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Numerical Algebra, Control and Optimization (NACO)
 

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

Pages: 781 - 816, Volume 1, Issue 4, December 2011

doi:10.3934/naco.2011.1.781       Abstract        References        Full Text (632.4K)       Related Articles

Demetres D. Kouvatsos - Networks and Performance Engineering Research Group, Informatics Research Institute, University of Bradford, Bradford, BD7 1DP, United Kingdom (email)
Jumma S. Alanazi - Networks and Performance Engineering Research Group, Informatics Research Institute, University of Bradford, Bradford, BD7 1DP, United Kingdom (email)
Kevin Smith - Networks and Performance Engineering Research Group, Informatics Research Institute, University of Bradford, Bradford, BD7 1DP, United Kingdom (email)

Abstract: 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.

Keywords:  Queueing network models with blocking (QNMs-B), first-come-first-served (FCFS), maximum entropy (ME) principle, Blocking-After-Service (BAS), Blocking-Before-Service (BBS), Repetitive-Service (RS), Blocking with Random (RS-RD) and Fixed (RS-FD) destinations, generalized exponential (GE) distribution.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: June 2011;      Revised: September 2011;      Published: November 2011.

 References