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The Effect of Operation Time of the Server on the Performance of Finite-Source Retrial Queues with Two-Way Communications to the Orbit

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In this paper a retrial queuing system is considered with the help of two-way communication where the server is subject to random breakdowns. This is a M/M/1//N type of system so the population of the source is finite. The server becoming idle enables calls the customers in the orbit (outgoing call or secondary customers). The service time of the primary and secondary customers follows exponential distribution with different rates μ1 and μ2 respectively. All the random variables included in the model construction are assumed to be totally independent of each other. The novelty of this paper is to show the effect of the different distributions of failure time on the main performance measures such as the mean waiting time of an arbitrary customer or the utilization of the service unit. In order to achieve a valid comparison a fitting process is done; thus, in case of every distribution the mean value and dispersion is the same. Graphical illustrations are given with the help of the self-developed simulation program.

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Correspondence to J. Sztrik.

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Proceedings of the XXXVI International Seminar on Stability Problems for Stochastic Models, Petrozavodsk, Russia, 22–26 June, 2020. Part I.

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Sztrik, J., Tóth, Á., Pintér, Á. et al. The Effect of Operation Time of the Server on the Performance of Finite-Source Retrial Queues with Two-Way Communications to the Orbit. J Math Sci 267, 196–204 (2022).

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