Continuous Time Analysis of Dynamic Matching in Heterogeneous Networks

This paper addresses the problem of dynamic matching in heterogeneous networks, where agents are subject to compatibility restrictions and stochastic arrival and departure times. In particular, we consider networks with one type of easy-to-match agents and multiple types of hard-to-match agents, each subject to its own set of compatibility constraints. Such a setting arises in many real-world applications, including kidney exchange programs and carpooling platforms, where some participants may have more stringent compatibility requirements than others. We introduce a novel approach to modeling dynamic matching by establishing ordinary differential equation (ODE) models, offering a new perspective for evaluating various matching algorithms. We study two algorithms, the Greedy Algorithm and the Patient Algorithm, which prioritize the matching of compatible hard-to-match agents over easy-to-match agents in heterogeneous networks. Our results show the trade-off between the conflicting goals of matching agents quickly and optimally, offering insights into the design of real-world dynamic matching systems. We present simulations and a real-world case study using data from the Organ Procurement and Transplantation Network to validate theoretical predictions.