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 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 223 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.cam.2008.02.009
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.519-533
  • Keywords: Performability, State explosion, Two stage tandem networks
  • Middle East Technical University Northern Cyprus Campus Affiliated: Yes

Abstract

Analytical solutions for two-dimensional Markov processes suffer from the state space 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 failures 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 employed. © 2008 Elsevier B.V. All rights reserved.