Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails

Sergey Foss, Masakiyo Miyazawa

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We consider a single-server GI / GI / 1 queueing system with feedback. We assume the service time distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer’s sojourn time in two cases: the customer arrives in an empty system, and the customer arrives in the system in the stationary regime. In particular, in the case of Poisson input we obtain more explicit formulae than those in the general case. As auxiliary results, we find the tail asymptotics for the busy period distribution in a single-server queue with an intermediate varying service times distribution and establish the principle-of-a-single-big-jump equivalences that characterise the asymptotics.

Original languageEnglish
Pages (from-to)1195-1226
Number of pages32
JournalJournal of Statistical Physics
Issue number3-4
Early online date19 Jun 2018
Publication statusPublished - Nov 2018


  • Feedback
  • Heavy-tailed and intermediate regularly varying distributions
  • Principle of a single big jump
  • Single-server queue
  • Sojourn time
  • Tail asymptotics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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