Approximate solution for two stage open networks with Markov-modulated queues minimizing the state space explosion problem


Gemikonakli O., Ever E., KOÇYİĞİT A.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.223, no.1, pp.519-533, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 223 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.cam.2008.02.009
  • Title of Journal : JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Page Numbers: pp.519-533
  • Keywords: Performability, Two stage tandem network, State explosion, SPECTRAL EXPANSION SOLUTION, FINITE QBD PROCESSES, COMPUTING SYSTEMS

Abstract

Analytical solutions for two-dimensional Markov processes suffer from the state explosion problem. Two stage tandem networks are effectively used for analytical modelling of various communication and computer systems which have tandem system behaviour. Performance evaluation of tandem systems with feedbacks can be handled with these models. However, because of the numerical difficulties caused by large state spaces, considering server failure and repairs at the second stage employing multiple servers has not been possible. The solution proposed in this paper is approximate with a high degree of accuracy. Using this approach, two stage open networks with multiple servers, break downs, and repairs at the second stage as well as feedback can be modelled as three-dimensional Markov processes and solved for performability measures. Results show that, unlike other approaches such as spectral expansion, the steady state solution is possible regardless of the number of servers empolyed. (C) 2008 Elsevier B.V. All rights reserved.