Link-based day-to-day network traffic dynamics and equilibria (original) (raw)
2015, Transportation Research Part B: Methodological
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A B S T R A C T Transportation networks are often subjected to perturbed conditions leading to traffic disequilibrium. Under such conditions, the traffic evolution is typically modeled as a dynamical system that captures the aggregated effect of paths-shifts by drivers over time. This paper proposes a day-today (DTD) dynamical model that bridges two important gaps in the literature. First, existing DTD models generally consider current path flows and costs, but do not factor the sensitivity of path costs to flow. The proposed DTD model simultaneously captures all three factors in modeling the flow shift by drivers. As a driver can potentially perceive the sensitivity of path costs with the congestion level based on past experience, incorporating this factor can enhance real-world consistency. In addition, it smoothens the time trajectory of path flows, a desirable property for practice where the iterative solution procedure is typically terminated at an arbitrary point due to computational time constraints. Second, the study provides a criterion to classify paths for an origin-destination pair into two subsets under traffic disequilibrium: expensive paths and attractive paths. This facilitates flow shifts from the set of expensive paths to the set of attractive paths, enabling a higher degree of freedom in modeling flow shift compared to that of shifting flows only to the shortest path, which is behaviorally restrictive. In addition, consistent with the real-world driver behavior, it also helps to preclude flow shifts among expensive paths. Improved behavioral consistency can lead to more meaningful path/link time-dependent flow profiles for developing effective dynamic traffic management strategies for practice. The proposed DTD model is formulated as the dynamical system by drawing insights from micro-economic theory. The stability of the model and existence of its stationary point are theoretically proven. Results from computational experiments validate its modeling properties and illustrate its benefits relative to existing DTD dynamical models.
Traffic Dynamics in Pursuit of Equilibrium
Journal of the Eastern Asia Society for Transportation Studies, 2007
This paper studies how equilibrium is achieved in day-to-day traffic dynamics. Trip-makers update their perceived cost on a daily basis and adjust their route choice accordingly. The limiting behavior of day-to-day dynamics is characterized by the notion of equilibrium, which forms a stationary state. The attractiveness of an equilibrium state is examined by stability and can be quantified by its attraction basin. This paper illustrates how instability, as well as the problem of non-convergence from states outside the attraction basin, can be removed by modifying network configuration. This paper further investigates other attractors including cycles and chaos that are associated with the dynamic process in the pursuit of traffic equilibrium.
2000
This paper proposes an analytical method for stability analysis of traffic flows in a traffic network with an advanced traveller information system. The presented model describes within-day development of queues when drivers affected by real-time traffic information choose their paths en route. The model reduces to a system of differential equations with delays and discontinuous right hand sides. Equilibrium points
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