| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 100 === Queuing is one of the features of modern civilized society. The more civilized the society, the more common the phenomenon is. Generally, guests do not like to wait, neither do the service providers like the resulting increase cost. Therefore, the Queueing Theorem has come to existence. We consider M/M/R warm standby machine repair problem with balking, reneging, and service pressure coefficient. First, we establish the steady-state equation, and then apply the birth-and-death process to calculate the steady-state probability, following by coding Maple programs to execute the system performance measurement. Focusing on the cost function F(R,S,μ,r), we use the direct search method to find the optimum value(R*,S*)， with the optimum number of repairmen R and standby machines S , having μ and r fixed. Next, we use the Quasi-Newton method to calculate the optimum cost F(R*,S*,μ*,r*) with fixed(R*,S*).
An artificial intelligence method of optimization that rises in recent years, the Particle Swarm Optimization, PSO, is a random search algorithm with a base of random population. In this paper, we use Maple to operate the PSO optimization, finding the minimal cost in the queueing system, with the aid of simultaneous multiple particle searching and the iterative method. We apply several examples to compare the minimal cost by the PSO and the Quasi-Newton method respectively, suggesting that the PSO can offer lower cost than the Quasi-Newton method does, with the rate of improvement as high as more than 30%.
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