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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/156434


    Title: 某些動態服務線上有效計算等候時間的方法 (II)
    An Efficient Approach to Solving Certain Service Waiting Time with Dynamic Queueing Models (Ii)
    Authors: 陸行
    Contributors: 應數系
    Date: 2018-10
    Issue Date: 2025-03-31 11:55:28 (UTC+8)
    Abstract: 在此研究計畫中，我們調查受價格影響的佇列機制。這種機制包括兩個平行佇列，一個是收費 的佇列，另一個不收費。收費的佇列為了保證最大的等候時間，而且資源在預算控管下其佇列只 提供有限的位置；但不收費的佇列不受人數限制，其等候的時間可能比較長。顧客排隊時可以選 擇加入收費的佇列或不收費的佇列，我們要調查受收費佇列的價格會對兩種佇列產生何種影響。 因為排隊長度會影響顧客的付費意願，在計算時必須動態地考慮排隊人數變化對於整體等候時 間的影響，傳統的等候線計算模型無法呈現這種動態性的排隊機制。以類生死過程建立之計算矩 陣，其矩陣幾何解(Matrix geometric solution)需要佔用大量的計算時間。其傳統的計算方法也 無法有效性且快捷的找出相關的機率分配值。我們於計畫中提出以特徵值做核心的計算方法，解 出穩態機率分配(Stationary probability distribution)。以此機率分配可以依據排隊長度變化 快速地提出正確計算且有效之價格分析。於去年(第一年)計畫內，我們建立一計算方法和其理論 分析與證明，解出佇列的等候時間。今年(第二年)則將價格設為變數，計算價格對佇列的影響和 繁忙系統(Busy period)的使用效率的機率分配。由於顧客以排隊的長度和價格作為是否加入收費 佇列的依據，這種動態變化不是傳統的繁忙系統公式所能解出，我們必須利用卡塔蘭組合數 (Catalan number)建立此系統的動態排隊行為模式，進而計算其機率分配，希望能有效地計算相 關的評估再以模擬數據驗證之。
    In this project, we look into a scheme of price-affected queues in which there is a two-tier service system with heterogeneous delay sensitivity via a two parallel queue model. A two-tier service system with one free and one toll service channels is constructed for consideration in the proposal. While the free system offers free service with a long wait time, the toll system offers paid service with a guaranteed maximum expected wait time. We investigate the effects of the toll system's pricing and service guarantee policies on the performance of the two-tier service system. Depending on the special structure of the infinitesimal generator matrix, some innovative and efficient computational algorithms are developed for evaluating their performance. We had proved that the proposed approach is a more efficient algorithm than Geometric-Matrix method for solving this two-tier service queueing model, especially when the buffer size is large last year (the first year). After attaining the stationary probability it studies the busy period of a two-tier service system this year (the second year). A system state pathway formulation by Catalan numbers is given to compute the probabilities for serving n customers in a busy period and expressions for the first two moments are to be derived. A study of transient queue length fluctuations during a busy period provides quantitative measures that enable proactive resource management for optimal system performance and capacity utilization.
    Relation: 科技部, MOST106-2221-E004-008, 106.08-107.07
    Data Type: report
    Appears in Collections:[應用數學系] 國科會研究計畫

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