Performance potentials based stochastic optimization and parallel algorithm for a class of CQN

We provide new derivative formulas of the steady-state performance cost for a class of CPN (Closed Queuing Network) defined on an admissible policy set. Three fundamental quantities, performance potentials, realization factors and group inverse of the infinitesimal generator involved in the derivative formulas are given. Some simulation-based algorithms are used to estimate these performance potentials by analyzing a single sample path of CQN, and the two main methods, parallel matrix computation and CRN, are introduced to calculate these quantities. The algorithm of the optimal service policy to minimize the performance cost is obtained by using a parallel stochastic optimization method driven by a performance potential-based gradient estimate.