Analysis of M/M/1 queueing system with two priority classes

The present paper investigates the two-class priority M/M/1 queueing system, where the prioritized first class customers are served under first-come, first served (FCFS) preemptive resume discipline and have finite room capacity. The second class customers have infinite waiting space and low priority i.e. during the service of a low priority customer, if a high priority customer joins the system, then the low priority customer's service is interrupted and will be resumed again when there is no high priority customer present in the system. Our aim is to get explicit expressions for the generating functions of the steady state probabilities in terms of Chebyshev's polynomial of second kind have obtained. A recursive method is employed to solve the steady-state equations governing the model. Moreover, the expressions for the mean queue length, the marginal distributions of high and low priority customers are also given. The derivation is based only on the general structure of the system and the generating function involved, and thus is simpler than previous methods. We examine the effect of number of high priority customers, input and output rates on the average queue lengths of low and high priority classes by looking at a numerical illustration.