Adaptive performance optimization of loosely coupled processors

Routing stationary Poisson arrivals at a common scheduler probabilistically to N heterogeneous processors with exponential service distributions is considered. The objective is to minimize the overall average response time. Based on the solution to the known parameter problem, an adaptive estimator is proposed for the scheduler to learn the optimal routing probabilities when the system parameters are not known a priori. The demand is assumed to be less than the overall capacity to ensure the existence of a stable solution. The adaptive estimator utilizes the data that the scheduler can gather on its own, without any communication overhead. It is designed to function well even when a subset of processors are useless and should not receive jobs. The adaptive estimator converges to the optimum with probability 1 and in the mean square sense. Simulation experiments are presented to demonstrate its performance in a variety of practical situations. An extension involving additional unknown arrivals at individual processors is worked out