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Methodology and Computing in Applied Probability

, Volume 21, Issue 4, pp 1395–1406 | Cite as

M/M/1 Retrial Queue with Collisions and Transmission Errors

  • Lamia LakaourEmail author
  • Djamil Aïssani
  • Karima Adel-Aissanou
  • Kamel Barkaoui
Article

Abstract

In this paper, an M/M/1 retrial queue with collisions and transmission errors is considered. The collision may occur when a primary arriving customer finds the server busy while the transmission errors usually occur due to an erroneous packet or due to a non-ideal channel condition. We apply the generating function method to derive the joint distribution of the server state and the orbit length in steady state and we obtain important system characteristics. Finally, we present numerical examples to show the applicability of the model.

Keywords

Retrial queue Collisions Transmission errors Classical retrial rate Generating function 

Mathematics Subject Classification (2010)

60K25 68M20 

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Notes

Acknowledgments

The authors would like to thank the referee for valuable suggestions and comments that help to improve the presentation of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Lamia Lakaour
    • 1
    Email author
  • Djamil Aïssani
    • 1
  • Karima Adel-Aissanou
    • 1
  • Kamel Barkaoui
    • 2
  1. 1.Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Exact SciencesBejaia UniversityBejaiaAlgeria
  2. 2.CEDRICConservatoire National des Arts et MétiersParisFrance

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