, Volume 48, Issue 1, pp 63-126

Entropy maximisation and queueing network models

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Abstract

Over recent years it has become increasingly evident that “classical” queueing theory cannot easily handle complex queueing systems and networks with many interacting elements. As a consequence, alternative ideas and tools, analogous to those applied in the field of Statistical Mechanics, have been proposed in the literature. In this context, the principles of Maximum Entropy (ME) and Minimum Relative Entropy (MRE), a generalisation, provide consistent methods of inference for characterising the form of an unknown but true probability distribution, based on information expressed in terms of known to exist true expected values or when, in addition, there exists a prior estimate of the unknown distribution. This paper traces the progress achieved so far towards the creation of ME and MRE product-form approximations and related algorithms for the performance analysis of general Queueing Network Models (QNMs) and indicates potential research extensions in the area.

Earlier research on entropy maximisation and QNMs was sponsored by the UK Science and Engineering Research Council (SERC) with grant GR/D/12422, while recent and current work is supported by SERC grants GR/F/29271 and GR/H/18609. Research on Complex I/O subsystems was funded by Metron Technology Ltd., UK, under grant JJCA415.