Approximation of Performance Measures in an M/G/1 Queue with Breakdowns

Abstract

We present a new perturbation bound in an M/G/I queueing system with breakdowns and repairs. Our analysis is based on bounding the distance of stationary distributions in a suitable functional space. This leads to understand how the breakdowns of the server will affect the system’s level of performance. In order to give an idea about the application of our approach in practice, we give a numerical example which would show the difference between explicit analytical estimates of errors and real simulated errors. It also allows for evaluating the potential of our approach. Eventually, we will point out directions of further research.

Key Words:

• Breakdowns
• M/G/I queue
• perturbation
• strong stability
• simulation
• stability inequalities

Additional information

Notes on contributors

Karim Abbas

Karim Abbas is an Assistant Professor of Mathematics at the Department of Operations Research at the University of Beja’ia, Algeria. He received a doctorate in Applied Mathematics from University of Beja’ia. He is a member of the LAMOS Laboratory (Modelling and Optimization of Systems). His main current research interests include perturbation analysis of Markov chains (stability problem), Taylor series expansions in performance analysis (applications in queueing systems). At present he develops the techniques for strong stability method allow to establish numerical algorithms for bounding the approximating error, and he published many scientific papers on these research topics.

Djamil Aïssani

Djamil Aïssani is Full Professor of Mathematics at the Department of Operations Research at the University of Bejaia, Algeria. He started his career at the University of Constantine in 1978. He received his Ph.D. in 1983 from Kiev State University (Soviet Union). He is at the University of Beja’ia since its opening in 1983/1984. Director of Research, Head of the Faculty of Science and Engineering Science (1999 – 2000), Director of the LAMOS Laboratory (Modelling and Optimization of Systems), Scientific Head of the Computer Science Doctorate School, he has taught in many universities (USTHB Algiers, Annaba, Rouen, Dijon, ENITA). He has published many papers on Markov chains, queueing systems, reliability theory, performance evaluation and their applications in such industrial areas as electrical and telecommunication networks and computer systems.