## Section: New Results

### Approximate optimality with bounded regret in dynamic matching models

In [29] , we consider a dynamic matching model with random arrivals. In prior work, authors have proposed policies that are stabilizing, and also policies that are approximately finite-horizon optimal. This paper considers the infinite-horizon average-cost optimal control problem. A relaxation of the stochastic control problem is proposed, which is found to be a special case of an inventory model, as treated in the classical theory of Clark and Scarf. The optimal policy for the relaxation admits a closed-form expression. Based on the policy for this relaxation, a new matching policy is proposed. For a parameterized family of models in which the network load approaches capacity, this policy is shown to be approximately optimal, with bounded regret, even though the average cost grows without bound.