Maximizing throughput in finite-source parallel queue systems

Motivated by the dispatching of trucks to shovels in surface mines, we study optimal routing in a Markovian finite-source, multi-server queueing system with heterogeneous servers, each with a separate queue. We formulate the problem of routing customers to servers to maximize the system throughput as a Markov Decision Process. When the servers are homogenous, we demonstrate that the Shortest Queue policy is optimal, and when the servers are heterogenous, we partially characterize the optimal policy and we present a near-optimal and simple-to-implement policy. We use the model to illustrate the substantial benefits of pooling, by comparing it to permanent assignment of customers to servers.