Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

Se Won Lee; Bara Kim; Jeongsim Kim

doi:10.1007/s10479-020-03717-2

Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

Se Won Lee, Bara Kim, Jeongsim Kim

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.

Original language	English
Pages (from-to)	505-518
Number of pages	14
Journal	Annals of Operations Research
Volume	310
Issue number	2
DOIs	https://doi.org/10.1007/s10479-020-03717-2
Publication status	Published - 2022 Mar

Keywords

Joint transform
Retrial queue
Two way communication

ASJC Scopus subject areas

Decision Sciences(all)
Management Science and Operations Research

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10.1007/s10479-020-03717-2

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title = "Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication",

abstract = "We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.",

keywords = "Joint transform, Retrial queue, Two way communication",

author = "Lee, {Se Won} and Bara Kim and Jeongsim Kim",

note = "Funding Information: We are grateful to the reviewers for valuable comments and suggestions. S.W. Lee{\textquoteright}s research was supported by the Pukyong National University Research Fund in 2019 (C-D-2019-1249). B. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government(MSIT) (No. 2020R1A2B5B01001864). J. Kim{\textquoteright}s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568). Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = mar,

doi = "10.1007/s10479-020-03717-2",

language = "English",

volume = "310",

pages = "505--518",

journal = "Annals of Operations Research",

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AU - Lee, Se Won

AU - Kim, Bara

AU - Kim, Jeongsim

N1 - Funding Information: We are grateful to the reviewers for valuable comments and suggestions. S.W. Lee’s research was supported by the Pukyong National University Research Fund in 2019 (C-D-2019-1249). B. Kim’s research was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government(MSIT) (No. 2020R1A2B5B01001864). J. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01065568). Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/3

Y1 - 2022/3

N2 - We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.

AB - We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.

KW - Joint transform

KW - Retrial queue

KW - Two way communication

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SN - 0254-5330

VL - 310

SP - 505

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JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 2

ER -

Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

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Keywords

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