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Analysis of a Retrial Queue with Limited Processor Sharing Operating in the Random Environment

  • Sergey Dudin
  • Alexander DudinEmail author
  • Olga Dudina
  • Konstantin Samouylov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10372)

Abstract

Queueing system with limited processor sharing, which operates in the Markovian random environment, is considered. Parameters of the system (pattern of the arrival rate, capacity of the server, i.e., the number of customers than can share the server simultaneously, the service intensity, the impatience rate, etc.) depend on the state of the random environment. Customers arriving when the server capacity is exhausted join orbit and retry for service later. The stationary distribution of the system states (including the number of customers in orbit and in service) is computed and expressions for the key performance measures of the system are derived. Numerical example illustrates possibility of optimal adjustment of the server capacity to the state of the random environment.

Keywords

Processor sharing Markovian arrival process Random environment 

Notes

Acknowledgments

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008) and by the Belarusian Republican Foundation for Fundamental Research (grant F16MV-003).

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Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  • Sergey Dudin
    • 1
    • 2
  • Alexander Dudin
    • 1
    Email author
  • Olga Dudina
    • 1
    • 2
  • Konstantin Samouylov
    • 2
  1. 1.Belarusian State UniversityMinskBelarus
  2. 2.RUDN UniversityMoscowRussia

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