Modelling manufacturing systems: A birth-death approach

An approximation method for modelling a manufacturing system is introduced. The system is considered as a queueing network, where each queue is limited in size, and interarrival and processing times are exponentially distributed. The birth-death approach is considered and an approximation method to reduce the dimension of the model is developed. The results are the marginal probability distribution of the number of units in each queue; other performance indices, such as mean queue lengths, utilizations of the working stations, and throughput can be easily obtained. The general procedure is applied to model, for example, queues in tandem, a split node, and a more complex network of queues. Simulation and, when possible, comparison with the exact solution show an acceptable error level of the proposed method.