Stability analysis of a multiclass retrial system with classical retrial policy

Abstract

We consider a multiserver retrial queueing system with a renewal input, K classes of customers, and a finite buffer. Service times are class-dependent, however, for each class, are independent, identically distributed (iid). A new class-i customer joins the primary system (servers and buffer), otherwise, if all servers and buffer are full, he joins the class-i (virtual) orbit, and attempts to enter the system after an exponentially distributed time with rate γi,i=1,…,K. The retrial discipline is classical because the attempts of different orbital (blocked) customers are independent. We exploit the regenerative structure of the (non-Markovian) queue-size process (total number of customers in the primary system and in orbits) to develop the stability analysis. First we establish the necessary stability conditions, and then show that these conditions are sufficient for stability as well. These conditions coincide with the known stability conditions of a conventional multiclass multiserver system with infinite buffer. Our analysis covers also the model in which, when a server is free, it makes an outgoing call which occupies the server for a server-dependent random time. Also we extend the stability analysis to the retrial system with a feedback when a served customer returns to the corresponding orbit with a positive probability.