Throughput analysis for queueing networks with finite capacities

Abstract

The objective of this study is to present an efficient method, based on decomposition approach, which yields tight throughput upper bounds for the general open and closed queueing networks with finite buffer capacities and under any commonly used blocking mechanism. Also, by using the throughput upper bound, we develop several procedures to effectively solve the design problems of queueing networks. First, we propose a simple method obtaining the throughput upper bounds for three special networks - tandem, split, and merge configurations - under various blocking mechanisms. Also, a throughput upper bound for a general open network is given by a recursive method. Computational experiments confirm that our method is superior to other existing methods. Second, we extend the proposed method to multiple server system and two special closed networks, cycle network and central server network. Third, we show that the existing throughput-bounding methods for twostage tandem queueing networks are improved via the duality results. Besides, we show the invalidity of the method proposed by Onvural and Perros by illustrating two counter-examples. Fourth, we deal with the following optimal design models of queueing networks: (i) arrangement of station (or server assignment), (ii) allocation of service rates (or workload), (iii) allocation of extra servers, and (iv) allocation of buffers. The computational experience well demonstrates the effectiveness of our approach, so it gives many implications to system designers. Finally, some future research directions are suggested.