在本篇論文中，我們研究M/M/R有限容量排隊系統，包含兩種及多種到達和服務模式。顧客的到達時間呈指數分配，服務者的服務時間亦呈指數分配。我們提出其穩態方程式，制定一些系統特性的數學表示。我們建立了兩個成本函數，分別找出其最佳解，前者在給定系統容量數的條件下，找出最佳的服務者數目；後者則是同時找出最佳的服務者數目和最佳的系統容量數。在給定系統參數值之下，我們提供了在最佳控制下的一些系統特性的數值資料，同時進行敏感度分析。

In this paper, we study the infinite source M/M/R queueing system with finite capacity N, where customers have multiple arrival modes. Arrival times of the customers obey the negative exponential distributions with parameters λi for the respective arrival mode i ( i = 1, 2, …, K ). Service times of the servers also follow the negative exponential distributions with parameters μi for the respective service mode i ( i = 1, 2, …, K ). The steady-state solutions and the expressions of the system characteristics are derived. We construct two cost models to determine the optimal solutions. In cost model 1, we determine the optimal number of servers. In cost model 2, we determine the optimal number of servers and the optimal system capacity, simultaneously. We present the numerical results for several system characteristics based on assumed numerical values given to the system parameters under optimal operating conditions. Sensitivity analysis is also investigated.

1. INTRODUCTION
1.1 Problem Statement
1.2 Literature Review
1.3 The Scope of the Study
2. STEADY-STATE RESULTS
2.1 Assumptions of the System
2.2 Steady-state equations and Solutions
2.3 System Characteristics
3. COST ANALYSIS AND SENSITIVITY ANALYSIS
3.1 Cost Analysis
3.2 Sensitivity Analysis
4. CONCLUSIONS AND FUTURE RESEARCH
4.1 Conclusions
4.2 Future Research

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