A Fast Lax-Hopf formula to solve the Lighthill-Whitham-Richards traffic flow model on networks

Efficient and exact algorithms are important for performing fast and accurate traffic network simulations with macroscopic traffic models. In this paper, we extend the semi-analytical Lax-Hopf algorithm in order to compute link inflows and outflows with the LWR model. Our proposed Fax Lax-Hopf algorithm has a very low computational complexity. We demonstrate that some of the original algorithm's operations (associated with the initial conditions) can be discarded, leading to a faster computation of boundary demand/supplies in network simulation problems, for general concave fundamental diagrams. Moreover, the computational cost can be further reduced for triangular Fundamental Diagrams and specific space-time discretizations. The resulting formulation has a performance comparable to the Link Transmission Model and, since it solves the original LWR model for a wide range of FD shapes, with any initial configuration, it is suitable to solve a broad range of traffic operations problems. As part of the analysis, we compare the performance of the proposed scheme to other well-known computational methods.Comment: 36 pages, 10 figure

MCRM: Mother Compact Recurrent Memory

LSTMs and GRUs are the most common recurrent neural network architectures used to solve temporal sequence problems. The two architectures have differing data flows dealing with a common component called the cell state (also referred to as the memory). We attempt to enhance the memory by presenting a modification that we call the Mother Compact Recurrent Memory (MCRM). MCRMs are a type of a nested LSTM-GRU architecture where the cell state is the GRU hidden state. The concatenation of the forget gate and input gate interactions from the LSTM are considered an input to the GRU cell. Because MCRMs has this type of nesting, MCRMs have a compact memory pattern consisting of neurons that acts explicitly in both long-term and short-term fashions. For some specific tasks, empirical results show that MCRMs outperform previously used architectures.Comment: Submitted to AAAI-1

Networked Traffic State Estimation Involving Mixed Fixed-mobile Sensor Data Using Hamilton-Jacobi equations

Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for highways modeled by a system of Lighthill Whitham Richards equations that is able to assimilate different sensor data available. We first present an equivalent formulation of the problem using a Hamilton-Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton-Jacobi equation are linear ones. We then pose the problem of estimating the traffic density given incomplete and inaccurate traffic data as a Mixed Integer Program. We then extend the density estimation framework to highway networks with any available data constraint and modeling junctions. Finally, we present a travel estimation application for a small network using real traffic measurements obtained obtained during Mobile Century traffic experiment, and comparing the results with ground truth data

Short range networks of wearables for safer mobility in smart cities

Ensuring safe and efficient mobility is a critical issue for smart city operators. Increasing safety not only reduces the likelihood of road injuries and fatalities, but also reduces traffic congestion and disruptions caused by accidents, increasing efficiency. While new vehicles are increasingly equipped with semi-automation, the added costs will initially limit the penetration rate of these systems. An inexpensive way to replace or augment these systems is to create networks of wearables (smart glasses, watches) that exchange positional and path data at a very fast rate between all users, identify collision risks and feedback collision resolution information to all users in an intuitive way through their smart glasses.Comment: Workshop on System and Control Perspectives for Smart City, IEEE CDC 201

Real-time Mobile Sensor Management Framework for city-scale environmental monitoring

Environmental disasters such as flash floods are becoming more and more prevalent and carry an increasing burden on human civilization. They are usually unpredictable, fast in development, and extend across large geographical areas. The consequences of such disasters can be reduced through better monitoring, for example using mobile sensing platforms that can give timely and accurate information to first responders and the public. Given the extended scale of the areas to monitor, and the time-varying nature of the phenomenon, we need fast algorithms to quickly determine the best sequence of locations to be monitored. This problem is very challenging: the present informative mobile sensor routing algorithms are either short-sighted or computationally demanding when applied to large scale systems. In this paper, a real-time sensor task scheduling algorithm that suits the features and needs of city-scale environmental monitoring tasks is proposed. The algorithm is run in forward search and makes use of the predictions of an associated distributed parameter system, modeling flash flood propagation. It partly inherits the causal relation expressed by a search tree, which describes all possible sequential decisions. The computationally heavy data assimilation steps in the forward search tree are replaced by functions dependent on the covariance matrix between observation sets. Taking flood tracking in an urban area as a concrete example, numerical experiments in this paper indicate that this scheduling algorithm can achieve better results than myopic planning algorithms and other heuristics based sensor placement algorithms. Furthermore, this paper relies on a deep learning-based data-driven model to track the system states, and experiments suggest that popular estimation techniques have very good performance when applied to precise data-driven models.Comment: for associated data and code, see https://drive.google.com/drive/folders/1gRz4T2KGFXtlnSugarfUL8r355cXb7Ko?usp=sharin

Unmanned Aerial Vehicle Path Planning for Traffic Estimation and Detection of Non-Recurrent Congestion

Unmanned aerial vehicles (UAVs) provide a novel means of extracting road and traffic information via video data. Specifically, by analyzing objects in a video frame, UAVs can be used to detect traffic characteristics and road incidents. Under congested conditions, the UAVs can supply accurate incident information where it is otherwise difficult to infer the road state from traditional speed-density measurements. Leveraging the mobility and detection capabilities of UAVs, we investigate navigation algorithms that seek to maximize information on the road/traffic state under non-recurrent congestion. We propose an active exploration framework that (1) assimilates UAV observations with speed-density sensor data, (2) quantifies uncertainty on the road/traffic state, and (3) adaptively navigates the UAV to minimize this uncertainty. The navigation algorithm uses the A-optimal information measure (mean uncertainty) and it depends on covariance matrices generated by an ensemble Kalman filter (EnKF). In the EnKF procedure, we incorporate nonlinear traffic observations through model diagnostic variables, and we present a parameter update procedure that maintains a monotonic relationship between states and measurements. We compare the traffic and incident state estimates resulting from the coupled UAV navigation-estimation procedure against corresponding estimates that do not use targeted UAV observations. Our results indicate that UAVs aid in detection of incidents under congested conditions where speed-density data are not informative

Physics Informed Data Driven model for Flood Prediction: Application of Deep Learning in prediction of urban flood development

Flash floods in urban areas occur with increasing frequency. Detecting these floods would greatlyhelp alleviate human and economic losses. However, current flood prediction methods are eithertoo slow or too simplified to capture the flood development in details. Using Deep Neural Networks,this work aims at boosting the computational speed of a physics-based 2-D urban flood predictionmethod, governed by the Shallow Water Equation (SWE). Convolutional Neural Networks(CNN)and conditional Generative Adversarial Neural Networks(cGANs) are applied to extract the dy-namics of flood from the data simulated by a Partial Differential Equation(PDE) solver. Theperformance of the data-driven model is evaluated in terms of Mean Squared Error(MSE) andPeak Signal to Noise Ratio(PSNR). The deep learning-based, data-driven flood prediction modelis shown to be able to provide precise real-time predictions of flood developmen

Robust Traffic Control Using a First Order Macroscopic Traffic Flow Model

Traffic control is at the core of research in transportation engineering because it is one of the best practices for reducing traffic congestion. It has been shown in recent years that the traffic control problem involving Lighthill-Whitham-Richards (LWR) model can be formulated as a Linear Programming (LP) problem given that the corresponding initial conditions and the model parameters in the fundamental diagram are fixed. However, the initial conditions can be uncertain when studying actual control problems. This paper presents a stochastic programming formulation of the boundary control problem involving chance constraints, to capture the uncertainty in the initial conditions. Different objective functions are explored using this framework, and case studies for both a single highway link and a small network are conducted. In addition, the optimal results are validated with Monte Carlo simulation.Comment: 12 pages, 10 figures, 1 tabl

A Control-Theoretic Approach for Scalable and Robust Traffic Density Estimation using Convex Optimization

Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic flow in road segments that are not equipped with sensors is of significant importance---thereby providing situational awareness and guiding real-time feedback control strategies. To that end, firstly we build a generalized traffic flow model for stretched highways with arbitrary number of ramp flows based on the Lighthill Whitham Richards (LWR) flow model. Secondly, we characterize the function set corresponding to the nonlinearities present in the LWR model, and use this characterization to design real-time and robust state estimators (SE) for stretched highway segments. Specifically, we show that the nonlinearities from the derived models are locally Lipschitz continuous by providing the analytical Lipschitz constants. Thirdly, the analytical derivation is then incorporated through a robust SE method given a limited number of traffic sensors, under the impact of process and measurement disturbances and unknown inputs. The estimator is based on deriving a convex semidefinite optimization problem. Finally, numerical tests are given showcasing the applicability, scalability, and robustness of the proposed estimator for large systems under high magnitude disturbances, parametric uncertainty, and unknown inputs.Comment: IEEE Transactions on Intelligent Transportation Systems, In Pres

Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction

Better machine understanding of pedestrian behaviors enables faster progress in modeling interactions between agents such as autonomous vehicles and humans. Pedestrian trajectories are not only influenced by the pedestrian itself but also by interaction with surrounding objects. Previous methods modeled these interactions by using a variety of aggregation methods that integrate different learned pedestrians states. We propose the Social Spatio-Temporal Graph Convolutional Neural Network (Social-STGCNN), which substitutes the need of aggregation methods by modeling the interactions as a graph. Our results show an improvement over the state of art by 20% on the Final Displacement Error (FDE) and an improvement on the Average Displacement Error (ADE) with 8.5 times less parameters and up to 48 times faster inference speed than previously reported methods. In addition, our model is data efficient, and exceeds previous state of the art on the ADE metric with only 20% of the training data. We propose a kernel function to embed the social interactions between pedestrians within the adjacency matrix. Through qualitative analysis, we show that our model inherited social behaviors that can be expected between pedestrians trajectories. Code is available at https://github.com/abduallahmohamed/Social-STGCNN.Comment: Accepted by CVPR 202