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標題: M[x]/M/1排隊系統含有多個假期及服務者會故障之最大熵值分析
Maximum entropy analysis to the M[x]/M/l queueing system with multiple vacations and server breakdowns
作者: 詹美娟
關鍵字: maximum entropy principle
出版社: 應用數學系
摘要: 在具有多重假期的M[x]/M/1 排隊系統中,我們考慮單一不可靠的服務者。一旦系統中變成空無一人時,服務者會離開系統為一個指數時間的假期。當他從假期返回時,如果有顧客在系統中等待,他會開始服務顧客;否則,他會享受另一個假期。服務者的故障時間及修理時間是服從負指數分配。根據服務者是處於假期、忙碌或者是故障的狀況有不同的顧客到達率。藉著使用最大熵值原理,我們建立系統中顧客數機率分配的近似公式,各種系統效能測度可以因而獲得。我們進行正確結果與最大熵值結果之間的比較分析。透過最大熵值結果,我們驗證出最大熵值原理方法對實用目的來說是足夠精確的。
We consider a single unreliable server in an M[x]/M/1 queueing system with multiple vacations. As soon as the system becomes empty, the server leaves the system for a vacation of exponential length. When he returns from the vacation, if there are customers waiting in the queue, he begins to serve the customers; otherwise, another vacation is taken. Breakdown times and repair times of the server are assumed to obey a negative exponential distribution. Arrival rate varies according to the server's status: vacation, busy, or breakdown. Using the maximum entropy principle, we develop the approximate formulae for the probability distributions of the number of customers in the system which are used to obtain various system performance measures. We perform a comparative analysis between the exact results and the maximum entropy results. We demonstrate, through the maximum entropy results, that the maximum entropy principle approach is accurate enough for practical purposes.
Appears in Collections:應用數學系所



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