A dynamical system model of the traffic assignment problem

In this paper we present a differential variational inequality formulation of dynamic network user equilibrium with elastic travel demand. We discuss its qualitative properties and provide algorithms for and examples of its solution.

Solving the road congestion problem is one of the most pressing issues in moderncities since it causes time wasting, pollution, higher industrial costs and huge roadmaintenance costs. Advances in ITS technologies and the advent of autonomousvehicles are changing mobility dramatically. They enable the implementation of acoordination mechanism, called coordinated traffic assignment, among the sat-navdevices aiming at assigning paths to drivers to eliminate congestion and to re-...

In (Jin, 2018), a new day-to-day dynamical system was proposed for drivers' departure time choice at a single bottleneck. Based on three behavioral principles, the nonlocal departure and arrival times choice problems were converted to the local scheduling payoff choice problem, whose day-to-day dynamics are described by the Lighthill-Whitham-Richards (LWR) model on an imaginary road of increasing scheduling payoff. Thus the departure time user equilibrium (DTUE), the arrival ...

This book covers static and dynamic traffic assignment models used in transportation planning and network analysis. Traffic assignment is the final step in the traditional planning process, and recent decades have seen many advances in formulating and solving such models. The book discusses classical solution methods alongside recent ones used in contemporary planning software. The primary audience for the book is graduate students new to transportation network analysis, an...

The traffic assignment problem is one of the most important transportation planning problems. The task faced by transportation planners, traffic engineers, and computer scientists is to generate high quality, approximate solutions of users equilibrium, that enable traffic scenario comparisons in a reasonable CPU time. We introduce the k Paths Subtracting-Adding (k-PSA) algorithm to approximate the user equilibrium of the traffic assignment problem. The k-PSA algorithm consist...

Advanced traffic navigation systems, which provide routing recommendations to drivers based on real-time congestion information, are nowadays widely adopted by roadway transportation users. Yet, the emerging effects on the traffic dynamics originating from the widespread adoption of these tools have remained largely unexplored until now. In this paper, we propose a dynamic model where drivers imitate the path preferences of previous drivers, and we study the properties of its...

Balancing traffic flow by influencing drivers' route choices to alleviate congestion is becoming increasingly more appealing in urban traffic planning. Here, we introduce a discrete dynamical model comprising users who make their own routing choices on the basis of local information and those who consider routing advice based on localized inducement. We identify the formation of traffic patterns, develop a scalable optimization method for identifying control values used for u...

The Static User Equilibrium is a powerful framework for the theoretical study of traffic. Despite the restricting assumption of stationary flows that intuitively limit its application to real traffic systems, many operational models implementing it are still used without an empirical validation of the existence of the equilibrium. We investigate its existence on a traffic dataset of three months for the region of Paris, FR. The implementation of an application for interactive...

In this short paper we describe natural logit population games dynamics that explain equilibrium models of origin-destination matrix estimation and (stochastic) traffic assignment models (Beckmann, Nesterov--de Palma). Composition of the proposed dynamics allows to explain two-stages traffic assignment models.

This paper proposes an iterative methodology to integrate large-scale behavioral activity-based models with dynamic traffic assignment models. The main novelty of the proposed approach is the decoupling of the two parts, allowing the ex-post integration of any existing model as long as certain assumptions are satisfied. A measure of error is defined to characterize a search space easily explorable within its boundaries. Within it, a joint distribution of the number of trips a...