Title: Priority Queue Formulation of Agent-Based Bathtub Model for Network Trip Flows in the Relative Space Show Chinese title

Title: 基于智能体的相对空间网络出行流浴盆模型的优先队列公式化

Abstract: Agent-based models have been extensively used to simulate the behavior of travelers in transportation systems because they allow for realistic and versatile modeling of interactions. However, traditional agent-based models suffer from high computational costs and rely on tracking physical locations, raising privacy concerns. This paper proposes an efficient formulation for the agent-based bathtub model (AB2M) in the relative space, where each agent's trajectory is represented by a time series of the remaining distance to its destination. The AB2M can be understood as a microscopic model that tracks individual trips' initiation, progression, and completion and is an exact numerical solution of the bathtub model for generic (time-dependent) trip distance distributions. The model can be solved for a deterministic set of trips with a given demand pattern (defined by the start time of each trip and its distance), or it can be used to run Monte Carlo simulations to capture the average behavior and variation stochastic demand patterns, described by probabilistic distributions of trip distances and departure times. To enhance the computational efficiency, we introduce a priority queue formulation, eliminating the need to update trip positions at each time step and allowing us to run large-scale scenarios with millions of individual trips in seconds. We systematically explore the scaling properties and discuss the introduction of biases and numerical errors. The systematic exploration of scaling properties of the modeling of individual agents in the relative space with the AB2M further enhances its applicability to large-scale transportation systems and opens up opportunities for studying travel time reliability, scheduling, and mode choices. Show Chinese abstract

Abstract: 基于代理的模型已被广泛用于模拟交通系统中旅行者的出行行为，因为它们允许对交互进行现实且灵活的建模。然而，传统的基于代理的模型存在高计算成本的问题，并依赖于跟踪物理位置，从而引发隐私问题。 本文提出了一种相对空间中基于代理的浴盆模型（AB2M）的有效公式化方法，其中每个代理的轨迹由到目的地剩余距离的时间序列表示。 AB2M 可以被理解为一种微观模型，它跟踪个体行程的发起、进展和完成，是对通用（时间相关的）行程距离分布浴盆模型的精确数值解。 该模型可以针对具有特定需求模式（由每个行程的出发时间和距离定义）的确定性行程集进行求解，或者可以用于运行蒙特卡洛模拟，以捕捉平均行为和随机需求模式的变化，这些模式由行程距离和出发时间的概率分布描述。 为了提高计算效率，我们引入了优先队列公式化方法，消除了在每个时间步更新行程位置的需求，使得能够在几秒钟内运行包含数百万个个体行程的大规模场景。 我们系统地探讨了模型的可扩展属性，并讨论了偏差和数值误差的引入。 通过 AB2M 在相对空间中对个体代理建模的可扩展属性的系统探索进一步增强了其在大规模交通系统中的适用性，并为研究旅行时间可靠性、调度和出行方式选择提供了机会。