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Numerical Analysis of Non-Reliable Retrial Queueing Systems with Collision and Blocking of Customers

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The aim of the investigation is a closed retrial queueing system with a finite source. The server can be reached from the source (primary request) or from the orbit (secondary request). If an incoming (primary or secondary) job finds the server busy, two modes are distinguished: the job is transferred to the orbit (no collision) or the job under service is interrupted and both of them are transferred to the orbit (collision). Requests in the orbit can retry reaching the server after a random waiting time. The nonreliable case when the server is subject to breakdown is also investigated. In case of breakdown, when the server is under repair, also two cases can be investigated. For the first, primary calls from the source can reach the system, and they will be sent to the orbit. For the second, the source is blocked, so primary customers are not able to step into the system. This paper focuses on the unreliable system with collision and blocking of parameters. These types of systems can be solved by numerical, asymptotical, and simulation methods. Our goal is to provide a new approach to the algorithmic solution for calculating the steady-state probabilities of the system. Using these quantities the main performance characteristics (utilization of the server, response time, etc.) can be calculated. Examples illustrate the effect of different parameters on the distribution of requests in the system.

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Correspondence to A. Kuki.

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

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Kuki, A., Sztrik, J., Bérczes, T. et al. Numerical Analysis of Non-Reliable Retrial Queueing Systems with Collision and Blocking of Customers. J Math Sci 248, 1–13 (2020).

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