Multivariate rational approximants for multiclass closed queuing networks

Closed Markovian networks of queues with multiclass customers and having a product form equilibrium state probability distribution are useful in the performance evaluation and design of computer and telecommunication systems. Therefore, the efficient computation of the normalizing function, the key element of the solution in product form, has attracted considerable effort. We consider a network that consists of one infinite-server (IS) station and one processor-sharing (PS) or FCFS single-server station. We use multivariate Newton-Pade approximants computed from data for small numbers of customers in each class, to estimate the normalizing function for a larger population in the network. The effectiveness and tremendous gain in computing time of this procedure are illustrated through various numerical experiments.