A New Ordering for Stochastic Majorization: Theory and Applications

In this paper, we develop a uniied approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings deened in Marshall and Olkin, by deening a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but diier for random vectors. Sample path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various fork-join queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with nite buuers.