Server assignment for multi-stage production systems with finite buffers

The authors consider a multi-stage production system with finite buffers under the so-called repetitive-server blocking mechanism, modelled by a tandem queueing system with blocking. The objective is to find to which stage each server should be assigned in order to maximize the throughput. For this server assignment problem the authors first derive a throughput upper bound which is found to be very close t the exact one to be used as a substitute measure. Based on this measure they show that the rules of placing the worst servers from the outermost stages by Yamazaki et al. for the case of no buffers, are effective for the case with buffers of equal size. For the general case with buffers of different sizes, the authors propose an algorithm based on the observation that the present throughput upper bound can be increased fastest by placing the fastest servers around the smallest buffered stage. Effectiveness of this algorithm as well as the proposed rules are well demonstrated by the extensive computational experiments conducted with a number of test examples ranging up to five stages.