Review articleTraffic state estimation on highway: A comprehensive survey
Introduction
Traffic state estimation (TSE) refers to the process of inference of traffic state variables, namely flow (veh/h), density (veh/km), speed (km/h), and other equivalent variables, on road segments, using partially observed and noisy traffic data. TSE plays an important role in traffic operations and planning. For example, traffic control, such as ramp metering, pricing, and information provision, requires precise traffic state information in order to mitigate congestion effectively. Strategic transportation planning such as infrastructure improvements also require traffic state information. These operation and planning tasks can be greatly improved by an efficient and accurate observation of the traffic state. However, the traffic state is not observed everywhere and practical measurements are usually noisy. Thus, the traffic state in unobserved areas needs to be estimated; and that in observed areas needs to be improved (denoised) as well. In this article, TSE is defined as the simultaneous estimation of flow, density, and speed on road segments with high spatiotemporal resolution,1 based on partially observed traffic data and a priori knowledge of traffic. Fig. 1 illustrates a conceptual procedure of TSE.
This article focuses on TSE on highways motivated by the following four reasons. First, highways play a significant role in road transportation systems, with high service capability in terms of the volume and speed. Second, they exhibit some controllability (Papageorgiou, Diakaki, Dinopoulou, Kotsialos, & Wang, 2003) because of the nature of vehicular traffic. Third, recent technology developments enable new applications with the use of various and heterogeneous traffic data. Fourth, because of the aforementioned reasons, numerous highway TSE methods with various features have been proposed to date, which are worth considering and summarizing.
For our best knowledge, there is no comprehensive survey on TSE, although more than a decade has passed from the early and influential work on highway TSE by Wang and Papageorgiou (2005) and there have been considerable advances in this field.2 This makes it difficult to assess available approaches, respective benefits, and potential improvements.
The aims of this article are to provide a comprehensive and systematic summary of highway TSE, to contribute toward a better understanding of state-of-the-art methods, and to identify future research directions. Note that this article does not determine which methodology outperforms others in terms of general performance metrics. Respective advantages or disadvantages of a TSE method need to be discussed separately, by considering the specification of the application. One of the aims of this article is to provide the fundamental materials for such discussion. To achieve these aims, this article characterizes existing TSE methods based on their three fundamental elements: estimation approaches, traffic flow models, and input data. The following briefly describes these elements (we will discuss the details in the corresponding sections later).
The estimation approach consists of methods that estimate the traffic state, based on a priori knowledge of traffic and partial observation. A priori knowledge (i.e., assumptions) could be physical traffic flow models and data-driven models, which is usually obtained by abstracting actual traffic by employing physical principles and statistical/machine-learning (ML) methods, respectively. In this study, the approaches are grouped into three categories, namely, model-driven, data-driven, and streaming-data-driven, according to types of a priori knowledge and input data they rely on. In short, model-driven ones rely on physical models of traffic which is characterized by empirical relation. Data-driven ones rely on dependence in historical-data and statistical/ML methods. Streaming-data-driven ones do not rely on these two previous elements. Because the assumptions vary greatly among the approaches, they have different advantages and disadvantages.
Traffic flow models describe the physical and theoretical aspects of traffic dynamics in the spatiotemporal domain. Therefore, they are used by model-driven TSE methods to infer the traffic state in an unobserved time–space region. Various models along with various solution methods have been proposed; and they have totally different advantages and disadvantages in terms of TSE.
The input data for TSE is the partial observation of traffic and is essential for TSE. Because of recent technology advances, the availability of novel data types (e.g., global positioning system (GPS), call detail record (CDR), on board diagnostics second generation (OBD2), etc.) is rapidly increasing in terms of both quality and quantity. This has resulted in the emergence of various TSE methods.
The remainder of this article is organized as follows. In Section 2, we briefly present highway traffic and TSE, along with fundamental terms and definitions. In Section 3, we summarize existing traffic models commonly used for TSE. In Section 4, we describe available measurements and data for traffic. In each sub- and sub-sub-section in Sections 3 and 4, general introduction on the corresponding topic and its application in TSE are discussed sequentially. In Section 5, we review TSE approaches, which mainly use models described in Section 3 and data described in Section 4. In Section 6, we summarize the survey results and propose future research directions.
Note that there are over 100 different methods to the TSE problem; thus, it is not practical to enumerate and explain them all in the core of this article. Therefore, only studies with substantial originality in terms of the aforementioned characteristics (i.e., approach, model, data) are referred in the main text. The remaining studies are summarized in Section 6 together with those explained in the main text. Case studies which did not propose new TSE methods are not reviewed in this article.
Section snippets
Highway traffic and state estimation
In this section, we provide preliminary information about highway traffic and basic introduction of TSE. For systematic introduction to state-of-art of traffic flow and its theory, see, for example, Treiber and Kesting (2013) and Garavello, Han, and Piccoli (2016).
Traffic flow models
In this section, we introduce the different frameworks used for traffic flow models and review their applications to TSE. Each section describes general introduction on each topic first, and then reviews its application to TSE. In Section 3.1, we explain a fundamental concept in traffic flow theory: the fundamental diagram (FD). In Section 3.2, we present the models that describe traffic in a link, and then in Section 3.3, we briefly describe the models for nodes.
Data
In this section, we introduce available traffic measurement data used for TSE. In general, they can be grouped into two categories based on their nature: stationary and mobile data. In addition, we introduce another independent categorization: disaggregated and aggregated. Fig. 9 illustrates this categorization. These types of data are utilized in either streaming and historical manner in TSE. For practical perspectives on traffic data collection, see Leduc (2008).
Estimation approaches
TSE approaches, which may be based on the models and data that we discussed in previous sections, are summarized in this section.
Summary of the survey
In this article, we have provided a comprehensive survey of existing methods for highway TSE problem. Existing TSE methods were characterized according to three elements which are fundamental to TSE: estimation approach, traffic flow model, and input data. Then their basic features, advantages, and disadvantages were discussed. The results would be useful for assessing the applicability of a TSE method and determining future research directions.
Acknowledgments
The part of this research is financially supported by the Japan Society for the Promotion of Science (KAKENHI Grant-in-Aid for JSPS Fellows 14J10218, Young Scientists (B) 16K18164, and Scientific Research (S) 26220906). The first author would like to thank Dr. Kentaro Wada (The University of Tokyo), Dr. Wataru Nakanishi (Tokyo Institute of Technology), Dr. Masami Yanagihara (Tokyo Metropolitan University), and Mr. Kouki Satsukawa (The University of Tokyo) for insightful discussion on traffic
Toru Seo received the Dr.Eng. degree from Tokyo Institute of Technology, Tokyo, Japan. He was Research Fellow (DC2) and (PD) of Japan Society for the Promotion of Science and visiting scholar at the University of California at Berkeley, and is currently a postdoctoral researcher at Tokyo Institute of Technology. He received the Best Paper Award at the IEEE 18th International Conference on Intelligent Transportation Systems, Kometani–Sasaki Award for Dissertation, and several Japanese awards.
References (225)
- et al.
Tracking survey for individual travel behaviour using mobile communication instruments
Transportation Research Part C: Emerging Technologies
(2004) - et al.
Motorway traffic parameter estimation from mobile phone counts
European Journal of Operational Research
(2006) - et al.
Phase transition model of non-stationary traffic flow: definition, properties and solution method
Transportation Research Part B: Methodological
(2013) - et al.
On sequential data assimilation for scalar macroscopic traffic flow models
Physica D: Nonlinear Phenomena
(2012) - et al.
Genetics of traffic assignment models for strategic transport planning
Transport Reviews
(2017) - et al.
A trade-off analysis between penetration rate and sampling frequency of mobile sensors in traffic state estimation
Transportation Research Part C: Emerging Technologies
(2014) - et al.
Detecting errors and imputing missing data for single-loop surveillance systems
Transportation Research Record: Journal of the Transportation Research Board (1855)
(2003) Estimating density and lane inflow on a freeway segment
Transportation Research Part A: Policy and Practice
(2003)Revisiting the empirical fundamental relationship
Transportation Research Part B: Methodological
(2014)- et al.
Roadway traffic monitoring from an unmanned aerial vehicle
Intelligent Transport Systems, IEE Proceedings
(2006)
A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections.
Transportation Research Part B: Methodological
A variational formulation of kinematic waves: Basic theory and complex boundary conditions
Transportation Research Part B: Methodological
A variational formulation of kinematic waves: solution methods
Transportation Research Part B: Methodological
On the variational theory of traffic flow: well-posedness, duality and applications
Networks and Heterogeneous Media
Traffic density estimation in vehicular ad hoc networks: A review
Ad Hoc Networks
High-resolution numerical relaxation approximations to second-order macroscopic traffic flow models
Transportation Research Part C: Emerging Technologies
Automatic calibration of the fundamental diagram and empirical observations on capacity
Transportation research board 88th annual meeting
Overview and analysis of vehicle automation and communication systems from a motorway traffic management perspective
Transportation Research Part A: Policy and Practice
An efficient realization of deep learning for traffic data imputation
Transportation Research Part C: Emerging Technologies
Discussion of traffic stream measurements and definitions
Data fusion in intelligent transportation systems: progress and challenges–a survey
Information Fusion
Arterial travel time forecast with streaming data: A hybrid approach of flow modeling and machine learning
Transportation Research Part B: Methodological
Enhancing privacy and accuracy in probe vehicle-based traffic monitoring via virtual trip lines
IEEE Transactions on Mobile Computing
A probabilistic stationary speed–density relation based on Newell’s simplified car-following model
Transportation Research Part B: Methodological
Statistical methods versus neural networks in transportation research: Differences, similarities and some insights
Transportation Research Part C: Emerging Technologies
Online traffic state estimation based on floating car data
Traffic and granular flow ’09
A survey of computational location privacy
Personal and Ubiquitous Computing
Guaranteed prediction and estimation of the state of a road network
Transportation Research Part C: Emerging Technologies
Fast parametric estimation for macroscopic traffic flow model
Proceedings of the 17th IFAC world congress
A synthesis of emerging data collection technologies and their impact on traffic management applications
European Transport Research Review
Estimating traffic flow rate on freeways from probe vehicle data and fundamental diagram
2015 IEEE 18th international conference on intelligent transportation systems
Origin-destination matrices estimation model using automatic vehicle identification data and its application to the Han-Shin expressway network
Transportation
Matrix and tensor based methods for missing data estimation in large traffic networks
IEEE Transactions on Intelligent Transportation Systems
Dirichlet problems for some hamilton–jacobi equations with inequality constraints
SIAM Journal on Control and Optimization
Derivation of continuum traffic flow models from microscopic follow-the-leader models
SIAM Journal on Applied Mathematics
Resurrection of “second order” models of traffic flow
SIAM Journal on Applied Mathematics
Travel time forecasting and dynamic origin-destination estimation for freeways based on bluetooth traffic monitoring
Transportation Research Record: Journal of the Transportation Research Board
Highway traffic state estimation with mixed connected and conventional vehicles
IEEE Transactions on Intelligent Transportation Systems
Three decades of driver assistance systems: Review and future perspectives
Intelligent Transportation Systems Magazine, IEEE
Individual speed variance in traffic flow: analysis of Bay area radar measurements
Transportation research board 91st annual meeting
A general phase transition model for vehicular traffic
SIAM Journal on Applied Mathematics
Traffic flow estimation using higher-order speed statistics
Transportation research board 92nd annual meeting
Deriving origin destination data from a mobile phone network
IET Intelligent Transport Systems
Probability hypothesis density filtering for real-time traffic state estimation and prediction
Networks and Heterogeneous Media
Exact solutions to traffic density estimation problems involving the lighthill–whitham–richards traffic flow model using mixed integer programming
2012 15th International IEEE conference on intelligent transportation systems
Networked traffic state estimation involving mixed fixed-mobile sensor data using Hamilton–Jacobi equations
Graph constrained-CTM observer design for the Grenoble south ring
The 13th IFAC symposium on control in transportation systems
A review of properties of flow–density functions
Transport Reviews
Bivariate relations in nearly stationary highway traffic
Transportation Research Part B: Methodological
Real-time freeway traffic state prediction: A particle filter approach
2011 IEEE 14th International conference on intelligent transportation systems
Cited by (319)
The dynamics of traffic congestion: Data from a freeway Electronic Toll Collection system
2024, Physica A: Statistical Mechanics and its ApplicationsA macro-micro approach to reconstructing vehicle trajectories on multi-lane freeways with lane changing
2024, Transportation Research Part C: Emerging TechnologiesAutomatic vehicle trajectory data reconstruction at scale
2024, Transportation Research Part C: Emerging TechnologiesContinuum modeling of freeway traffic flows: State-of-the-art, challenges and future directions in the era of connected and automated vehicles
2023, Communications in Transportation ResearchI-24 MOTION: An instrument for freeway traffic science
2023, Transportation Research Part C: Emerging Technologies
Toru Seo received the Dr.Eng. degree from Tokyo Institute of Technology, Tokyo, Japan. He was Research Fellow (DC2) and (PD) of Japan Society for the Promotion of Science and visiting scholar at the University of California at Berkeley, and is currently a postdoctoral researcher at Tokyo Institute of Technology. He received the Best Paper Award at the IEEE 18th International Conference on Intelligent Transportation Systems, Kometani–Sasaki Award for Dissertation, and several Japanese awards.
Alexandre M. Bayen received the Ph.D. degree from Stanford University, Stanford, CA, USA. He is currently The Liao-Cho Professor of Engineering, in the Department of Electrical Engineering and Computer Science and Civil and Environmental Engineering and the Director of the Institute for Transportation Studies with the University of California at Berkeley, Berkeley, CA, USA. He has authored two books and over 200 articles in peer-reviewed journals and conferences. Dr. Bayen was a recipient of the CAREER Award (NSF), the PECASE Award (The White House), the Huber Prize (ASCE), and the Ruberti Prize (IEEE).
Takahiko Kusakabe received the Dr.Eng. degree from Kobe University, Kobe, Japan. He was Research Fellow (DC2) and (PD) of Japan Society for the Promotion of Science, Assistant Professor at Tokyo Institute of Technology, Visiting Fellow at Queensland University of Technology, and is currently Assistant Professor at the Center for Spatial Information Science, the University of Tokyo. He received the Best Paper Award at the IEEE 18th International Conference on Intelligent Transportation Systems, Young Scholar Paper Award from Japan Society of Civil Engineers, and several Japanese awards.
Yasuo Asakura is a Professor at Tokyo Institute of Technology. After he received his Doctor of Engineering Degree from Kyoto University in 1988, he has been working at Ehime University for 14 years, Kobe University for 9 years and appointed at Tokyo Institute of Technology in 2011. His recent research interests include transport network reliability analysis, traffic incident management, disaster evacuation management, and advanced data collection and modeling of individual travel behavior.