An ODE Model for Dynamic Matching in Heterogeneous Networks

TL;DR

This paper introduces an ODE-based model for dynamic matching in heterogeneous networks, analyzing algorithms that balance quick matching and optimality, with validation through simulations and real-world data.

Contribution

It presents a novel ODE modeling approach for dynamic matching, comparing greedy and patient algorithms in heterogeneous networks with real-world applications.

Findings

Trade-off between matching speed and optimality

Validation with real-world organ transplant data

Insights into algorithm design for dynamic matching

Abstract

We study 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 compatibility constraints. Such a setting arises in many real-world applications, including kidney exchange programs and carpooling platforms. We introduce a novel approach to modeling dynamic matching by establishing the ordinary differential equation (ODE) model, which offers a new perspective for evaluating various matching algorithms. We study two algorithms, namely the Greedy and Patient Algorithms, where both algorithms prioritize matching compatible hard-to-match agents over easy-to-match agents in heterogeneous networks. Our results demonstrate 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 provide simulations and a real-world case study using data from the Organ Procurement and Transplantation Network to validate theoretical predictions.