A TRANSIENT DISCRETE-TIME QUEUING 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 superposi tion of the traffic generated by independent binary Markov sources. Th e functional equation describing the ATM multiplexer has been transfor med into a mathematically tractable form. This allows derivation of th e transient probability generating functions of the queue length and t he number of active sources in the system. Then, application of the fi nal value theorem results in the corresponding steady-state probabilit y generating functions, as well as packet delay. We also present close d form expressions for the transient and steady-state moments of the q ueue length. The pure transform approach used in the present analysis is an extension of the well-known classical method used in the transie nt analysis of single server queues with uncorrelated arrivals. As a r esult, the analysis is relatively easy to follow and gives an alternat ive solution of the ATM multiplexer that does not involve matrix opera tions. The matrix solutions usually assume that the probability genera ting matrix of the system has distinct eigenvalues, where the solution presented here does not have such restrictions. The paper presents si gnificant new simple results on the transient analysis of the ATM mult iplexer. (C) 1998 Elsevier Science B.V.