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^*

^*Corresponding author for this work

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

15 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

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Joint transform
Retrial queue
Two way communication

ASJC Scopus subject areas

General Decision Sciences
Management Science and Operations Research

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10.1007/s10479-020-03717-2

Cite this

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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.",

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AU - Lee, Se Won

AU - Kim, Bara

AU - Kim, Jeongsim

PY - 2022/3

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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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DO - 10.1007/s10479-020-03717-2

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SP - 505

EP - 518

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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