Asymptotic Analysis of RQ-System with Feedback and Batch Poisson Arrival Under the Condition of Increasing Average Waiting Time in Orbit

A. A. Nazarov, S. V. Rozhkova, E. Yu Titarenko

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The paper studies the retrial queueing system M [ n ] /M/1 with feedback and batch Poisson arrival. Customers for the system come in groups. Not more than one customer is served at once, others wait in the orbit. Having been served, the customer leaves the system or goes to re-service or into the orbit. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. A long delay between customers from the orbit is proposed as an asymptotic condition. It is proved that the asymptotic probability distribution of the number of customers in the orbit is Gaussian. As a result the parameters of this distribution are obtained. The calculations to determine the range of the method applicability are carried out. The accuracy of the approximation is compared to numerical results obtained by matrix method.

Original languageEnglish
Title of host publicationDistributed Computer and Communication Networks
Subtitle of host publicationControl, Computation, Communications - 23rd International Conference, DCCN 2020, Revised Selected Papers
EditorsVladimir M. Vishnevskiy, Dmitry V. Kozyrev, Konstantin E. Samouylov, Dmitry V. Kozyrev
PublisherSpringer Science and Business Media Deutschland GmbH
Pages327-339
Number of pages13
ISBN (Print)9783030662417
DOIs
Publication statusPublished - 2020
Event23rd International Conference on Distributed Computer and Communication Networks: Control, Computation, Communications , DCCN 2020 - Moscow, Russian Federation
Duration: 14 Sep 202018 Sep 2020

Publication series

NameCommunications in Computer and Information Science
Volume1337
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference23rd International Conference on Distributed Computer and Communication Networks: Control, Computation, Communications , DCCN 2020
CountryRussian Federation
CityMoscow
Period14.9.2018.9.20

Keywords

  • Asymptotic analysis
  • Batch arrival
  • Feedback
  • Queuing system
  • RQ system

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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