Two queues in tandem with retrial customers (Q2748550)

This paper deals with two single server queues (nodes) in tandem, in which customers to the first node arrive according to a Poisson process. The service times at the two nodes are independent and arbitrarily distributed random variables. There is no waiting position between the two nodes. At the time of service completion at node one, if the second node is busy, the first node gets blocked until the second node is empty. After completion of service at the second node the customer departs from the system. Further, the arriving customers who find the first node busy or blocked, behave like retrial customers. They join a (hypothetical) retrial queue of infinite capacity. The `constant retrial policy', in which the total retrial intensity is constant, is assumed. If node one is free at the time of the attempt, then the customer receives service immediately. Otherwise the demand is repeated later. For this model, using Markov renewal techniques, the generating function of the steady state probability distribution of the number of persons in the retrial group and other operating characteristics are obtained. Results for the model without retrials are deduced. A numerical illustration of the results for the special case of exponential service times is also provided.