柯沛程952221E025004

柯沛ç&...

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(期中進度報告) 具布瓦崧到達排隊系統之變異假期策略研究(2/3) The study for the Poisson input queue with variant vacation policies 計畫編號: NSC 95-2221-E-025-004- 執行期限: 95/08/01 ~ 96/07/31 主持人:柯昭川教授 台中技術學院統計系 一、中文摘要 本計畫在第二年研究二個變異的 假期 NT 策略下 M/G/1 排隊模式之控 制策略,其中服務者為不可信任且在 他的每一個忙碌週期前要求一般分配 的啟動時間,服務者假期週期的長度 由閒置週期到達的顧客數或時間來控 制。當系統沒有顧客時,服務者立即 取一個 T 長度假期且操作下列兩個不 同假期策略之其中一個: (1) 當等待服務顧客數達到 N 個或第 一位到達的顧客等待服務的時間 達到 T 單位時間,則服務者立即啟 動,準備提供服務。 (2) 當等待服務顧客數達到 N 個或自 上一個完成(忙碌)週期結束後時 間已經過 T 單位,服務者立即啟 動(開啟),準備提供服務。 我們推導這變異假期系統之穩態解析 特性,例如:系統中顧客數機率分配, 服務者忙碌期間分配與期望長度,及 服務者休息期間分配與期望長度等。 此外我們建立成本模式,求最佳的聯 合門檻 (N * , T * ) ,使成本達到最小。 關鍵詞 :成本模式 動態最佳化;馬 可夫鏈。 本 計 畫 第 一 年 部 分 成 果 已 被 Mathematical and Computer Modelling 接受 本計畫第二年的成果已 submit to Computers and Industrial Engineering 英文摘要 In the second-year project, we study the control policies of an M/G/1 queueing system with a startup and un-reliable server, in which the length of the vacation period is controlled either by the number of arrivals during the idle period, or by a timer. After all the customers are served in the queue exhaustively, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time
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units have elapsed since the end of the completion period. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. Furthermore, it is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. We analyze the system characteristics for each scheme. The total expected cost function per unit
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This note was uploaded on 11/27/2009 for the course IM MA420 taught by Professor Mar,lee during the Spring '09 term at National Taiwan University.

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柯沛ç&...

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