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

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.

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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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Correspondence to Lamia Lakaour.

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Lakaour, L., Aïssani, D., Adel-Aissanou, K. et al. M/M/1 Retrial Queue with Collisions and Transmission Errors. Methodol Comput Appl Probab 21, 1395–1406 (2019). https://doi.org/10.1007/s11009-018-9680-x

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Keywords

  • Retrial queue
  • Collisions
  • Transmission errors
  • Classical retrial rate
  • Generating function

Mathematics Subject Classification (2010)

  • 60K25
  • 68M20