Performance analysis and optimization of a retrial queue with working vacations and starting failures

This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the...

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Published inMathematical and computer modelling of dynamical systems Vol. 25; no. 5; pp. 463 - 481
Main Authors Yang, Dong-Yuh, Wu, Chia-Huang
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.09.2019
Taylor & Francis Ltd
Subjects
Algorithms
Failure analysis
Mathematical models
Matrix-geometric method
Optimization
Particle swarm optimization
Queues
Queuing theory
starting failure
Systems stability
working vacation
Online AccessGet full text
ISSN1387-3954
1744-5051
DOI10.1080/13873954.2019.1660378

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Abstract This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the matrix-geometric method to compute the stationary probability distribution of the orbit size. Some performance measures for the system are developed. We construct a cost model, and our objective is to determine the optimal service rates during normal and vacation periods that minimize the expected cost per unit time. The canonical particle swarm optimization (CPSO) algorithm is employed to deal with the cost optimization problem. Numerical results are provided to illustrate the effects of system parameters on the performance measures and the optimal service rates. These results depict the system behaviour and show how the CPSO algorithm can be used to find numerical solutions for optimal service rates.
AbstractList This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed queueing model is described in terms of the quasi-birth-death (QBD) process. We first derive the system stability condition. We then use the matrix-geometric method to compute the stationary probability distribution of the orbit size. Some performance measures for the system are developed. We construct a cost model, and our objective is to determine the optimal service rates during normal and vacation periods that minimize the expected cost per unit time. The canonical particle swarm optimization (CPSO) algorithm is employed to deal with the cost optimization problem. Numerical results are provided to illustrate the effects of system parameters on the performance measures and the optimal service rates. These results depict the system behaviour and show how the CPSO algorithm can be used to find numerical solutions for optimal service rates.
Author Yang, Dong-Yuh
Wu, Chia-Huang
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Snippet This paper presents a steady-state analysis of an M/M/1 retrial queue with working vacations, in which the server is subject to starting failures. The proposed...
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SubjectTerms Algorithms
Failure analysis
Mathematical models
Matrix-geometric method
Optimization
Particle swarm optimization
Queues
Queuing theory
starting failure
Systems stability
working vacation
Title Performance analysis and optimization of a retrial queue with working vacations and starting failures
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