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Join-Idle-Queue system with general service times : Large-scale limit of stationary distributions. / Foss, Sergey; Stolyar, Alexander L.

In: Performance Evaluation Review, Vol. 45, No. 2, 01.09.2017, p. 45-47.

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

Harvard

Foss, S & Stolyar, AL 2017, 'Join-Idle-Queue system with general service times: Large-scale limit of stationary distributions', Performance Evaluation Review, vol. 45, no. 2, pp. 45-47. https://doi.org/10.1145/3152042.3152058

APA

Foss, S., & Stolyar, A. L. (2017). Join-Idle-Queue system with general service times: Large-scale limit of stationary distributions. Performance Evaluation Review, 45(2), 45-47. https://doi.org/10.1145/3152042.3152058

Vancouver

Foss S, Stolyar AL. Join-Idle-Queue system with general service times: Large-scale limit of stationary distributions. Performance Evaluation Review. 2017 Sept 1;45(2):45-47. doi: 10.1145/3152042.3152058

Author

Foss, Sergey ; Stolyar, Alexander L. / Join-Idle-Queue system with general service times : Large-scale limit of stationary distributions. In: Performance Evaluation Review. 2017 ; Vol. 45, No. 2. pp. 45-47.

BibTeX

@article{9bf67066d29947c0aa334e667a3ac4fc,
title = "Join-Idle-Queue system with general service times: Large-scale limit of stationary distributions",
abstract = "A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1/μ, but otherwise is arbitrary. Arriving customers are to be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n → ∞ and the customer input flow rate is λn. Under the condition λ/μ < 1/2, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal λ/μ. In particular, this implies that the steady-state probability of an arriving customer having to wait for service vanishes.",
author = "Sergey Foss and Stolyar, {Alexander L.}",
year = "2017",
month = sep,
day = "1",
doi = "10.1145/3152042.3152058",
language = "English",
volume = "45",
pages = "45--47",
journal = "Performance Evaluation Review",
issn = "0163-5999",
publisher = "Association for Computing Machinery (ACM)",
number = "2",

}

RIS

TY - JOUR

T1 - Join-Idle-Queue system with general service times

T2 - Large-scale limit of stationary distributions

AU - Foss, Sergey

AU - Stolyar, Alexander L.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1/μ, but otherwise is arbitrary. Arriving customers are to be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n → ∞ and the customer input flow rate is λn. Under the condition λ/μ < 1/2, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal λ/μ. In particular, this implies that the steady-state probability of an arriving customer having to wait for service vanishes.

AB - A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1/μ, but otherwise is arbitrary. Arriving customers are to be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n → ∞ and the customer input flow rate is λn. Under the condition λ/μ < 1/2, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal λ/μ. In particular, this implies that the steady-state probability of an arriving customer having to wait for service vanishes.

UR - http://www.scopus.com/inward/record.url?scp=85041422385&partnerID=8YFLogxK

U2 - 10.1145/3152042.3152058

DO - 10.1145/3152042.3152058

M3 - Article

AN - SCOPUS:85041422385

VL - 45

SP - 45

EP - 47

JO - Performance Evaluation Review

JF - Performance Evaluation Review

SN - 0163-5999

IS - 2

ER -

ID: 9539990