Optimal resource allocation for multi-queue systems with a shared server pool

We study optimal allocation of servers for a system with multiple service facilities and with a shared pool of servers. Each service facility poses a constraint on the maximum expected sojourn time of a job. A central decision maker can dynamically allocate servers to each facility, where adding more servers results in faster processing speeds but against higher utilization costs. The objective is to dynamically allocate the servers over the different facilities such that the sojourn-time constraints are met at minimal costs. This situation occurs frequently in practice, e.g., in Grid systems for real-time image processing (iris scans, fingerprints). We model this problem as a Markov decision process and derive structural properties of the relative value function. These properties, which are hard to derive for multi-dimensional systems, give a full characterization of the optimal policy. We demonstrate the effectiveness of these policies by extensive numerical experiments.