Performance evaluation of a push–pull merge system with multiple suppliers, an intermediate buffer and a distribution centre with parallel machines/channels
研究了多供应商、中间缓冲区和并行机器配送中心组成的推拉合并系统，通过连续时间马尔可夫过程建模并解析求解，为系统性能评估提供算法。
This paper examines a push–pull merge system with external demand. Multiple reliable non-identical suppliers feed a buffer that is located immediately upstream a distribution centre (DC) with parallel identical reliable machines. The DC performs another operation on the items stored in the preceding buffer and the finished products are stored in another buffer (the finished products buffer) immediately downstream the DC. Customers arrive to the system according to a Poisson process with given intensity λ and remove a finished product from the buffer of finished products. The size of a customer demand is equal to one. Both suppliers and the identical machines at DC have exponential service rates. The considered system is modelled as a continuous-time Markov process with discrete states. An algorithm that generates the transition matrix for any value of the parameters of the system is developed and all possible transition equations are derived and solved analytically. Once the transition matrix is known the performance measures of the model under consideration can be easily evaluated.