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Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails. / Foss, Sergey; Miyazawa, Masakiyo.

In: Journal of Statistical Physics, Vol. 173, No. 3-4, 01.11.2018, p. 1195-1226.

Research output: Contribution to journal › Article › peer-review

Harvard

Foss, S & Miyazawa, M 2018, 'Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails', Journal of Statistical Physics, vol. 173, no. 3-4, pp. 1195-1226. https://doi.org/10.1007/s10955-018-2079-9

APA

Foss, S., & Miyazawa, M. (2018). Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails. Journal of Statistical Physics, 173(3-4), 1195-1226. https://doi.org/10.1007/s10955-018-2079-9

Vancouver

Foss S, Miyazawa M. Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails. Journal of Statistical Physics. 2018 Nov 1;173(3-4):1195-1226. doi: 10.1007/s10955-018-2079-9

Author

Foss, Sergey ; Miyazawa, Masakiyo. / Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails. In: Journal of Statistical Physics. 2018 ; Vol. 173, No. 3-4. pp. 1195-1226.

BibTeX

@article{6314bed259954d50995809fd8cc9279b,
title = "Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails",
abstract = "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{\textquoteright}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.",
keywords = "Feedback, Heavy-tailed and intermediate regularly varying distributions, Principle of a single big jump, Single-server queue, Sojourn time, Tail asymptotics, INTERVAL, RANDOM-WALK",
author = "Sergey Foss and Masakiyo Miyazawa",
note = "Publisher Copyright: {\textcopyright} 2018, The Author(s).",
year = "2018",
month = nov,
day = "1",
doi = "10.1007/s10955-018-2079-9",
language = "English",
volume = "173",
pages = "1195--1226",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "3-4",

}

RIS

TY - JOUR

T1 - Customer Sojourn Time in GI / GI / 1 Feedback Queue in the Presence of Heavy Tails

AU - Foss, Sergey

AU - Miyazawa, Masakiyo

N1 - Publisher Copyright: © 2018, The Author(s).

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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.

KW - Feedback

KW - Heavy-tailed and intermediate regularly varying distributions

KW - Principle of a single big jump

KW - Single-server queue

KW - Sojourn time

KW - Tail asymptotics

KW - INTERVAL

KW - RANDOM-WALK

UR - http://www.scopus.com/inward/record.url?scp=85048654214&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-2079-9

DO - 10.1007/s10955-018-2079-9

M3 - Article

AN - SCOPUS:85048654214

VL - 173

SP - 1195

EP - 1226

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -

ID: 14048589