Simplified Analysis of Queueing Systems with Random Requirements

  • Konstantin E. Samouylov
  • Yuliya V. Gaidamaka
  • Eduard S. Sopin
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)

Abstract

In this work, a simplification approach for analysis of queueing systems with random requirements is proposed. The main point of the approach is to keep track of only total amount of occupied system resources. Therefore, we cannot know the exact amount of resources released by the departure of a customer, so we assume it a random variable with conditional cumulative distribution function depending on only number of customers in the system and total occupied resources at the moment just before the departure. In the chapter, we briefly describe the queuing system with random requirements, the simplification method and show that in case of Poisson arrival process simplified system has exactly the same stationary probability distribution as the original one.

Keywords

Queuing system Limited resources Probabilistic characteristics Insensitivity 

Notes

Acknowledgements

The reported study was supported by the Russian Science Foundation, research project No. 16-11-10227. We thank Prof. Valeriy Naumov for the methodic assistance and scientific guidance in the preparation of this chapter, as well as for the constant and invaluable attention to our scientific work.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Konstantin E. Samouylov
    • 1
    • 2
  • Yuliya V. Gaidamaka
    • 1
    • 2
  • Eduard S. Sopin
    • 1
    • 2
  1. 1.Peoples’ Friendship University of Russia (RUDN University)MoscowRussia
  2. 2.Institute of Informatics Problems, FRC CSC RASMoscowRussia

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