Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks
This paper presents a discrete-time Geo/G/1 retrial queue with two waiting buffers to model an ATM network, in which the server begins a single vacation in cases where the system is empty at the instant of a service completion. New arriving customer who finds the server being on vacation can decide...
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2019-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2019/4193404 |
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doaj-bc4f9c8cda6441b0bef47a61f115ccfb2020-11-25T01:18:09ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/41934044193404Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM NetworksShan Gao0Xianchao Wang1School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, ChinaSchool of Computer and Information Engineering, Fuyang Normal University, Fuyang 236037, ChinaThis paper presents a discrete-time Geo/G/1 retrial queue with two waiting buffers to model an ATM network, in which the server begins a single vacation in cases where the system is empty at the instant of a service completion. New arriving customer who finds the server being on vacation can decide to either enter the retrial buffer with some probability p or leave the system with complementary probability 1−p. But the new arriving customer can begin its service immediately if he finds the server idle and join the original buffer if he finds the server busy. We first carry out an extensive analysis of the model by using the supplementary variable method and the generating function approach, and give some performance measures, such as server’s state probabilities and mean queue lengths in the original buffer, retrial buffer, and in the system. Secondly, we give the generating function of the sojourn time of a customer in the system and prove that Little’s law still holds in our model. Sensitivity analysis and cost optimization are finally given for illustrative purposes.http://dx.doi.org/10.1155/2019/4193404 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shan Gao Xianchao Wang |
spellingShingle |
Shan Gao Xianchao Wang Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks Mathematical Problems in Engineering |
author_facet |
Shan Gao Xianchao Wang |
author_sort |
Shan Gao |
title |
Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks |
title_short |
Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks |
title_full |
Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks |
title_fullStr |
Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks |
title_full_unstemmed |
Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks |
title_sort |
analysis of a single server retrial queue with server vacation and two waiting buffers based on atm networks |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2019-01-01 |
description |
This paper presents a discrete-time Geo/G/1 retrial queue with two waiting buffers to model an ATM network, in which the server begins a single vacation in cases where the system is empty at the instant of a service completion. New arriving customer who finds the server being on vacation can decide to either enter the retrial buffer with some probability p or leave the system with complementary probability 1−p. But the new arriving customer can begin its service immediately if he finds the server idle and join the original buffer if he finds the server busy. We first carry out an extensive analysis of the model by using the supplementary variable method and the generating function approach, and give some performance measures, such as server’s state probabilities and mean queue lengths in the original buffer, retrial buffer, and in the system. Secondly, we give the generating function of the sojourn time of a customer in the system and prove that Little’s law still holds in our model. Sensitivity analysis and cost optimization are finally given for illustrative purposes. |
url |
http://dx.doi.org/10.1155/2019/4193404 |
work_keys_str_mv |
AT shangao analysisofasingleserverretrialqueuewithservervacationandtwowaitingbuffersbasedonatmnetworks AT xianchaowang analysisofasingleserverretrialqueuewithservervacationandtwowaitingbuffersbasedonatmnetworks |
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