Modelling and optimisation of a two-server queue with multiple vacations and working breakdowns

This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduc...

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Veröffentlicht in:International journal of production research Jg. 58; H. 10; S. 3036 - 3048
Hauptverfasser: Yang, Dong-Yuh, Chen, Yi-Hsuan, Wu, Chia-Huang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Taylor & Francis 18.05.2020
Taylor & Francis LLC
Schlagworte:
Algorithms
Breakdown
canonical particle swarm optimisation algorithm
heterogeneous servers
Markov analysis
Mathematical models
matrix geometric method
multiple vacations
Particle swarm optimization
Performance evaluation
Queues
Servers
working breakdown
ISSN:0020-7543, 1366-588X
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Zusammenfassung:This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Sever 2 is unreliable and may break down while serving customers. When a breakdown occurs, Server 2 reduces the service rate rather than halting service. We formulate this queueing model as a quasi birth-and-death (QBD) process, using the matrix geometric method to compute the stationary distribution of system size. We also develop several measures to evaluate the performance of the system. A cost model based on system performance measures is formulated as a heuristic cost optimisation problem subject to stability conditions. A canonical particle swarm optimisation algorithm is used to obtain numerical solutions for the approximate optimal service rates of Server 1 and Server 2. Moreover, we present numerical results showing the effects of various parameters on the approximate optimal service rates as well as a practical example illustrating the application of the proposed model.
Bibliographie:ObjectType-Article-1
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ISSN:0020-7543
1366-588X
DOI:10.1080/00207543.2019.1624856