Information Theoretic Decomposition of GE-Type Closed Queueing Networks with Finite Capacity and Multiple Servers

In this paper, the information theoretic principle of Minimum Relative Entropy (MRE), given fully decomposable subset and aggregate mean value constraints, is applied, in conduction with classical queueing theory, to extend earlier works and derive new analytic approximations for the conditional and marginal state probabilities of arbitrary closed queueing network models (QNMs-B) with Generalised Exponential (GE) multiple server stations and RS blocking. A generalised MRE decomposition algorithm is developed in the context of a multilevel variable aggregation scheme and is based on asymptotic connections to infinite capacity multiple server queues and related closed-form expressions for the determination of the effective and overall flows in the network. The GE/GE/c/k;N censored queue with GE-type interarrival-time and service-time distributions, multiple servers, minimum queue length k and finite capacity N, is used as the building block in the solution process. Numerical results are included to illustrate the credibility of the proposed MRE decomposition algorithm against simulation.