Comparative Analysis of Methods of Residual and Elapsed Service Time in the Study of the Closed Retrial Queuing System M/GI/1//N with Collision of the Customers and Unreliable Server

  • Anatoly Nazarov
  • Janos SztrikEmail author
  • Anna Kvach
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


The aim of the present paper is to investigate a finite-source M/GI/1 retrial queuing system with collision of the customers where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. The method of elapsed service time and the method of residual service time are considered using asymptotic approach under the condition of unlimited growing number of sources. It is proved, as it was expected, that basic characteristics of the system, such as the stationary probability distribution of the server states and the asymptotic average of the normalized number of customers in the system are the same and do not depend on the applied method.


Finite-source queuing system Closed queuing systems Retrial queue Collision Server breakdowns and repairs Unreliable server Asymptotic analysis Method of residual service time Method of elapsed service time 



The publication was financially supported by the Ministry of Education and Science of the Russian Federation (Agreement number 02.a03.21.0008) and by Peoples Friendship University of Russia (RUDN University).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.National Research Tomsk State UniversityTomskRussia
  2. 2.Department of Applied Probability and InformaticsPeoples’ Friendship University of RussiaMoscowRussia
  3. 3.University of DebrecenDebrecenHungary

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