Unfinished work for the queue under D-policy with incomplete information on service times

Bara Kim; Jeongsim Kim; Jerim Kim

doi:10.1016/j.jkss.2012.08.001

Unfinished work for the queue under D-policy with incomplete information on service times

Bara Kim, Jeongsim Kim, Jerim Kim

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We will consider the queueing model under D-policy with incomplete information on service times. The operator does not know the actual service time of an arriving customer at each arrival epoch, but the correlated amount of the service time is known. We derive the Laplace-Stieltjes transform of the unfinished work and then obtain the mean and variance of the unfinished work. In numerical examples, the distribution function of the unfinished work is calculated by numerically inverting the Laplace-Stieltjes transform. The mean and variance of the unfinished work are depicted.

Original language	English
Pages (from-to)	205-213
Number of pages	9
Journal	Journal of the Korean Statistical Society
Volume	42
Issue number	2
DOIs	https://doi.org/10.1016/j.jkss.2012.08.001
Publication status	Published - 2013 Jun

Bibliographical note

Funding Information:
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 ( 2012-0004219 ).

Keywords

Bivariate exponential distribution
D-policy
Unfinished work

ASJC Scopus subject areas

Statistics and Probability

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10.1016/j.jkss.2012.08.001

Cite this

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title = "Unfinished work for the queue under D-policy with incomplete information on service times",

abstract = "We will consider the queueing model under D-policy with incomplete information on service times. The operator does not know the actual service time of an arriving customer at each arrival epoch, but the correlated amount of the service time is known. We derive the Laplace-Stieltjes transform of the unfinished work and then obtain the mean and variance of the unfinished work. In numerical examples, the distribution function of the unfinished work is calculated by numerically inverting the Laplace-Stieltjes transform. The mean and variance of the unfinished work are depicted.",

keywords = "Bivariate exponential distribution, D-policy, Unfinished work",

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note = "Funding Information: 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 ( 2012-0004219 ).",

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doi = "10.1016/j.jkss.2012.08.001",

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N2 - We will consider the queueing model under D-policy with incomplete information on service times. The operator does not know the actual service time of an arriving customer at each arrival epoch, but the correlated amount of the service time is known. We derive the Laplace-Stieltjes transform of the unfinished work and then obtain the mean and variance of the unfinished work. In numerical examples, the distribution function of the unfinished work is calculated by numerically inverting the Laplace-Stieltjes transform. The mean and variance of the unfinished work are depicted.

AB - We will consider the queueing model under D-policy with incomplete information on service times. The operator does not know the actual service time of an arriving customer at each arrival epoch, but the correlated amount of the service time is known. We derive the Laplace-Stieltjes transform of the unfinished work and then obtain the mean and variance of the unfinished work. In numerical examples, the distribution function of the unfinished work is calculated by numerically inverting the Laplace-Stieltjes transform. The mean and variance of the unfinished work are depicted.

KW - Bivariate exponential distribution

KW - D-policy

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JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

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ER -

Unfinished work for the queue under D-policy with incomplete information on service times

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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