Abstract
In this paper retrial queuing systems with a finite number of sources and collisions of the customers is considered, where the server is subjects to random breakdowns and repairs depending on whether it is idle or busy. The novelty of this system comparing to the previous ones is that the service time is assumed to follow a general distribution while the source times, retrial times, servers lifetime and repair time are supposed to be exponentially distributed. A new numerical algorithm for finding the joint probability distribution of the number of customers in the system and the server’s state is proposed. Several numerical examples and Figures show the effect of different input parameters on the main steady state performance measures, such as mean response and waiting time of the customers, probability of collision and retrials.
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Acknowledgments
The work/publication of J. Sztrik is supported by the EFOP-3.6.1-16-2016-00022 project. The project is co-financed by the European Union and the European Social Fund.
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Nazarov, A., Sztrik, J., Kvach, A., Kuki, A. (2019). An Algorithmic Approach for the Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_2
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