Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation

This research analyzes a multi-server retrial queue with two types of calls: working vacation and working breakdown. The incoming call may enter the retrial queue and attempt to seize a server after a random delay if all the servers are unavailable upon arrival. In its idle time, the server makes ou...

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Main Authors: Tzu-Hsin Liu, He-Yao Hsu, Fu-Min Chang
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Algorithms
Subjects:
Online Access:https://www.mdpi.com/1999-4893/18/1/24
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author Tzu-Hsin Liu
He-Yao Hsu
Fu-Min Chang
author_facet Tzu-Hsin Liu
He-Yao Hsu
Fu-Min Chang
author_sort Tzu-Hsin Liu
collection DOAJ
description This research analyzes a multi-server retrial queue with two types of calls: working vacation and working breakdown. The incoming call may enter the retrial queue and attempt to seize a server after a random delay if all the servers are unavailable upon arrival. In its idle time, the server makes outgoing calls. All the servers take a synchronous working vacation when the system empties after regular service. The system may fail at any time due to disasters, forcing all the calls within the service area to leave the system and causing all the main servers to fail. When the main servers fail, the repair process begins immediately. The standby servers serve arriving customers at a lower level of service during the working breakdown or working vacation. For this model, we derive an explicit expression for the stationary distribution with the help of the quasi-birth-and-death process and the matrix geometric method. Further, the formulas of various system performance indices are developed. An application example is given and several numerical experiments are performed to verify the analytical results. We also perform the comparative analysis of retrial queues with/without two-way communication and two-way communication retrial queues with/without disasters. The results reveal that the proper consideration of outgoing calls to the server can reduce the average time spent in the buffer. Furthermore, a more reliable server reduces the server idle rate.
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spelling doaj-art-a79872ed76c44ca9a37a3b20e85bac4f2025-01-24T13:17:31ZengMDPI AGAlgorithms1999-48932025-01-011812410.3390/a18010024Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working VacationTzu-Hsin Liu0He-Yao Hsu1Fu-Min Chang2Department of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, TaiwanPh.D. Program of Business Administration in Industrial Development, Department of Business Administration, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, TaiwanDepartment of Finance, Chaoyang University of Technology, 168, Jifeng East Road, Wufeng District, Taichung City 41349, TaiwanThis research analyzes a multi-server retrial queue with two types of calls: working vacation and working breakdown. The incoming call may enter the retrial queue and attempt to seize a server after a random delay if all the servers are unavailable upon arrival. In its idle time, the server makes outgoing calls. All the servers take a synchronous working vacation when the system empties after regular service. The system may fail at any time due to disasters, forcing all the calls within the service area to leave the system and causing all the main servers to fail. When the main servers fail, the repair process begins immediately. The standby servers serve arriving customers at a lower level of service during the working breakdown or working vacation. For this model, we derive an explicit expression for the stationary distribution with the help of the quasi-birth-and-death process and the matrix geometric method. Further, the formulas of various system performance indices are developed. An application example is given and several numerical experiments are performed to verify the analytical results. We also perform the comparative analysis of retrial queues with/without two-way communication and two-way communication retrial queues with/without disasters. The results reveal that the proper consideration of outgoing calls to the server can reduce the average time spent in the buffer. Furthermore, a more reliable server reduces the server idle rate.https://www.mdpi.com/1999-4893/18/1/24disastermulti-server retrial queuerepairsynchronous working vacationtwo-way communication
spellingShingle Tzu-Hsin Liu
He-Yao Hsu
Fu-Min Chang
Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
Algorithms
disaster
multi-server retrial queue
repair
synchronous working vacation
two-way communication
title Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
title_full Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
title_fullStr Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
title_full_unstemmed Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
title_short Multi-Server Two-Way Communication Retrial Queue Subject to Disaster and Synchronous Working Vacation
title_sort multi server two way communication retrial queue subject to disaster and synchronous working vacation
topic disaster
multi-server retrial queue
repair
synchronous working vacation
two-way communication
url https://www.mdpi.com/1999-4893/18/1/24
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AT heyaohsu multiservertwowaycommunicationretrialqueuesubjecttodisasterandsynchronousworkingvacation
AT fuminchang multiservertwowaycommunicationretrialqueuesubjecttodisasterandsynchronousworkingvacation