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

Sergey Foss, Masakiyo Miyazawa

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)1195-1226
Число страниц32
ЖурналJournal of Statistical Physics
Том173
Номер выпуска3-4
DOI
СостояниеОпубликовано - 1 ноя 2018

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