A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times

It is well known that discrete-time queues are more appropriate than their continuous-time counterparts for modelling computer and telecommunication systems. This paper is concerned with a discrete-time Geo/G/1 retrial queue with general retrial times, Bernoulli feedback and the server subjected to starting failures. In this paper, we generalize the previous works in discrete-time retrial queue with unreliable server due to starting failures in the sense that we consider general service with Bernoulli feedback and general retrial times. We analyse the Markov chain underlying the considered queueing system and present some performance measures of the system in steady-state. We provide two stochastic decomposition laws and as application we give bounds for the distance between the system size distribution of our model and the corresponding model without retrials. Besides, some numerical results are given to illustrate the impact of the unreliability and the feedback on the performance of the system. We also investigate the relation between our discrete-time system and its continuous counterpart.