A Discrete Time Retrial Queue with Retrial Due to Server Failures

We considered an unreliable Geo/Geo/1 retrial queue with infinite-capacity orbit and normal queue. In this model it is assume that if the server subjected to starting failures and breakdown during services of a customer, the customer leaves the server, joins a retrial group and repeatedly attempts to access the server in random intervals to get service. We study the Markov chain underlying the considered queuing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.