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In the realm of heterogeneous mixed autonomy, vehicles experience dynamic spatial correlations and nonlinear temporal interactions in a complex, non-Euclidean space. These complexities pose significant challenges to traditional…
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and…
This paper aims to predict the traffic flow at one road segment based on nearby traffic volume and weather conditions. Our team also discover the impact of weather conditions and nearby traffic volume on the traffic flow at a target point.…
For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep…
The central points of communication network flow has often been identified using graph theoretical centrality measures. In real networks, the state of traffic density arises from an interplay between the dynamics of the flow and the…
This work is a geometrical approach to the optimization problem motivated by transportation system management. First, an attempt has been made to furnish a comprehensive account of geometric programming based on the elementary Finsler…
Arc-based traffic assignment models (TAMs) are a popular framework for modeling traffic network congestion generated by self-interested travelers who sequentially select arcs based on their perceived latency on the network. However,…
We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a…
Effective traffic optimization strategies can improve the performance of transportation networks significantly. Most exiting works develop traffic optimization strategies depending on the local traffic states of congested road segments,…
We combine the power flow model with the proportionally fair optimization criterion to study the control of congestion within a distribution electric grid network. The form of the mathematical optimization problem is a convex second order…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted…
Path optimization is a fundamental concern across various real-world scenarios, ranging from traffic congestion issues to efficient data routing over the internet. The Traffic Assignment Problem (TAP) is a classic continuous optimization…
We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles, acting as agents,…
Effective congestion management along signalized corridors is essential for improving productivity and reducing costs, with arterial travel time serving as a key performance metric. Traditional approaches, such as Coordinated Signal Timing…
Over the years, reinforcement learning has emerged as a popular approach to develop signal control and vehicle platooning strategies either independently or in a hierarchical way. However, jointly controlling both in real-time to alleviate…
Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…
In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose…