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A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. (English) Zbl 1244.93053
Summary: A generic Maximum Entropy (ME) product-form approximation is proposed for arbitrary single class open First-Come-First-Served (FCFS) Queueing Network Models with Blocking (QNMs-B), subject to bursty GE-type interarrival and service times and the mixed Blocking Mechanisms (BMs) of Blocking-After-Service (BAS), Blocking-Before-Service (BBS) and Repetitive-Service (RS) Blocking with Random Destinations (RS-RD) and Fixed Destinations (RS-FD). A new GE-type analytic framework is devised, based on the ME analysis of a virtual multiple class GE/GE/1/N+U queueing system with finite capacity, \(N (N>1)\) augmented by \(U (U\geq 1)\) auxiliary-waiting lines, to determine the first two moments of BAS- and BBS-dependent effective service times towards a node-by-node decomposition of the entire network. In this context, a unified ME algorithm is devised for the approximate analysis of arbitrary open FCFS QNMs-B with a mixture of the BMs of BAS, BBS, RS-RD and RS-FD. Typical numerical tests are carried out to assess the credibility of the unified ME algorithm against discrete event simulation and also establish GE-type experimental performance bounds. A critique on the feasibility of ME formalism for QNMs-B and suggested extensions are included.
MSC:
93B40 Computational methods in systems theory (MSC2010)
90B22 Queues and service in operations research
93A30 Mathematical modelling of systems (MSC2010)
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