Asymptotic Analysis of Retrial Queueing System M/GI/1 with Collisions and Impatient Calls

  • Elena DanilyukEmail author
  • Svetlana Moiseeva
  • Anatoly Nazarov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1109)


In the paper, the retrial queueing system of M/GI/1 type with input Poison flow of events, collisions and impatient calls is considered. The delay time of calls in the orbit and the impatience time of calls in the orbit have exponential distribution. Service time on server is with any distribution function. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a long delay of calls in orbit and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given.


Retrial queueing system Collisions Impatient calls Asymptotic analysis 



This work is financially supported by the Russian Foundation for Basic Research according to the research project No. 19-41-703002.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Elena Danilyuk
    • 1
    Email author
  • Svetlana Moiseeva
    • 1
  • Anatoly Nazarov
    • 1
  1. 1.National Research Tomsk State UniversityTomskRussia

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