Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18667
標題: 排隊長度與服務者相關之有限容量M/M/3排隊系統
Queue-Dependent Servers in an M/M/3 Queueing System with Finite Capacity
作者: 戴亢袁
關鍵字: Queue-Dependent Servers
排隊長度
Queue Size
出版社: 應用數學系
摘要: 本篇論文裡,我們研究在穩態狀況下,服務者數目隨顧客人數之增加而增加的有限容量M/M/3排隊系統。我們假設在第一位服務者前面等待服務之顧客人數累積到N個的時候(N為決策變數),第二位服務者立即進入此系統並且開始服務顧客,當顧客人數繼續增加且累積到M個的時候(M亦為決策變數),第三位服務者立即進入此系統服務顧客。我們也假設系統的容量為有限且這三位服務者的服務率都不相同。 首先,我們推導此系統之穩態解,然後,推導出此系統的特徵值,諸如排隊之顧客人數的期望值及系統中顧客人數的期望值。最後,我們建立一個成本之間的關係模式,進而決定在此系統下,提供第二位服務者及第三位服務者時的最佳排隊長度N和M以使系統獲得最大利益。
In this thesis, a finite M/M/3 queueing system is analyzed in steady state by assuming that the number of servers changes depending on the number of customers in the system. We suppose that when the number of customers waiting in front of the first server reaches a specific level, denoted by N, which is a decision variable, the second server joins the system immediately and begins serving. When the number of customers in the system increases to another specific level, say ,M (M > N), which is also a decision variable, the third server joins the system immediately and begins serving. We assume that the service abilities of each server are different. The system characteristics such as the expected number of customers in the queue, the expected number of customers in the system are derived. A relationship among the costs is developed to determine the optimal queue lengths N and M simultaneously of providing the second server and the third server in order to obtain the maximum profit. Special cases are also presented.
URI: http://hdl.handle.net/11455/18667
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