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The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking

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This paper investigates, using a simulation program, a retrial queuing system with a single server which is subject to random breakdowns. The number of sources of calls is finite, and collisions can take place. We assume that the failure of the server blocks the system’s operation such that newly arriving customers cannot enter the system, contrary to an earlier paper where the failure does not affect the arrivals. All the random variables included in the model construction are assumed to be independent of each other, and all times are exponentially distributed except for the service time, which is gamma distributed. The novelty of this analysis is the inspection of the blocking effect on the performance measures using different distributions. Various figures represent the impact of the squared coefficient of the variation of the service time on the main performance measures such as the mean and variance of the number of customers in the system, the mean and variance of the response time, the mean and variance of the time a customer spends in the service, and the mean and variance of the sojourn time in the orbit.

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Authors and Affiliations

  1. University of Debrecen, Debrecen, Hungary

    A. Tóth, T. Bérczes, J. Sztrik & A. Kuki

  2. Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria

    W. Schreiner

Authors
  1. A. Tóth
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  2. T. Bérczes
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  3. J. Sztrik
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  4. A. Kuki
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  5. W. Schreiner
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Corresponding author

Correspondence to A. Tóth.

Additional information

Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.

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Tóth, A., Bérczes, T., Sztrik, J. et al. The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking. J Math Sci 246, 548–559 (2020). https://doi.org/10.1007/s10958-020-04759-4

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  • DOI: https://doi.org/10.1007/s10958-020-04759-4

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