Asymptotically optimal parallel resource assignment with interference

Motivated by scheduling in multi-cell wireless networks and resource allocation in computer systems, we study a service facility with two types of users (or jobs) having heterogeneous size distributions. Our model may be viewed as a parallel two-server model, where either both job types can be served in parallel, each by a dedicated server, or both servers are simultaneously allocated to one type only (also known as "cycle stealing"). A special instance of the model is the coupled-processors model. In this paper, the aggregate service capacity is assumed to be largest when both job types are served in parallel, but giving preferential treatment to one of the job classes may be advantageous when aiming at minimization of the number of jobs, or when job types have different economic values, for example. The model finds applications in third generation wireless networks and in resource allocation of computer systems. For practical reasons, these application areas do not allow for centralized control. Still, knowledge of the theoretical achievable (centralized) optimum is extremely valuable to estimate the scope for improvement of the implemented decentralized control. We therefore set out to determine the optimal server allocation policies that in some appropriate sense minimize the total number of users in the system. At any given moment, the optimal resource allocation depends on the numbers of users present in each class. For some particular cases we can determine the optimal policy exactly, but in general this is not analytically feasible. Therefore, we study asymptotically optimal policies in the fluid limit which prove to be close to optimal. These policies can be characterized by either linear or exponential switching curves. We compare our results with existing approximations based on optimization in the heavy traffic regime, where threshold-based strategies and so-called Max-Weight policies are known to be asymptotically optimal. By simulations we show that our simple computable switching-curve strategies based on the fluid analysis in general perform well and that significant gains can be achieved compared to (i) the strategy that maximizes the aggregate service capacity at all times, (ii) the strategy that maximizes the job departure rate at all times, (iii) the threshold-based policies, and (iv) the Max-Weight policies.