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On large delays in multi-server queues with heavy tails

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On large delays in multi-server queues with heavy tails. / Foss, Sergey; Korshunov, Dmitry.
In: Mathematics of Operations Research, Vol. 37, No. 2, 05.2012, p. 201-218.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Foss, S & Korshunov, D 2012, 'On large delays in multi-server queues with heavy tails', Mathematics of Operations Research, vol. 37, no. 2, pp. 201-218. https://doi.org/10.1287/moor.1120.0539

APA

Foss, S., & Korshunov, D. (2012). On large delays in multi-server queues with heavy tails. Mathematics of Operations Research, 37(2), 201-218. https://doi.org/10.1287/moor.1120.0539

Vancouver

Foss S, Korshunov D. On large delays in multi-server queues with heavy tails. Mathematics of Operations Research. 2012 May;37(2):201-218. Epub 2012 Mar 20. doi: 10.1287/moor.1120.0539

Author

Foss, Sergey ; Korshunov, Dmitry. / On large delays in multi-server queues with heavy tails. In: Mathematics of Operations Research. 2012 ; Vol. 37, No. 2. pp. 201-218.

Bibtex

@article{e9f1b8bd56254c7aa39ccd92cf20b272,
title = "On large delays in multi-server queues with heavy tails",
abstract = "We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s − k big jumps” in this case (here k is the integer part of ρ), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.",
keywords = "FCFS multi-server queue, stationary waiting time, heavy tails , large deviations, long-tailed distribution, subexponential distribution, existence of moments",
author = "Sergey Foss and Dmitry Korshunov",
year = "2012",
month = may,
doi = "10.1287/moor.1120.0539",
language = "English",
volume = "37",
pages = "201--218",
journal = "Mathematics of Operations Research",
issn = "0364-765X",
publisher = "INFORMS Inst.for Operations Res.and the Management Sciences",
number = "2",

}

RIS

TY - JOUR

T1 - On large delays in multi-server queues with heavy tails

AU - Foss, Sergey

AU - Korshunov, Dmitry

PY - 2012/5

Y1 - 2012/5

N2 - We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s − k big jumps” in this case (here k is the integer part of ρ), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

AB - We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s − k big jumps” in this case (here k is the integer part of ρ), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

KW - FCFS multi-server queue

KW - stationary waiting time

KW - heavy tails

KW - large deviations

KW - long-tailed distribution

KW - subexponential distribution

KW - existence of moments

U2 - 10.1287/moor.1120.0539

DO - 10.1287/moor.1120.0539

M3 - Journal article

VL - 37

SP - 201

EP - 218

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 2

ER -