An unreliable single server retrial queue with collisions and transmission errors

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.

Keywords:

• Retrial queue
• collisions
• transmission errors
• unreliable server
• generating function

Acknowledgement

The authors would like to thank the referees for valuable comments and constructive suggestions that help to improve the presentation of the paper.