Asymptotically Optimal Parallel Resource Assignment With Interference

Motivated by scheduling in cellular wireless networks and resource allocation in computer systems, many researchers have studied a service facility with two classes of users having heterogeneous service requirement distributions. In this paper, we will study the case with three classes of users and three servers. The aggregate service capacity is assumed to be largest when all the classes are served in parallel, but giving preferential treatment to one of the classes may be advantageous when aiming at min-imization of the number of users, or when classes have different economic values.We set out to determine the allocation policies that minimize the total number of users in the system. For some particular cases we can determine the optimal policy exactly, but in general this is not feasible. We then study the optimal policies in the fluid regime, which prove to be close to optimal in the original stochastic model in some sense.