An Efficient and Accurate Decomposition Method for Open Finite-and Infinite-buffer Queueing Networks

We address a decomposition approach for the evaluation of large, open networks of mixed finiteand infinite-buffer queues with phase-type distributed service and interarrival times. Such queueing networks can be seen as high-level specifications of continuous-time Markov chains (CTMCs). However, these CTMCs can become very large (in case all buffers are finite) or even infinitely large. To avoid these large state spaces we decompose such queueing networks in separate queues which can be solved efficiently using matrix-geometric or spectral expansion techniques, or specialised Markovian techniques for the solution of a finite system of global balance equations. However, since we allow for job losses and feedbacks to occur, we cannot decompose the overall model in a single pass to models of the individual queues; instead we have to iterate the decomposition procedure, so as to incorporate correctly the changes in the traffic streams. This paper extends our earlier work on open networks of (finite-buffer) PH|PH|1|K queues [10, 11] by replacing a number of approximation steps with exact results. The paper presents the theoretical background as well as some validation results.