Traffic Operations and Management

Solving N-Player Dynamic Routing Games with Congestion: A Mean Field Approach

Cabannes, Theophile
Lauriere, Mathieu
Perolat, Julien
Marinier, Raphael
Girgin, Sertan
2021

The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic...

Parallel Network Flow Allocation in Repeated Routing Games via LQR Optimal Control

Gibson, Marsalis
You, Yiling
Bayen, Alexandre
2021

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...

Learning Generalizable Multi-Lane Mixed-Autonomy Behaviors in Single Lane Representations of Traffic

Kreidieh, Abdul Rahman
Zhao, Yibo
Parajuli, Samyak
Bayen, Alexandre
2021

Reinforcement learning techniques can provide substantial insights into the desired behaviors of future autonomous driving systems. By optimizing for societal metrics of traffic such as increased throughput and reduced energy consumption, such methods can derive maneuvers that, if adopted by even a small portion of vehicles, may significantly improve the state of traffic for all vehicles involved. These methods, however, are hindered in practice by the difficulty of designing efficient and accurate models of traffic, as well as the challenges associated with optimizing for the behaviors of...

Boundary Control of Conservation Laws Exhibiting Shocks

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

This chapter focuses on control of systems of conservation laws with boundary data. Problems with one or two boundaries are considered and, in particular, we focus on cases where shocks may be developed by the solution. However, for completeness we briefly discuss in Sect. 2.2 other existing results where singularities are prevented via suitable feedback controls such as in [32].

Control Problems for Hamilton-Jacobi Equations Co-authored by Alexander Keimer

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

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.

Decentralized Control of Conservation Laws on Graphs

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

Conservation and/or balance laws on networks in the recent years have been the subject of intense study, since a wide range of different applications in real life can be covered by such a research.

Distributed Control for Conservation Laws

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

This chapter focuses on control of systems of conservation laws with distributed parameters. Problem with different parameterized fluxes is addressed: in particular, we deal with cases where the control is the maximal speed and look for continuous dependence of the solution on parameters.

Lagrangian Control of Conservation Laws and Mixed Models

Bayen, Alexandre
Monache, Maria Laura Delle
Garavello, Mauro
Goatin, Paola
Piccoli, Benedetto
2022

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].

A Holistic Approach to the Energy-Efficient Smoothing of Traffic via Autonomous Vehicles

Hayat, Amaury
Gong, Xiaoqian
Lee, Jonathan
Truong, Sydney
McQuade, Sean T.
Bayen, Alexandre
2022

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...