Expansion method for the throughput analysis of open finite manufacturing/queueing networks with N-policy

In this paper we consider arbitrary topology manufacturing (queueing) systems with finite buffers and N-policy. N-policy involves a queueing system in which the machine (server) is assigned to alternative jobs when it becomes idle and becomes available only after the queue builds up to a predetermined level of N jobs. We use the decomposition, isolation and expansion methodologies to calculate the throughput of the system. The methodology is tested rigorously by using orthogonal arrays to design the experiments in order to cover a large experimental region. The results of the methodology are compared with simulation results. To this end, we also develop a simulation model (which in itself is quite challenging). The differences in the two results are investigated using t-tests. Based on the results, the methodology proves to be remarkably accurate and robust over a broad range of parameters.