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Queueing system with passive servers

Author

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  • Alexander N. Dudin
  • Valentina I. Klimenok

Abstract

In this paper the authors introduce systems in which customers are served by one active server and a group of passive servers. The calculation of response time for such systems is rendered by analyzing a special kind of queueing system in a synchronized random environment. For an embedded Markov chain, sufficient conditions for the existence of a stationary distribution are proved. A formula for the corresponding vector generating function is obtained. It is a matrix analog of the Pollaczek-Khinchin formula and is simultaneously a matrix functional equation. A method for solving this equation is proposed.

Suggested Citation

  • Alexander N. Dudin & Valentina I. Klimenok, 1996. "Queueing system with passive servers," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-20, January.
    • Handle: RePEc:hin:jnijsa:417476
    DOI: 10.1155/S1048953396000184
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    Cited by:

    1. Nitin Kumar & U. C. Gupta, 2020. "A Renewal Generated Geometric Catastrophe Model with Discrete-Time Markovian Arrival Process," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1293-1324, September.
    2. S. K. Samanta & M. L. Chaudhry & A. Pacheco, 2016. "Analysis of B M A P/M S P/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 419-440, June.

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