Large deviations of the waiting time in the GI/G/1 queue with random order service

Bara Kim; Jeongsim Kim

doi:10.1007/s11134-012-9331-9

Large deviations of the waiting time in the GI/G/1 queue with random order service

Bara Kim, Jeongsim Kim

Department of Mathematics

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

3 Citations (Scopus)

Abstract

We consider the GI/G/1 queue where customers are served in random order and the service time distribution has a finite exponential moment. We derive the large deviations result for the waiting time distribution by showing that the asymptotic decay rate of the waiting time distribution is the same as that of the busy period distribution.

Original language	English
Pages (from-to)	431-443
Number of pages	13
Journal	Queueing Systems
Volume	74
Issue number	4
DOIs	https://doi.org/10.1007/s11134-012-9331-9
Publication status	Published - 2013 Aug

Bibliographical note

Funding Information:
Acknowledgments The first author’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0004133). The second author’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0011887).

Keywords

Busy period
GI/G/1 queue
Large deviations
Random order service discipline
Waiting time

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/s11134-012-9331-9

Cite this

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abstract = "We consider the GI/G/1 queue where customers are served in random order and the service time distribution has a finite exponential moment. We derive the large deviations result for the waiting time distribution by showing that the asymptotic decay rate of the waiting time distribution is the same as that of the busy period distribution.",

keywords = "Busy period, GI/G/1 queue, Large deviations, Random order service discipline, Waiting time",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: Acknowledgments The first author{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0004133). The second author{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0011887).",

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AU - Kim, Jeongsim

N1 - Funding Information: Acknowledgments The first author’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0004133). The second author’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0011887).

PY - 2013/8

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N2 - We consider the GI/G/1 queue where customers are served in random order and the service time distribution has a finite exponential moment. We derive the large deviations result for the waiting time distribution by showing that the asymptotic decay rate of the waiting time distribution is the same as that of the busy period distribution.

AB - We consider the GI/G/1 queue where customers are served in random order and the service time distribution has a finite exponential moment. We derive the large deviations result for the waiting time distribution by showing that the asymptotic decay rate of the waiting time distribution is the same as that of the busy period distribution.

KW - Busy period

KW - GI/G/1 queue

KW - Large deviations

KW - Random order service discipline

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ER -

Large deviations of the waiting time in the GI/G/1 queue with random order service

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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