MONTE-CARLO SUMMATION AND INTEGRATION APPLIED TO MULTICLASS QUEUING-NETWORKS

Although many closed multiclass queuing networks have a product-form s olution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the applicatio n of Monte Carlo summation in order to determine the normalization con stant, throughputs, and gradients of throughputs. A class of importanc e-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then th e original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evalu ating performance measures based on integral representations of the no rmalization constant; a theory for optimal importance sampling is deve loped. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidl y solve networks that cannot be handled by the techniques in the exist ing literature.