
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Zhang, F., Chen, Y. On periodic phenomena and stationary distribution of queueing system M/G/1 with group arrivals and batch service. Acta Mathematicae Applicatae Sinica 4, 207–222 (1988). https://doi.org/10.1007/BF02006218

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  • DOI: https://doi.org/10.1007/BF02006218

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