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.

翻译：本文研究了异构网络中的动态匹配问题，其中智能体受到兼容性限制以及随机到达和离开时间的影响。特别地，我们考虑了一类易匹配智能体与多类难匹配智能体共存的网络，每类智能体均受其自身兼容性约束的制约。这种设定出现在许多实际应用中，包括肾脏交换计划和拼车平台，其中某些参与者可能具有比其他参与者更严格的兼容性要求。我们引入了一种新颖的动态匹配建模方法，通过建立常微分方程模型，为评估各种匹配算法提供了新视角。我们研究了两种算法——贪婪算法与耐心算法，这两种算法在异构网络中优先匹配兼容的难匹配智能体而非易匹配智能体。我们的结果揭示了在快速匹配与最优匹配这两个相互冲突目标之间的权衡，为实际动态匹配系统的设计提供了见解。我们通过模拟实验以及使用器官获取与移植网络数据进行的实际案例研究，验证了理论预测的有效性。