Dynamic programming for the stochastic matching model on general graphs: the case of the `N-graph'

In this paper, we address the optimal control of stochastic matching models on general graphs and single arrivals having fixed arrival rates, as introduced in \cite{MaiMoy16}. On the N-shaped' graph, by following the dynamic programming approach of \cite{BCD19}, we show that a Threshold’-type policy on the diagonal edge, with priority to the extreme edges, is optimal for the discounted cost problem and linear holding costs.