在本篇論文中，作者研究一個具有多階級、多個服務單位並且有排隊長度限制的優先佇列系統。其中針對不同優先順序的階級，對抵達過程與服務時間給予假設。本研究提供一個簡單且通用的方法，分別在可以插隊與不可以插隊的系統規則下使用有限馬可夫鏈，並在穩定狀態下，找出系統中不同階級服務對象的數量分配情形。接著，再進一步得到穩定狀態下，每種階級在系統中數量的邊際分配。透過數值分析的結果，比較本篇提出的方法在不同模型下的表現並以圖形化方式呈現系統特性。

A multi-class priority queueing system with finite capacity and service count threshold is investigated in this paper. For customers of each priority class, we give different assumptions about the arrival process and service mechanism. Under preemptive-resume and nonpreemptive priority service disciplines, we provide a simple and intuitive way to find the steady-state distributions of the number of customers in the system by the approach of finite Markov chain imbedding. Furthermore, the marginal steady-state distributions can be obtained. Numerical results and illustrations are given to show the characteristics of the system.

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