Traffic Operations and Management

In this article, we study the repeated routing game problem on a parallel network with affine latency functions on each edge. We cast the game setup in a LQR control theoretic framework, leveraging the Rosenthal potential formulation. We use control techniques to analyze the convergence of the game dynamics with specific cases that lend themselves to optimal control. We design proper dynamics parameters so that the conservation of flow is guaranteed. We provide an algorithmic solution for the general optimal control setup using a multiparametric quadratic programming approach (explicit MPC...

A vehicle with different (eventually controlled) dynamics from general traffic along a street may reduce the road capacity, thus generating a moving bottleneck, and can be used to act on the traffic flow. The interaction between the controlled vehicle and the surrounding traffic, and the consequent flow reduction at the bottleneck position, can be described either by a conservation law with space dependent flux function [200], or by a strongly coupled PDE-ODE system proposed in [112, 208].

The technological advancements in terms of vehicle on-board sensors and actuators, as well as for infrastructures, open an unprecedented scenario for the management of vehicular traffic. We focus on the problem of smoothing traffic by controlling a small number of autonomous vehicles immersed in the bulk traffic stream. Specifically, we aim at dissipating stop-and-go waves, which are ubiquitous and proven to increase fuel consumption tremendously and reduce. Our approach is holistic, as it is based on a large collaborative effort, which ranges from mathematical models for traffic and...

In this chapter, we introduce Hamilton-Jacobi PDEs. These PDEs are related to conservation laws and their solutions are the anti-derivative (in space) of the Entropy solutions of the corresponding conservation law, given that some assumptions are satisfied.