Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

Jerim Kim; Jeongsim Kim; Bara Kim

doi:10.1007/s11134-010-9180-3

Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

Jerim Kim
, Jeongsim Kim
, Bara Kim

Department of Mathematics

Chungbuk National University
Korea University

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

8 Scopus citations

Abstract

We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index -β, β > 1. The waiting time distribution is shown to have a regularly varying tail with index 1-β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with random order service policy.

Original language	English
Pages (from-to)	365-383
Number of pages	19
Journal	Queueing Systems
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s11134-010-9180-3
State	Published - 2010

Keywords

M/G/1 retrial queue
Random order service
Regular variation
Stochastic comparison
Waiting time distribution

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10.1007/s11134-010-9180-3

Cite this

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title = "Regularly varying tail of the waiting time distribution in M/G/1 retrial queue",

abstract = "We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index -β, β > 1. The waiting time distribution is shown to have a regularly varying tail with index 1-β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with random order service policy.",

keywords = "M/G/1 retrial queue, Random order service, Regular variation, Stochastic comparison, Waiting time distribution",

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T1 - Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

AU - Kim, Jerim

AU - Kim, Jeongsim

AU - Kim, Bara

PY - 2010

Y1 - 2010

N2 - We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index -β, β > 1. The waiting time distribution is shown to have a regularly varying tail with index 1-β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with random order service policy.

AB - We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index -β, β > 1. The waiting time distribution is shown to have a regularly varying tail with index 1-β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with random order service policy.

KW - M/G/1 retrial queue

KW - Random order service

KW - Regular variation

KW - Stochastic comparison

KW - Waiting time distribution

UR - https://www.scopus.com/pages/publications/77955096384

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DO - 10.1007/s11134-010-9180-3

M3 - Article

AN - SCOPUS:77955096384

SN - 0257-0130

VL - 65

SP - 365

EP - 383

JO - Queueing Systems

JF - Queueing Systems

IS - 4

ER -

Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

Abstract

Keywords

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