The waiting time distribution for a correlated queue with exponential interarrival and service times

Bara Kim; Jeongsim Kim

doi:10.1016/j.orl.2018.02.001

The waiting time distribution for a correlated queue with exponential interarrival and service times

Bara Kim, Jeongsim Kim

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We are concerned with the analysis of the waiting time distribution in an M∕M∕1 queue in which the interarrival time between the nth and the (n+1)th customers and the service time of the nth customer are correlated random variables with Downton's bivariate exponential distribution. In this paper we show that the conditional waiting time distribution, given that the waiting time is positive, is exponential.

Original language	English
Pages (from-to)	268-271
Number of pages	4
Journal	Operations Research Letters
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2018.02.001
Publication status	Published - 2018 Mar

Keywords

Bivariate exponential distribution
Correlated queue
Workload

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2018.02.001

Cite this

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title = "The waiting time distribution for a correlated queue with exponential interarrival and service times",

abstract = "We are concerned with the analysis of the waiting time distribution in an M∕M∕1 queue in which the interarrival time between the nth and the (n+1)th customers and the service time of the nth customer are correlated random variables with Downton's bivariate exponential distribution. In this paper we show that the conditional waiting time distribution, given that the waiting time is positive, is exponential.",

keywords = "Bivariate exponential distribution, Correlated queue, Workload",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: We are grateful to the reviewer for valuable comments and suggestions, which greatly improved this paper. B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2017R1D1A1B03029542 ). Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

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doi = "10.1016/j.orl.2018.02.001",

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AU - Kim, Jeongsim

N1 - Funding Information: We are grateful to the reviewer for valuable comments and suggestions, which greatly improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2017R1D1A1B03029542 ). Publisher Copyright: © 2018 Elsevier B.V.

PY - 2018/3

Y1 - 2018/3

N2 - We are concerned with the analysis of the waiting time distribution in an M∕M∕1 queue in which the interarrival time between the nth and the (n+1)th customers and the service time of the nth customer are correlated random variables with Downton's bivariate exponential distribution. In this paper we show that the conditional waiting time distribution, given that the waiting time is positive, is exponential.

AB - We are concerned with the analysis of the waiting time distribution in an M∕M∕1 queue in which the interarrival time between the nth and the (n+1)th customers and the service time of the nth customer are correlated random variables with Downton's bivariate exponential distribution. In this paper we show that the conditional waiting time distribution, given that the waiting time is positive, is exponential.

KW - Bivariate exponential distribution

KW - Correlated queue

KW - Workload

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EP - 271

JO - Operations Research Letters

JF - Operations Research Letters

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ER -

The waiting time distribution for a correlated queue with exponential interarrival and service times

Abstract

Keywords

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