Traffic Theory

A Unified Software Framework to Enable Solution of Traffic Assignment Problems at Extreme Scale

Ugirumurera, Juliette
Gomes, Gabriel
Porter, Emily
Li, Xiaoye S.
Bayen, Alexandre M.
2018

We describe a modular software framework for solving user equilibrium traffic assignment problems. The design is based on the formulation of the problem as a variational inequality. Unlike most existing traffic assignment software which focus on specific traffic models, our framework accommodates various traffic models, but also enables using parallel computation in high performance computing environments to speed up large-scale equilibrium calculations. We compare the solutions obtained under several models: static, Merchant-Nemhauser, `CTM with instantaneous travel time', and `CTM with...

Sensitivity Analysis and Relaxation of the Static Traffic Assignment Problem with Capacity Constraints

Cabannes, Theophile
Glista, Elizabeth
Dwarakanath, Kshama
Rao, Xu
Veeravalli, Tanya
Bayen, Alexandre M.
2019

This article introduces sensitivity analysis, reduction of the feasible set around the optimal solution, and LP and QP relaxations on convex, capacity-constrained network flow problems to evaluate the impact of a change in link capacity on the optimal flow allocation. This is done in the context of the static traffic assignment problem under capacity constraints [TAP-C], to understand the impact of traffic incidents on traffic flow in road networks, though the results also apply beyond transportation.The dual formulation of the convex [TAP-C] using gener-alized travel costs is exploited to...

Well-Posedness of Networked Scalar Semilinear Balance Laws Subject to Nonlinear Boundary Control Operators

Tang, Shu-Xia
Keimer, Alexander
Bayen, Alexandre M.
2019

Networked scalar semilinear balance laws are used as simplified macroscopic vehicular traffic models. The related initial boundary value problem is investigated, on a finite interval. The upstream boundary datum is determined by a nonlinear feedback control operator, representing the fact that traffic routing might be influenced in real time by the traffic information on the entire network. The main contribution of the present work lies in the appropriate design of nonlinear boundary control operators which meanwhile guarantee the well-posedness of the resultant systems. In detail, two...

A Study on Minimum Time Regulation of a Bounded Congested Road with Upstream Flow Control

Tang, Shu-Xia
Keimer, Alexander
Goatin, Paola
Bayen, Alexandre M.
2019

This article is motivated by the practical problem of controlling traffic flow by imposing restrictive boundary conditions. For a one-dimensional congested road segment, we study the minimum time control problem of how to control the upstream vehicular flow appropriately to regulate the downstream traffic into a desired (constant) free flow state in minimum time. We consider the Initial-Boundary Value Problem (IBVP) for a scalar nonlinear conservation law, associated to the Lighthill-Whitham-Richards (LWR) Partial Differential Equation (PDE), where the left boundary condition, also treated...

Inter-Level Cooperation in Hierarchical Reinforcement Learning

Rahman Kreidieh, Abdul
Berseth, Glen
Trabucco, Brandon
Parajuli, Samyak
Levine, Sergey
Bayen, Alexander M.
2019

Hierarchies of temporally decoupled policies present a promising approach for enabling structured exploration in complex long-term planning problems. To fully achieve this approach an end-to-end training paradigm is needed. However, training these multi-level policies has had limited success due to challenges arising from interactions between the goal-assigning and goal-achieving levels within a hierarchy. In this article, we consider the policy optimization process as a multi-agent process. This allows us to draw on connections between communication and cooperation in multi-agent RL, and...

A Macroscopic Traffic Flow Model with Finite Buffers on Networks: Well-Posedness by Means of Hamilton-Jacobi Equations

Laurent-Brouty, Nicolas
Keimer, Alexander
Goatin, Paola
Bayen, Alexandre
2020

We introduce a model dealing with conservation laws on networks and coupled boundary conditions at the junctions. In particular, we introduce buffers of fixed arbitrary size and time dependent split ratios at the junctions , which represent how traffic is routed through the network, while guaranteeing spill-back phenomena at nodes. Having defined the dynamics at the level of conservation laws, we lift it up to the Hamilton-Jacobi (H-J) formulation and write boundary datum of incoming and outgoing junctions as functions of the queue sizes and vice-versa. The Hamilton-Jacobi formulation...

Learning Optimal Traffic Routing Behaviors Using Markovian Framework in Microscopic Simulation

Cabannes, T.
Li, J.
Wu, F.
Dong, H.
Bayen, A.M.
2020

This article applies the existing Markovian traffic assignment framework to novel traffic control strategies. In the Markovian traffic assignment framework, transition matrices are used to derive the traffic flow allocation. In contrast to the static traffic assignment, the framework only requires flow split ratio at every intersection, bypassing the need of computing path flow allocation. Consequently, compared to static traffic assignment, drivers’ routing behaviors can be modeled with fewer variables. As a result, it could be used to improve the efficiency of traffic management,...

Block Simplex Signal Recovery: Methods, Trade-Offs, and an Application to Routing

Wu, Cathy
Pozdnukhov, Alexey
Bayen, Alexandre M.
2020

This paper presents the problem of block simplex constrained signal recovery, which has been demonstrated to be a suitable formulation for estimation problems in networks such as route flow estimation in traffic. There are several natural approaches to this problem: compressed sensing, Bayesian inference, and convex optimization. This paper presents new methods within each framework and assesses their respective abilities to reconstruct signals, with the particular emphasis on sparse recovery, ability to incorporate prior information, and scalability. We then apply these methods to route...

Zero-Shot Autonomous Vehicle Policy Transfer: From Simulation to Real-World via Adversarial Learning

Chalaki, Behdad
Beaver, Logan E.
Remer, Ben
Jang, Kathy
Vinitsky, Eugene
Bayen, Alexandre
Malikopoulos, Andreas A.
2020

In this article, we demonstrate a zero-shot transfer of an autonomous driving policy from simulation to University of Delaware's scaled smart city with adversarial multi-agent reinforcement learning, in which an adversary attempts to decrease the net reward by perturbing both the inputs and outputs of the autonomous vehicles during training. We train the autonomous vehicles to coordinate with each other while crossing a roundabout in the presence of an adversary in simulation. The adversarial policy successfully reproduces the simulated behavior and incidentally outperforms, in terms of...

Optimizing Mixed Autonomy Traffic Flow With Decentralized Autonomous Vehicles and Multi-Agent RL

Vinitsky, Eugene
Lichtle, Nathan
Parvate, Kanaad
Bayen, Alexandre
2020

We study the ability of autonomous vehicles to improve the throughput of a bottleneck using a fully decentralized control scheme in a mixed autonomy setting. We consider the problem of improving the throughput of a scaled model of the San Francisco-Oakland Bay Bridge: a two-stage bottleneck where four lanes reduce to two and then reduce to one. Although there is extensive work examining variants of bottleneck control in a centralized setting, there is less study of the challenging multi-agent setting where the large number of interacting AVs leads to significant optimization difficulties...