# American Institute of Mathematical Sciences

2011, 1(4): 781-816. doi: 10.3934/naco.2011.1.781

## A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms

 1 Networks and Performance Engineering Research Group, Informatics Research Institute, University of Bradford, Bradford, BD7 1DP, United Kingdom, United Kingdom, United Kingdom

Received  June 2011 Revised  September 2011 Published  November 2011

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 (RS-RD) and Fixed (RS-FD) destinations. 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 $U (U\geq1)$ 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.
Citation: Demetres D. Kouvatsos, Jumma S. Alanazi, Kevin Smith. A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. Numerical Algebra, Control and Optimization, 2011, 1 (4) : 781-816. doi: 10.3934/naco.2011.1.781
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