Sequential Bottleneck Decomposition: An Approximation Method for Generalized Jackson Networks

Abstract

In heavy traffic analysis of open queueing networks, processes of interest such as queue lengths and workload levels are generally approximated by a multidimensional reflected Brownian motion (RBM). Decomposition approximations, on the other hand, typically analyze stations in the network separately, treating each as a single queue with adjusted interarrival time distribution. We present a hybrid method for analyzing generalized Jackson networks that employs both decomposition approximation and heavy traffic theory: Stations in the network are partitioned into groups of “bottleneck subnetworks” that may have more than one station; the subnetworks then are analyzed “sequentially” with heavy traffic theory. Using the numerical method of J. G. Dai and J. M. Harrison for computing the stationary distribution of multidimensional RBMs, we compare the performance of this technique to other methods of approximation via some simulation studies. Our results suggest that this hybrid method generally performs better than other approximation techniques, including W. Whitt's QNA and J. M. Harrison and V. Nguyen's QNET.