具有容量C之M/G/1佇列系統性能分析

Performance Analysis of M/G/1 Queue with Capacity C

姜玲鳳(Ling-Feng Chiang)

指導教授 ： 王居尉

亞洲大學/資訊學院/電腦與通訊學系碩士班/碩士(2006年)

摘要

相較於傳統的佇列理論假設系統的服務器在一時間僅能服務一個客戶，本論文提出另一種具有同時可以處理多個客戶服務器的佇列系統，在實際的應用上，如具有多重處理功能的中央處理器是這個提議的佇列系統的一個很好的例子，我們稱此佇列系統為具有容量 的佇列系統。本論文將處理具有容量 之M/G/1 系統的數學分析，特別強調於在給定參數下的平均等待時間的機率分佈，並將以M/M/1 系統為例進行數值分析，以探討到達速率及服務速率對系統的平均等待時間及穩定性的影響。

關鍵字

M/G/1佇列模式、容量、平均等待時間、佇列長度

並列摘要

In contrast to the conventional queueing system assuming a server can serve custom at a given time, an alternative queueing system in which a server is assumed to be able to serve customs concurrently is proposed in this thesis. In practical applications, the central processor unit with multi-task capacity is a good example of the proposed system. We call this system a queueing system with capacity . This thesis deals with the mathematical analysis of the M/G/1 queue with capacity , with focus on the derivation of mean waiting time for a given set of parameters. In addition, we use the M/M/1 queue to do numerical computation so as to evaluate the impacts of arrival rate and service rate on the mean waiting time and system’s stability.

並列關鍵字

M/G/1 queueing model ,capacity ,mean waiting time , queueing length .

參考文獻

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