Utility-Maximizing Resource Control: Diffusion Limit and Asymptotic Optimality for a Two-Bottleneck Model

We study a stochastic network that consists of two servers shared by two classes of jobs. Class 1 jobs require a concurrent occupancy of both servers while class 2 jobs use one server only. The traffic intensity is such that both servers are bottlenecks, meaning the service capacity is equal to the offered workload. The real-time allocation of the service capacity among the job classes takes the form of a solution to an optimization problem that maximizes a utility function. We derive the diffusion limit of the network and establish its asymptotic optimality. In particular, we identify a cost objective associated with the utility function, and show that it is minimized at the diffusion limit by the utility-maximizing allocation within a broad class of “fair” allocation schemes. The model also highlights the key issues involved in multiple bottlenecks.