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 analyzed in isolation. In most existing decomposition algorithms for continuous-time networks, the output of a queue is usually approximated as a renewal process, which becomes 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. Furthermore, the single nodes may have infinite or finite buffers. Customers who arrive at a full buffer will get lost. In principle, the analysis of an individual queue as an MMPP/G/1(/ K) system delivers a wide range of performance measures. For different examples of tandem networks, stationary mean queue lengths at arbitrary time are compared to simulation data. The relative errors of the results, which are computed promptly by the decomposition component of the tool TimeNET, remain within a reasonable range.