Optimization of Dynamic Matching Models

The bipartite matching model was born in the work of Gale and Shapley, who proposed the stable marriage problem in the 1960s. In this paper we consider a dynamic setting, modeled as a multi-class queueing network or MDP model. The goal is to compute a policy for the matching model that is optimal in the average cost sense. Computation of an optimal policy is not possible in general, but we obtain insight by considering relaxations. The main technical result is a form of “heavy traffic” asymptotic optimality. For a parameterized family of models in which the network load approaches capacity, a variant of the MaxWeight policy is approximately optimal, with bounded regret, even though the average cost grows without bound. Numerical results demonstrate that the policies introduced in this paper typically have much lower cost when compared to polices considered in prior work.