On Path-based Marginal Cost of Heterogeneous Traffic Flow for General Networks

2026-02-05

AI Summary

This study addresses the challenge of accurately computing path marginal costs (PMCs) in heterogeneous traffic flows, where interactions among multiple vehicle classes and nondifferentiability near system optimum complicate traditional approaches. The authors propose a novel method that explicitly models inter-class vehicle interactions by decomposing PMC into intra-class and inter-class components. A conversion factor derived from heterogeneous link dynamics is introduced to capture vehicle-class coupling effects, while a smooth approximation scheme resolves the nondifferentiability issue. Embedded within a dynamic traffic assignment framework, the approach successfully solves the two-class system optimal problem on both synthetic and real-world large-scale networks, significantly reducing total travel costs and accurately revealing the competitive relationships among vehicle classes under system-optimal conditions.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Path marginal cost (PMC) is a crucial component in solving path-based system-optimal dynamic traffic assignment (SO-DTA), dynamic origin-destination demand estimation (DODE), and network resilience analysis. However, accurately evaluating PMC in heterogeneous traffic conditions poses significant challenges. Previous studies often focus on homogeneous traffic flow of single vehicle class and do not well address the interactive effect of heterogeneous traffic flows and the resultant computational issues. This study proposes a novel but simple method for approximately evaluating PMC in complex heterogeneous traffic condition. The method decomposes PMC into intra-class and inter-class terms and uses conversion factor derived from heterogeneous link dynamics to explicitly model the intricate relationships between vehicle classes. Additionally, the method considers the non-differentiable issue that arises when mixed traffic flow approaches system optimum conditions. The proposed method is tested on a small corridor network with synthetic demand and a large-scale network with calibrated demand from real-world data. Results demonstrated that our method exhibits superior performance in solving bi-class SO-DTA problems, yielding lower total travel cost and capturing the multi-class flow competition at the system optimum state.

Problem

• Path marginal cost
• Heterogeneous traffic flow
• System-optimal dynamic traffic assignment
• Inter-class interaction
• Non-differentiability

Innovation

• Path marginal cost
• Heterogeneous traffic flow
• System-optimal dynamic traffic assignment
• Inter-class interaction
• Non-differentiable optimization