A transient discrete-time queueing analysis of the ATM multiplexer

In this paper, we present a transient discrete-time queueing analysis of the ATM multiplexer whose arrival process consists of the superposition of the traffic generated by independent binary Markov sources. The functional equation describing the ATM multiplexer has been transformed into a mathematically tractable form. This allows derivation of the transient probability generating functions of the queue length and the number of active sources in the system. Then, application of the final value theorem results in the corresponding steady-state probability generating functions, as well as packet delay. We also present closed form expressions for the transient and steady-state moments of the queue length. The pure transform approach used in the present analysis is an extension of the well-known classical method used in the transient analysis of single server queues with uncorrelated arrivals. As a result, the analysis is relatively easy to follow and gives an alternative solution of the ATM multiplexer that does not involve matrix operations. The matrix solutions usually assume that the probability generating matrix of the system has distinct eigenvalues, where the solution presented here does not have such restrictions. The paper presents significant new simple results on the transient analysis of the ATM multiplexer.