Multi-class multi-server queueing networks for production systems design

Product form queueing networks with multiple customer classes and multiple server stations arise in the design and performance evaluation of stochastic jobshop models of manufacturing, warehousing and logistic systems. Real-size models of this type cannot be solved by the classical Mean Value Analysis (MVA) algorithm, due to its exponential computational complexity in the number of classes. Consolidated (pseudo) polynomial approximation methods have been proposed in literature since some decades. They are based on the transformation of the recursive MVA equations in a system of nonlinear equations to be solved iteratively. Unfortunately these contributions do not cover the case of stations with multiple servers. A new technique based on the idea of class aggregation to cope with the latter case, under a first-come-first-served policy is presented. Preliminary numerical experiments are encouraging upon comparison against the exact MVA algorithm.