Multilevel aggregation of central server models: a minimum relative entropy approach

Abstract

The principle of minimum relative entropy (MRE) may be viewed as a method of inference for characterizing the form of an unknown but true probability distribution based on information expressed in terms of an estimate of the unknown distribution and known to exist true expected values. Given fully decomposable subset and aggregate mean queue length and flow-balance constraints under a hierarchical decomposition scheme, the principle is used, in conjunction with asymptotic connections to infinite capacity queues, to derive new closed-form approximations for the conditional and marginal state probabilities of a general central server model. It is shown that the MRE joint state probability, subject to the prior information available, is of product-form, and it reduces to the exact solution obtained if the network was separable. This kind of analysis provides a novel interpretation of the notion of multilevel aggregation and introduces the basis of a new methodology for the performance analysis of queueing network models (QNMs). Moreover, it helps to explain the robustness of separable queueing networks. Comments on the extension of the work towards a universal MRE hierarchical decomposition alogorithm for general QNMs are included.