Asymptotic Analysis of a Queueing Model With Bursty Traffic

Many models of queueing systems assume that arrivals occur according to a Poisson process. Intuitively, the Poisson process may be characterized by the properties that events occur one at a time and do not depend on the past history of events. Typically, this situation arises when there are large numbers of users of a system, as in the case of arrivals of calls to a central office, since one arrival does not significantly affect the probability of another. Fortunately, these models are often mathematically tractable. For other systems the Poisson assumptions are not realistic. Often arrivals are indicative of overall activity and give information about the probability of future arrivals. For example, suppose that all arrivals * Bell Laboratories, Holmdel, N.J. ·"Copyright 1983, American Telephone & Telegraph Company. Copying in printed form for private use is permitted without payment of royalty provided that each reproduction is done without alteration and that the Journal reference and copyright notice are included on the first page. The title and abstract, but no other portions, of this paper may be copied or distributed royalty free by computer-based and other informationservice systems without further permission. Permission to reproduce or republish any other portion of this paper must be obtained from the Editor.