| Summary: | 碩士 === 國立臺北商業大學 === 資訊與決策科學研究所 === 107 === This thesis analyzes an M/M/2 queue with multiple vacations, working breakdowns and heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and leaves for a vacation when the system becomes empty. Sever 2 is unreliable and may break down unexpectedly while serving customers. When a breakdown occurs, Server 2 still works rather than halting service. For this queueing system, we use the matrix geometric method to compute the stationary distribution of system size and develop several system performance measures. We formulate a cost optimization model, and employ the canonical particle swarm optimization algorithm to obtain the optimal service rates of Server 1 and Server 2. Numerical examples are given to show the effects of system parameters on the approximated optimal service rates. Finally, we present a practical example to illustrate the application of this system.
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