Monte Carlo summation and integration applied to multiclass queuing networks

Abstract

Although many closed multiclass queuing networks have a product-form solution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. A class of importance-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then the original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evaluating performance measures based on integral representations of the normalization constant; a theory for optimal importance sampling is developed. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidly solve networks that cannot be handled by the techniques in the existing literature.