Analysis of a discrete-time queue with general three-state Markovian traffic sources

In this paper, we analyze the performance characteristics of an ATM switch, where cell arrivals are generated according to a three-state Markovian arrival law. This arrival process is an extension for the two-state ON/OFF source model that has already been extensively treated in the literature, and it allows a much more flexible modeling of a wide variety of VBR sources. As a result, for the finite storage capacity case, the system contents distribution, as well as the cell loss ratio are derived. On the other hand, for the infinite storage capacity case, a method for deriving an expression for the probability generating function of the system contents is presented. Furthermore, an approximation (consisting of multiple geometric terms) for the tail distribution of the system contents is given. The accuracy of this approximation as well as the impact of the traffic parameters on the buffer behavior are discussed via some numerical examples.