在本篇論文中提及的佇列系統（Queueing system）包含N個相同的處理器。工作（Jobs）進入此系統的速率是根據卜松程序（Poisson Process）。在系統內的所有工作中，最多有M個工作是處於預備狀態可以被同時處理。其餘的工作必須在等待佇列中等待。當處理器處理完一個子工作（Task）之後，它會隨機選取M個預備工作中的其中一個，並處理這個工作的其中一個子工作。每個工作一開始的時候僅包含一個可執行的子工作。當一個子工作執行結束之後，它將引發零個或多個子工作。當一個工作的所有子工作都結束時，這個工作也就結束了。
要對這樣的系統做精確的分析是十分困難的。在這篇論文中，我們得一個準確的近似值計算方法來計算工作在此系統的平均回應時間。最後，我們也針對工作的特性及系統參數對系統效能的影響做研究。

The queueing system considered in this thesis consists of N identical servers. Jobs arrive at the system according to a Poisson process. Among all the jobs in the system, a maximum of M jobs can be ready for service simultaneously. The rest of the jobs must wait in a waiting queue. When a service becomes available, one of the jobs currently ready for service is selected randomly and then one of the task belonging to the selected job is chosed for service. A job consists of one task initially. Zero or more tasks may become ready for service when a task finished service. A job completes it service when all of its tasks are completed. Exact performance analysis of a multi-server system serving parallel jobs with general task graphs is very difficult. In this thesis, we obtain an accurate approximation to the mean job response time. The effects of the characteristics of the jobs and system parameters on the system performance are also studied.