Stochastic Analysis of an M/G/1 Retrial Queue with FCFS

  • Mohamed Boualem
  • Mouloud Cherfaoui
  • Natalia Djellab
  • Djamil Aïssani
Conference paper

DOI: 10.1007/978-3-319-22476-3_8

Part of the Contributions to Statistics book series (CONTRIB.STAT.)
Cite this paper as:
Boualem M., Cherfaoui M., Djellab N., Aïssani D. (2015) Stochastic Analysis of an M/G/1 Retrial Queue with FCFS. In: Ould Saïd E., Ouassou I., Rachdi M. (eds) Functional Statistics and Applications. Contributions to Statistics. Springer, Cham

Abstract

The main goal of this paper is to investigate stochastic analysis of a single server retrial queue with a First-Come-First-Served (FCFS) orbit and non-exponential retrial times using the monotonicity and comparability methods. We establish various results for the comparison and monotonicity of the underlying embedded Markov chain when the parameters vary. Moreover, we prove stochastic inequalities for the stationary distribution and some simple bounds for the mean characteristics of the system. We validate stochastic comparison method by presenting some numerical results illustrating the interest of the approach.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mohamed Boualem
    • 1
  • Mouloud Cherfaoui
    • 2
    • 3
  • Natalia Djellab
    • 4
  • Djamil Aïssani
    • 5
  1. 1.Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of TechnologyUniversity of BejaiaBejaiaAlgeria
  2. 2.Research Unit LaMOS (Modeling and Optimization of Systems)University of BejaiaBejaiaAlgeria
  3. 3.Department of MathematicsUniversity of BiskraBiskraAlgeria
  4. 4.Laboratory LaPS, Department of MathematicsUniversity of AnnabaAnnabaAlgeria
  5. 5.Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact SciencesUniversity of BejaiaBejaiaAlgeria

Personalised recommendations