An unreliable single server retrial queue with collisions and transmission errors

Lamia Lakaour, Djamil Aissani, Karima Adel-Aissanou, Kamel Barkaoui and Sofiane Ziani

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 4, 1085-1109

Abstract: The present paper deals with the performance evaluation of an M/M/1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that have dealt with retrial queues by considering all the above-mentioned aspects (collisions, transmission errors and unreliable server). This queue can be used as a mathematical model of several computer systems and telecommunication networks. We apply the generating function method to derive the joint distribution of the server state and the orbit length in the steady state, and we obtain some performance measures. Finally, we provide numerical illustrations to show the effectiveness and the applicability of the model.

Date: 2022
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DOI: 10.1080/03610926.2020.1758943

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