含單一可移動及會故障服務者之 -方策 M/G/1 排隊系統之最大熵値研究

This thesis analyzes a single removable and unreliable server in the -policy M/G/1 queueing system in which the server breaks down according to a Poisson process and the repair time obeys an arbitrary distribution. We assume that when the number of customers in the system reaches N, turn the server on with probability p and leave it off with probability (1 − p). The use of maximum entropy approach is to develop the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system. We perform the comparative analysis between approximate results and exact results with four different service time and repair time distributions, including exponential,uniform, gamma, and deterministic. It appears from numerical results that the maximum entropy approach is sufficiently accurate for practical use and based on the maximum entropy approach , we demonstrate that the -policy M/G(G)/1 queueing system is sufficiently robust to the variations of service time distribution and repair time distribution functions.