Decomposition of general queueing networks with MMPP inputs and customer losses

Abstract

For nontrivial general (open) queueing networks, decomposition often represents the only feasible solution method besides simulation. The network is partitioned into individual nodes which are analyzed in isolation with respect to approximate internal traffic representations. The quality of the quickly obtained results very much depends on the descriptors for the traffic processes within the network, which may be split and merged before traversing the next queue. Recently, one of the existing decomposition formalisms based on renewal processes as traffic descriptors has been extended in order to include semi-Markov processes (SMPs) and Markov-modulated Poisson processes (MMPPs) with two states. However, due to the restriction to tandem networks, no operations for the splitting and and merging were provided. The numerical procedures for the splitting of SMPs and the superposition of MMPPs proposed in this paper render the extended decomposition framework available for general queueing networks. The correlations in the traffic processes, which are known to have a considerable impact on performance measures, are taken into account to some extent. Moreover, in addition to renewal processes, MMPP inputs—as they frequently arise in computer communication modeling—increase the range of applications of general queueing networks. Numerical experiments on different network configurations illustrate the capabilities and accuracy of the extended decomposition framework.