Abstract

The analytic method for entropy maximisation, subject to marginal mean value constraints, is applied to characterise new product-form approximations for arbitrary FCFS (first-come-first-served) queueing networks with multiple server queues and general interarrival and service times under repetitive-service blocking involving both fixed and random destinations. For open queueing networks the maximum entropy solution suggests a decomposition into individual finite capacity multiple server queues with a censored arrival process and revised service-times. For closed queueing networks the product-form solution of open networks is initially modified to satisfy constraints on population and flow conservation and is in turn truncated and efficiently implemented via a convolution type recursive procedure with time complexity of O( M 2 L 2), where M is the number of queues and L is the fixed population of the network. The FCFS GE/GE/ c/ K; N censored queue with GE (generalised exponential) interarrival-time and service-time distributions, c ( c ≧ 1) multiple servers, minimum queue length, K ( K ⩾ 0) and finite capacity, N ( K < N < + ∞), is exactly analysed in the context of maximum entropy and used as a ‘building block’ for the approximate analysis of general queueing networks. Validation examples are presented for assessing the numerical accuracy of the maximum entropy method (MEM) and favourable comparisons against simulation results are made.

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