53,973 research outputs found
Dimension Reduction for Origin-Destination Flow Estimation: Blind Estimation Made Possible
This paper studies the problem of estimating origin-destination (OD) flows
from link flows. As the number of link flows is typically much less than that
of OD flows, the inverse problem is severely ill-posed and hence prior
information is required to recover the ground truth. The basic approach in the
literature relies on a forward model where the so called traffic assignment
matrix maps OD flows to link flows. Due to the ill-posedness of the problem,
prior information on the assignment matrix and OD flows are typically needed.
The main contributions of this paper include a dimension reduction of the
inquired flows from to , and a demonstration that for the first
time the ground truth OD flows can be uniquely identified with no or little
prior information. To cope with the ill-posedness due to the large number of
unknowns, a new forward model is developed which does not involve OD flows
directly but is built upon the flows characterized only by their origins,
henceforth referred as O-flows. The new model preserves all the OD information
and more importantly reduces the dimension of the inverse problem
substantially. A Gauss-Seidel method is deployed to solve the inverse problem,
and a necessary condition for the uniqueness of the solution is proved.
Simulations demonstrate that blind estimation where no prior information is
available is possible for some network settings. Some challenging network
settings are identified and discussed, where a remedy based on temporal
patterns of the O-flows is developed and numerically shown effective
Statistical Traffic State Analysis in Large-scale Transportation Networks Using Locality-Preserving Non-negative Matrix Factorization
Statistical traffic data analysis is a hot topic in traffic management and
control. In this field, current research progresses focus on analyzing traffic
flows of individual links or local regions in a transportation network. Less
attention are paid to the global view of traffic states over the entire
network, which is important for modeling large-scale traffic scenes. Our aim is
precisely to propose a new methodology for extracting spatio-temporal traffic
patterns, ultimately for modeling large-scale traffic dynamics, and long-term
traffic forecasting. We attack this issue by utilizing Locality-Preserving
Non-negative Matrix Factorization (LPNMF) to derive low-dimensional
representation of network-level traffic states. Clustering is performed on the
compact LPNMF projections to unveil typical spatial patterns and temporal
dynamics of network-level traffic states. We have tested the proposed method on
simulated traffic data generated for a large-scale road network, and reported
experimental results validate the ability of our approach for extracting
meaningful large-scale space-time traffic patterns. Furthermore, the derived
clustering results provide an intuitive understanding of spatial-temporal
characteristics of traffic flows in the large-scale network, and a basis for
potential long-term forecasting.Comment: IET Intelligent Transport Systems (2013
Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting
Spatiotemporal forecasting has various applications in neuroscience, climate
and transportation domain. Traffic forecasting is one canonical example of such
learning task. The task is challenging due to (1) complex spatial dependency on
road networks, (2) non-linear temporal dynamics with changing road conditions
and (3) inherent difficulty of long-term forecasting. To address these
challenges, we propose to model the traffic flow as a diffusion process on a
directed graph and introduce Diffusion Convolutional Recurrent Neural Network
(DCRNN), a deep learning framework for traffic forecasting that incorporates
both spatial and temporal dependency in the traffic flow. Specifically, DCRNN
captures the spatial dependency using bidirectional random walks on the graph,
and the temporal dependency using the encoder-decoder architecture with
scheduled sampling. We evaluate the framework on two real-world large scale
road network traffic datasets and observe consistent improvement of 12% - 15%
over state-of-the-art baselines.Comment: Published as a conference paper at ICLR 201
Applications of sensitivity analysis for probit stochastic network equilibrium
Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported
Network tomography for integer-valued traffic
A classic network tomography problem is estimation of properties of the
distribution of route traffic volumes based on counts taken on the network
links. We consider inference for a general class of models for integer-valued
traffic. Model identifiability is examined. We investigate both maximum
likelihood and Bayesian methods of estimation. In practice, these must be
implemented using stochastic EM and MCMC approaches. This requires a
methodology for sampling latent route flows conditional on the observed link
counts. We show that existing algorithms for doing so can fail entirely,
because inflexibility in the choice of sampling directions can leave the
sampler trapped at a vertex of the convex polytope that describes the feasible
set of route flows. We prove that so long as the network's link-path incidence
matrix is totally unimodular, it is always possible to select a coordinate
system representation of the polytope for which sampling parallel to the axes
is adequate. This motivates a modified sampler in which the representation of
the polytope adapts to provide good mixing behavior. This methodology is
applied to three road traffic data sets. We conclude with a discussion of the
ramifications of the unimodularity requirements for the routing matrix.Comment: Published at http://dx.doi.org/10.1214/15-AOAS805 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Non-recurrent Traffic Congestion Detection with a Coupled Scalable Bayesian Robust Tensor Factorization Model
Non-recurrent traffic congestion (NRTC) usually brings unexpected delays to
commuters. Hence, it is critical to accurately detect and recognize the NRTC in
a real-time manner. The advancement of road traffic detectors and loop
detectors provides researchers with a large-scale multivariable
temporal-spatial traffic data, which allows the deep research on NRTC to be
conducted. However, it remains a challenging task to construct an analytical
framework through which the natural spatial-temporal structural properties of
multivariable traffic information can be effectively represented and exploited
to better understand and detect NRTC. In this paper, we present a novel
analytical training-free framework based on coupled scalable Bayesian robust
tensor factorization (Coupled SBRTF). The framework can couple multivariable
traffic data including traffic flow, road speed, and occupancy through sharing
a similar or the same sparse structure. And, it naturally captures the
high-dimensional spatial-temporal structural properties of traffic data by
tensor factorization. With its entries revealing the distribution and magnitude
of NRTC, the shared sparse structure of the framework compasses sufficiently
abundant information about NRTC. While the low-rank part of the framework,
expresses the distribution of general expected traffic condition as an
auxiliary product. Experimental results on real-world traffic data show that
the proposed method outperforms coupled Bayesian robust principal component
analysis (coupled BRPCA), the rank sparsity tensor decomposition (RSTD), and
standard normal deviates (SND) in detecting NRTC. The proposed method performs
even better when only traffic data in weekdays are utilized, and hence can
provide more precise estimation of NRTC for daily commuters
Traffic state estimation using stochastic Lagrangian dynamics
This paper proposes a new stochastic model of traffic dynamics in Lagrangian
coordinates. The source of uncertainty is heterogeneity in driving behavior,
captured using driver-specific speed-spacing relations, i.e., parametric
uncertainty. It also results in smooth vehicle trajectories in a stochastic
context, which is in agreement with real-world traffic dynamics and, thereby,
overcoming issues with aggressive oscillation typically observed in sample
paths of stochastic traffic flow models. We utilize ensemble filtering
techniques for data assimilation (traffic state estimation), but derive the
mean and covariance dynamics as the ensemble sizes go to infinity, thereby
bypassing the need to sample from the parameter distributions while estimating
the traffic states. As a result, the estimation algorithm is just a standard
Kalman-Bucy algorithm, which renders the proposed approach amenable to
real-time applications using recursive data. Data assimilation examples are
performed and our results indicate good agreement with out-of-sample data
State-dependent Priority Scheduling for Networked Control Systems
Networked control systems (NCS) have attracted considerable attention in
recent years. While the stabilizability and optimal control of NCS for a given
communication system has already been studied extensively, the design of the
communication system for NCS has recently seen an increase in more thorough
investigation. In this paper, we address an optimal scheduling problem for a
set of NCS sharing a dedicated communication channel, providing performance
bounds and asymptotic stability. We derive a suboptimal scheduling policy with
dynamic state-based priorities calculated at the sensors, which are then used
for stateless priority queuing in the network, making it both scalable and
efficient to implement on routers or multi-layer switches. These properties are
beneficial towards leveraging existing IP networks for control, which will be a
crucial factor for the proliferation of wide-area NCS applications. By allowing
for an arbitrary number of concurrent transmissions, we are able to investigate
the relationship between available bandwidth, transmission rate, and delay. To
demonstrate the feasibility of our approach, we provide a proof-of-concept
implementation of the priority scheduler using real networking hardware.Comment: 8 pages, 4 figures, accepted for publication at 2017 American Control
Conference (ACC
Learning Probabilistic Trajectory Models of Aircraft in Terminal Airspace from Position Data
Models for predicting aircraft motion are an important component of modern
aeronautical systems. These models help aircraft plan collision avoidance
maneuvers and help conduct offline performance and safety analyses. In this
article, we develop a method for learning a probabilistic generative model of
aircraft motion in terminal airspace, the controlled airspace surrounding a
given airport. The method fits the model based on a historical dataset of
radar-based position measurements of aircraft landings and takeoffs at that
airport. We find that the model generates realistic trajectories, provides
accurate predictions, and captures the statistical properties of aircraft
trajectories. Furthermore, the model trains quickly, is compact, and allows for
efficient real-time inference.Comment: IEEE Transactions on Intelligent Transportation System
A Comprehensive Survey on Graph Neural Networks
Deep learning has revolutionized many machine learning tasks in recent years,
ranging from image classification and video processing to speech recognition
and natural language understanding. The data in these tasks are typically
represented in the Euclidean space. However, there is an increasing number of
applications where data are generated from non-Euclidean domains and are
represented as graphs with complex relationships and interdependency between
objects. The complexity of graph data has imposed significant challenges on
existing machine learning algorithms. Recently, many studies on extending deep
learning approaches for graph data have emerged. In this survey, we provide a
comprehensive overview of graph neural networks (GNNs) in data mining and
machine learning fields. We propose a new taxonomy to divide the
state-of-the-art graph neural networks into four categories, namely recurrent
graph neural networks, convolutional graph neural networks, graph autoencoders,
and spatial-temporal graph neural networks. We further discuss the applications
of graph neural networks across various domains and summarize the open source
codes, benchmark data sets, and model evaluation of graph neural networks.
Finally, we propose potential research directions in this rapidly growing
field.Comment: Minor revision (updated tables and references
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