Priority queue formulation of agent-based bathtub model for network trip flows in the relative space

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 variations of stochastic demand patterns. To enhance the computational efficiency, we introduce a priority queue formulation for AB²M, 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 of AB²M and discuss the introduction of biases and numerical errors. Finally, we analyze the upper bound of the computational complexity of the AB²M and the benefits of the priority queue formulation and downscaling on the computational cost. 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.