Static and decentralized-adaptive load balancing in a star configured distributed computing system

The problem of minimizing the average job response time (sojourn time) in a star configured distributed computing system (DCS) with N peripheral processors and one central processor is studied. Each peripheral processor (satellite) receives a stream of Poisson arrivals. A job arriving at a satellite S_i will be processed with a probability (1-P_i) by itself and routed to the central site for remote processing with probability P_i. The service time distribution at each processor is arbitrary with means 1/μ_i and second moments E[Y_i²], i=0,…,N. We first develop an algorithm to compute the optimal routing probabilities when the arrival and the service parameters are known a priori. We then develop an adaptive estimator to be used by each satellite to compute its optimal routing probability, when the parameters (everywhere) are unknown a priori, a copy of the algorithm runs on each peripheral processor and uses the sojourn time measurements that the peripheral processor can gather on its own from those jobs that are sent to the central processor and returned to the originating site after service