Moment analysis for traffic associated with Markovian queueing systems

A study is made of various traffic processes associated with Markovian queuing systems, and the moments of the traffic processes are analyzed. The purpose of the study is to develop a means of computing the moments efficiently so as to extend the conventional method of representing the traffic processes to a larger class of queuing systems. As an outcome of the analysis, the recurrence formulae for computing the moments including cross-covariances between multiple traffic processes are derived and expressed in terms of the infinitesimal generator, steady-state probability vector of the Markovian queuing system and a matrix describing traffic rate. The main feature of the analysis is in the utilization of the special block-partitioned structure of the matrices involved. The results are of wide application for the study of various telecommunication networks. Two examples of applications for the Markovian queuing model with batch arrivals and a multislot integrated services system are presented.>