A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. (English) Zbl 1244.93053

Kouvatsos, Demetres D.; Alanazi, Jumma S.; Smith, Kevin

Numer. Algebra Control Optim. 1, No. 4, 781-816 (2011).

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)

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