這一篇論文裡，我們討論如何計算開放式有限容量等候系統的穩定機率。其中到達時間和服務時間的機率分配都是Coxian分配。我們利用向量表示法（Product-Form Method）求解穩定機率，並建立C_{k}/C_{m}/1/4與C_{k}/C_{m}/1/6的穩定機率之表格。在使用向量表示法的過程中，計算所需的時間與系統容量無關。因此，在我們計算穩定機率的經驗中，當N>100時，我們可以明顯感覺出向量表示法比一般傳統方法有更快的計算速度。 / In this thesis, we study the C_{k}/C_{m}/1/N open queueing system with finite capacity, N. We use the product-form method to solve the steady-state probabilities and give tables of numerical results in examples of C_{k}/C_{m}/1/4 and C_{k}/C_{m}/1/6. The merit of this method is that the computation time is independent of N. In our computational experiments, we have observed that when the capacity size of queueing system, N>100, the computing efficiency of the product-form method is much better than that of a traditional method.