HEAVY TRAFFIC ANALYSIS OF A MARKOV-MODULATED QUEUE WITH FINITE-CAPACITY AND GENERAL SERVICE TIMES

We consider a set of N independent sources, each of which alternates b etween ''on'' and ''off'' states. When a source is on, it generates a Poisson arrival stream to a finite-capacity queue with a general serve r. We derive the balance equations satisfied by the joint steady-state distribution of the queue length and the number of ''on'' sources. Th en we analyze the problem in the heavy traffic limit where N --> infin ity and the average arrival rate is nearly equal to the mean service r ate. The capacity is scaled to be O(root N). The first two terms in th e asymptotic series are characterized as solutions to elliptic partial differential equations (PDEs) with appropriate boundary conditions. W e then develop numerical and asymptotic methods for solving these PDEs . The analysis makes use of singular perturbation techniques and speci al functions.