Gap Value in Simulation-Based Dynamic Traffic Assignment Models: Why Does It Exist and How to Reduce It?
Corresponding Author: Jiangtao Liu, Arizona State University
Presented By: Jiangtao Liu, Arizona State University
Abstract
Wardorp’s user equilibrium has been acknowledged as a realistic approximation of travel behavior where each traveler seeks to minimize his/her cost of transportation. The equilibrium condition is usually defined as that all used paths have minimal and equal travel times/costs for the same trip in static traffic assignment models or for the same trip with start time in dynamic traffic assignment models. In many simulation based DTA applications, it is desirable to have zero gap value between the travel cost of all used paths and the least cost of the trip, because the gap value of each trip has been widely used to evaluate the convergence of the proposed algorithm for user equilibrium in both analytical and simulation-based dynamic traffic assignment models.
In this presentation, we revisit the gap value and focus on whether or not it is realistically to expect zero gap in dynamic traffic assignment models with tight capacity constraints. First, we demonstrate that Wardorp’s user equilibrium may not exist when the tight link capacity is highly respected. One extreme case is that the paths with a least-cost value cannot satisfy the travel demand of the trip due to their limited path/link capacity. As a result, some travelers have to accept a longer path to finish the trip and a positive gap value is generated. This leads to a challenge for dynamic traffic assignment model where the temporal and spatial link capacity is significantly crucial to capture dynamic queues. Further, we show that a smaller gap value may not represent a better solution when each traveler just choose his/her own best route in a capacitated traffic network, which is paradoxical to traditional static assignment approaches that aim to minimize all gap values to reach user equilibrium. Finally, we propose that the tight capacity constraint could invoke travelers’ bounded rationality. One agent-based mathematical model under space-time network representations is developed and efficiently solved. Meanwhile, we also discuss how we can use simulation-based dynamic assignment models as a good approximation to find user equilibrium in the context of minimizing the gap values of all trips.