A TAYLOR SERIES APPROACH TO THE NUMERICAL ANALYSIS OF THE M/G/1//N QUEUE UNDER MULTIPLE VACATION POLICY OF THE SERVER

 

Fazia Rahmoune, Djamil Aissani

 

Abstract

 

This paper presents a functional approximation of the M/G/1//N queue under multiple vacation policy of the Server built on a Taylor series approximation. The work presented is a part of research project on numerical algorithms based on series expansions of Markov chains with finite state space S. Numerical examples are carried out to illustrate the performance of the approach, while numerical bounds are provided for quantities from stochastic reliability models to optimize the preventive maintenance policy, after modeling by vacation queuing systems.

 

Lecture Notes in Management Science (2011) Vol. 3: 565-576

3rd International Conference on Applied Operational Research, Proceedings

© Tadbir Operational Research Group Ltd. All rights reserved.

www.tadbir.ca

 

ISSN 2008-0050 (Print)

ISSN 1927-0097 (Online)

 

ARTICLE OUTLINE

 

·         Introduction

·         Preliminaries On Finite Markov Chains

·         Taylor Series In The M/G/1//N Queue With Multiple Vacations Of The Server

·         Description Of The Models

·         Transition Kernels

·         The Taylor Series Representation For ΠQ

·         Convergence Of The Series

·         Bounding The Remainder Term

·         Algorithm

·         Results And Numerical Examples

·         Conclusion

·         References

 

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