MRE hierarchical decomposition of general queueing network models

Abstract

The principle of Minimum Relative Entropy (MRE), given fully decomposable subset and aggregate mean queue length, utilisation and flow-balance constraints, is used in conjunction with asymptotic connections to infinite capacity queues, to derive new analytic approximations for the conditional and marginal state probabilities of single class general closed queueing network models (QNMs) in the context of a multilevel variable aggregation scheme. The concept of subparallelism is applied to preserve the flow conservation and a universal MRE hierarchical decomposition algorithm is proposed for the approximate analysis of arbitrary closed queueing networks with single server queues and general service-times. Heuristic criteria towards an optimal coupling of network's units at each level of aggregation are suggested. As an illustration, the MRE algorithm is implemented iteratively by using the Generalised Exponential (GE) distributional model to approximate the service and asymptotic flow processes in the network. This algorithm captures the exact solution of separable queueing networks, while for general queueing networks it compares favourably against exact solutions and known approximations.