Algorithms of decentralized optimization for a class of closed queueing network by using performance potentials

Optimization algorithms are provided for a class of closed queueing networks with a general performance cost that depends on both the state of the network systems and the service rate of each server. Three quantities, i.e., realization factors, performance potential and group inverse of the infinitesimal generator, are used to calculate the derivative of the steady-state performance cost with respect to the service rate. An optimal policy is obtained by using a direct gradient search method so as to minimize the performance cost. A numerical example has been used to illustrate the application of the proposed algorithms.