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標題: M/Eκ/1 排隊系統含有可移動服務站之最佳控制
Optimal Control of an M/Eκ/1 Queueing System with Removable Service Station
作者: 黃惠美
Huang, Hui-Mei
關鍵字: Queueing system
Removable service station
N -政策
出版社: 應用數學研究所
摘要: 本篇論文分別討論有限及無限容量的 M/Eκ/1排隊系統含有一可移動服務 站之最佳控制,而以N-政策為控制決策。所謂N-政策,乃指系統中顧客個 數累積至N 位時,服務站則立即被開啟,以服務顧客;而當系統中所有顧 客都被服務完時,則服務站立刻被關閉,此時顧客到達系統時並未被立即 服務,只有當系統中的顧客個數再累積至N 位時,才又開始被服務站服務 。如此的循環一直重覆進行著。首先我們分別推導出在有限及無限容量時 系統的穩定特徵值,諸如系統中顧客數的機率分配及顧客數的期望值等。 其結果含概了下列三種排隊系統:(1) 標準 M/M/1排隊系統;(2) 標準 M/Eκ/1排隊系統;(3) 含有一可移動服務站之 M/M/1 排隊系統。最後我 們定義出每單位時間的總穩態期望成本,然後決定出控制參數N 的最佳解 N*,使成本函數達到最小值。
This thesis studies the optimal control N-policy of a removable service station in an M/Eκ/1 queueing systems with infinite and finite capacities, respectively, under steady-state conditions. The N-policy is to turn the service station on when the queue size reaches N which is a positive integer, and turn it off when the system is empty. We develop the steady-state characteristics of the infinite capacity and finite capacity systems such as the probability distributions of the number of customers in the system, the expected number of customers in the system, and so on. The controllable M/Eκ/1 queueing system generalizes the ordinary M/M/1 queueing system, the ordinary M/E κ/1 queueing system, and the controllable M/M/1 queueing system. We derive the total expected cost functions per unit time, and determine the optimal value of the control parameter N, say N*, in order to minimize the cost functions for these two systems.
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