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. Scope and purpose Manufacturing systems these days are complex networks of service stations with finite capacities. In order to model such networks, researchers usually resort to simulation modeling just to capture the finite capacity restriction. However, a recently reported approximation technique, called the expansion methodology, has proven to be extremely robust. In this paper, an additional complication is introduced to the manufacturing system. In order to increase the utilization of machines (or minimize machine idle time), the work at a station is actually accumulated while the machine at that station is assigned to alternative jobs as soon as it becomes idle. The machine keeps processing these alternative jobs till the accumulated work at the station reaches a predetermined level of N jobs. In order to capture all these complications, this paper uses decomposition, isolation and expansion methodologies to develop an analytical (approximation) technique to model such a system. System throughput is used as the overall measure of performance. The technique is thoroughly tested and is found to be reliable, easy to program and robust.