Output models of MAP/PH/1(/K) queues for an efficient network decomposition

For non-trivial (open) queueing networks, traffic-based decomposition often represents the only feasible—and at the same time fast—solution method besides simulation. The network is partitioned into individual nodes which are analyzed in isolation with respect to approximate internal traffic representations. Since the correlations of network traffic may have a considerable impact on performance measures, they must be captured to some extent by the employed traffic descriptors. The decomposition methodology presented in this paper is based on Markovian arrival processes (MAPs), whose correlation structure is determined from the busy-period behavior of the upstream queues. The resulting compact MAPs in connection with sophisticated moment-matching techniques allow an efficient decomposition of large queueing networks. Numerical experiments demonstrate the substantially enhanced precision due to improved output models compared with the experiments of Heindl and Telek [MAP-based decomposition of tandem networks of ·/PH/1(/K) queues with MAP input, in: Proceedings of the 11th GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communication Systems, Aachen, Germany, 2001, pp. 179–194].