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Sojourn Time Analysis for Processor Sharing Loss Queuing System with Service Interruptions and MAP Arrivals

  • Konstantin Samouylov
  • Eduard Sopin
  • Irina Gudkova
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 678)

Abstract

Processor sharing (PS) queuing systems are widely investigated by research community and applied for the analysis of wire and wireless communication systems and networks. Nevertheless, only few works focus on finite queues with both PS discipline and service interruptions. In the paper, compared with the previous results we analyze a finite capacity PS queuing system with Markovian arrival process, unreliable server, service interruptions, and an upper limit of the number of customers it serves simultaneously. For calculating the mean sojourn time, unlike a popular but computational complex technique of inverse Laplace transform we use an effective method based on embedded Markov chain. A practical example concludes the paper.

Keywords

Queuing system Processor sharing Egalitarian processor sharing Unreliable server Interruption Probability distribution Recursive algorithm Sojourn time Absorbing Markov chain 

Notes

Acknowledgements

The authors are grateful to the Director Research of the Service Innovation Research Institute, Professor Valeriy Naumov, for useful advices.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Konstantin Samouylov
    • 1
    • 2
  • Eduard Sopin
    • 1
    • 2
  • Irina Gudkova
    • 1
    • 2
  1. 1.Department of Applied Probability and InformaticsRUDN UniversityMoscowRussia
  2. 2.Institute of Informatics Problems, FRC CSC RASMoscowRussia

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