SAMPLE PATH CRITERIA FOR WEAK MAJORIZATION

We present two forms of weak majorization, namely, very weak majorizat ion and p-weak majorization that can be used as sample path criteria i n the analysis of queueing systems. We demonstrate how these two crite ria can be used in making comparisons among the joint queue lengths of queueing systems with blocking and/or multiple classes, by capturing an interesting interaction between state and performance descriptors. As a result, stochastic orderings on performance measures such as the cumulative number of losses can be derived. We describe applications t hat involve the determination of optimal policies in the context of lo ad-balancing and scheduling.