Simple, Efficient Computation of the Generalized Throughput of Jackson Networks

A Gauss-Seidel (successive substitutions) method for solving the generalized throughput equation for (possible unstable) Jackson networks is considered. It is shown that a monotonicity property of the Gauss-Seidel operator can be exploited to produce two sequences of throughput estimates: one converging to the true throughput from below and the other from above. Thus, the two can be computed together and the computation stopped when their difference is small. A simple bound on the rate of convergence is given, and a heuristic for organizing the computation to accelerate convergence is suggested.