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

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

8 Citations (Scopus)

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
Publication status	Published - 2010

Bibliographical note

Funding Information:
J. Kim’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076674). B. Kim’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076600).

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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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",

author = "Jerim Kim and Jeongsim Kim and Bara Kim",

note = "Funding Information: J. Kim{\textquoteright}s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076674). B. Kim{\textquoteright}s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076600).",

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AU - Kim, Jerim

AU - Kim, Jeongsim

AU - Kim, Bara

N1 - Funding Information: J. Kim’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076674). B. Kim’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076600).

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

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SN - 0257-0130

VL - 65

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JO - Queueing Systems

JF - Queueing Systems

IS - 4

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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