Decomposition of General Tandem Queueing Networks with MMPP Input

Abstract

For tandem queueing networks with generally distributed service times, decomposition often is the only feasible solution method besides simulation. The network is partitioned into individual nodes which are analysed in isolation. In existing decomposition algorithms for continuous-time networks, the output of a queue is usually approximated as a renewal process, which serves as the arrival process to the next queue. In this paper, the internal traffic processes are described as semi-Markov processes (SMPs) and Markov modulated Poisson processes (MMPPs). Thus, correlations in the traffic streams, which are known to have a considerable impact on performance, are taken into account to some extent. A two-state MMPP, which arises frequently in communications modeling, serves as input to the first queue of the tandem network. For tandem networks with infinite or finite buffers, stationary mean queue lengths at arbitrary time computed quasi-promptly by the decomposition component of the tool TimeNET are compared to simulation.