An algorithmic approach for analysis of finite-source retrial systems with unreliable servers

Authors:
Nawel Gharbi;Claude Dutheillet
Affiliations:
Computer Science Department, University of Sciences and Technology USTHB, BP. 32 El Alia 16111 Algiers, Algeria;LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

This paper aims at presenting an approach for analyzing finite-source retrial systems with servers subject to breakdowns and repairs, using Generalized Stochastic Petri Nets (GSPNs). This high-level formalism allows a simple representation of such systems with different breakdown disciplines. From the GSPN model, a Continuous Time Markov Chain (CTMC) can be automatically derived. However, for multiserver retrial systems with unreliable servers, the models may have a huge state space. Using the GSPN model as a support, we propose an algorithm for directly computing the infinitesimal generator of the CTMC without generating the reachability graph. In addition, we develop the formulas of the main stationary performance and reliability indices, as a function of the number of servers, the size of the customer source and the stationary probabilities. Through numerical examples, we discuss the effect of the system parameters and the breakdown disciplines on performance.