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.

翻译：我们研究异构网络中的动态匹配问题，其中代理节点受兼容性限制及随机到达与离开时间的影响。具体而言，我们考虑包含一类易匹配代理与多类难匹配代理的网络，每类代理均具有各自的兼容性约束。这类情境广泛存在于肾脏交换计划与拼车平台等现实应用中。我们通过建立常微分方程（ODE）模型提出了一种动态匹配建模的新方法，为评估各类匹配算法提供了全新视角。研究分析了贪婪算法（Greedy）与耐心算法（Patient）两种方法，两种算法在异构网络中均优先匹配兼容的难匹配代理。研究结果揭示了快速匹配与最优匹配这对矛盾目标之间的平衡关系，为现实世界动态匹配系统的设计提供了启示。我们通过数值模拟及基于器官获取与移植网络（Organ Procurement and Transplantation Network）数据的真实案例研究，验证了理论预测的有效性。