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

TL;DR

This paper develops a dynamic programming approach to determine optimal control policies for stochastic matching models on general graphs, specifically demonstrating the optimality of threshold policies on N-shaped graphs with linear costs.

Contribution

It extends the dynamic programming framework to N-graphs, establishing the optimality of threshold policies for discounted costs and linear holding costs in stochastic matching models.

Findings

Threshold policies are optimal for N-graphs with discounted costs.

Priority to extreme edges improves matching efficiency.

The approach generalizes previous models to more complex graph structures.

Abstract

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.