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標題: M/M/R 有限容量排隊系統含阻礙, 放棄, 以及服務者故障之效能測度分析
Performance Measures Analysis of the M/M/R Queueing System with Finite Capacity plus Balking, Reneging, and Server Breakdowns
作者: 張英仲
關鍵字: balk
server breakdowns
出版社: 應用數學系
摘要: 在本篇論文,我們研究 M/M/R 有限容量排隊系統,包含阻礙、放棄,以及服務者故障。顧客到達服從卜瓦松過程,參數是 。而顧客被服務的時間則是服從指數分配,參數是 。顧客到達具有 (1-bn) 的機率遇到阻礙 (不進入排隊) 以及放棄 (進入排隊後卻離開) 的時間依照指數分配。服務者在任何時間都可能會故障,甚至沒有顧客在這排隊系統中,故障率是 。當服務者故障時,它會馬上被送去修理,修理率是 。假設服務者的故障時間跟修理時間都是服從指數分配。我們使用matrix- geometric method 去推導穩態的機率,而多種系統效能測度可以因而獲得。接著發展一個成本模型,用以決定最佳的服務者個數。在給定的系統參數值之下,我們計算出一些系統測度分析的數值結果。同時,我們也研究了敏感度分析。
In this thesis, we study the M/M/R queueing system with finite capacity plus balking, reneging, and server breakdowns. Customers arrive following a Poisson process with parameter . The service times of the customers according to a negative exponential distribution with parameter . Arriving customers balk (do not enter) with a probability (1-bn) and renege (leave the queue after entering) according to a negative exponential distribution. The server can break down at any time with breakdown rate even if no customers are in the system. When the server fails, he is immediately repaired at a repair rate . Breakdown times and repair times of the servers are assumed to follow a negative exponential distribution. We use a matrix- geometric method to derive the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is developed to determine the optimum number of servers. Numerical results are presented in which several system performance measures are evaluated based on assumed numerical values given to the system parameters. Sensitivity analysis is also investigated.
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