Optimal Resource Allocation Under The Best Station Weights In Gen- Eralized Jackson Network

In this paper, we focus on the resource allocation problem in generalized Jackson network. Under certain cost constraints, we should allocate proper resource capacity to each server station to minimize the sum of weighted queue lengths when the network achieves steady-state. Given a fixed weight vector, we can propose the corresponding allocation method. However, in some applications the controller of the network don’t know the weight vector in advance, or the weight vector may be changeable. Thus, we regard the weight vector as another variable and discuss the best and worst weight vector, as well as the corresponding queue lengths. Roughly speaking, they can be regarded as the lower and upper bound for the expectation of queue length. For the best one, we can devise the corresponding greedy schedule. For the worst one, we can get the minimum guaranteed performance which we can surely achieved with proper schedule.For the networks with produce-form solutions, we give out the analytical solutions of the best and worst weight. For those without product-form solutions, we discuss the condition in which the worst weight occurs. Then, we prove the existence and uniqueness of the worst weight and propose a sequence of iterations to achieve the worst weight. At last, we conduct some easy numerical experiments.