An M/G/1 two phase multi‐optional retrial queue with Bernoulli feedback, non‐persistent customers and breakdown and repair

This paper has been motivated by the interactive voice response system (IVRS). This system has now become a common phenomenon in our everyday life. In this paper, we consider a Poisson arrival queueing system with a single server and two essential phases of heterogeneous service. The customer who completes the first phase has a choice of k‐options to choose for the second phase of service. The customer, who finds the server busy upon arrival, can either join the orbit or he/she can leave the system. After completion of both phases, the customer can decide to try again for service by joining the orbit or he/she can leave the system. The server is subject to sudden breakdowns and repairs. We assume that the breakdowns of the system can occur even when the system is idle. By using the supplementary variables technique, we have obtained the steady state probability generating functions of the orbit size and the system size. We obtain a stochastic decomposition law for the system. We present numerical results to illustrate the sensitivity of the system. We obtain some useful performance measures of the system.