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Dynamic Traffic Assignment and Sustainable Transport Systems
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Special issue information.
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A special issue of Sustainability (ISSN 2071-1050). This special issue belongs to the section " Sustainable Transportation ".
Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 10182
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Dear Colleagues,
Dynamic traffic assignment (DTA) is one of the most important foundational theories in intelligent transportation systems (ITSs). DTA models and technologies could be used in the field of traffic planning, traffic control and management, transportation policy evaluation and online transportation systems. In recent years, technological advances have paved the way for the development of transportation systems, and have had a huge impact on the research of dynamic traffic assignment. Advanced technologies such as artificial intelligence, autonomous driving, wireless communication, and electric vehicles provide users with real-time information about traffic conditions and allow travelers to choose different travel modes, travel routes and real-time decisions. Such advanced technologies may have made the basis of DTA models’ change, such as the travel choice principle, travel demand evaluation, and traffic behaviors. Further, the application scenarios and effects of DTA models will also change greatly. All of this will have enormous potential for enhancing the sustainability of transportation systems.
In this Special Issue, we invite the submission of research papers that specifically address the potential related advanced technologies with dynamic traffic assignment models for enhancing the sustainability of transportation systems. The scope of this Special Issue is to cover DTA model and theory, DTA with autonomous driving, electric vehicles, shared traffic and other related advanced technologies. Topics of interest with a general focus on dynamic traffic assignment and sustainable transport systems include but are not limited to:
- Dynamic traffic assignment model and theory;
- Travel choice principle and traffic flow propagation models;
- Effective algorithms for solving DTA problems;
- Online DTA model and efficiency;
- Application of DTA models for traffic management and control;
- DTA model and application under autonomous driving environment;
- DTA model and application under electric vehicle environment;
- DTA model and application under shared traffic environment;
- DTA model and application under other advanced technologies environment;
- DTA and sustainable transport systems.
Dr. Zhiheng Li Dr. Jiyuan Tan Dr. Kai Zhang Dr. Yang Zhou Guest Editors
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Dynamic Traffic Assignment
Early Experiences
Current Practices
Research Needs
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Activity Based Models
Network Assignment
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(opens new window) is a hot topic in travel forecasting.
# Background
Traditional user equilibrium highway assignment models predict the effects of congestion and the routing changes of traffic as a result of that congestion. They neglect, however, many of the details of real-world traffic operations, such as queuing, shock waves, and signalization. Currently, it is common practice to feed the results of user equilibrium traffic assignments into dynamic network models as a mechanism for evaluating these policies. The simulation models themselves, however, do not predict the routing of traffic, and therefore are unable to account for re-routing owing to changes in congestion levels or policy, and can be inconsistent with the routes determined by the assignment. Dynamic network models overcome this dichotomy by combining a time-dependent shortest path algorithm with some type of simulation (often meso or macroscopic) of link travel times and delay. In doing so it allows added reality and consistency in the assignment step, as well as the ability to evaluate policies designed to improve traffic operations. These are some of the main benefits of dynamic network models .
DTA models can generally be classified by how they model link or intersection delay. Analytical DTA models treat it in the same manner as static equilibrium assignment models, with no explicit representation of signals. Link capacity functions, often similar or identical to those used in static assignment, are used to calculate link travel times. Analytical models have been widely used in research and for real-time control system applications. Simulation-based DTA models include explicit representation of traffic control devices. Such models require detailed signal parameters to include phasing, cycle length, and offsets for each signal in the network. Delay is calculated for each approach, with vehicles moving from one link to the next only if available downstream capacity is available. The underlying traffic model is often different, but at the network level such models behave in a similar fashion.
Demand is specified in the form of origin–destination matrices for short time intervals, typically 15 minutes each. Trips are typically randomly loaded onto the network during each time interval. As with traffic microsimulation models, adequate downstream capacity must be present to load the trips onto the network. The shortest paths through time and space are found for each origin–destination pair, and flows loaded to these paths. A generalized flowchart of the process is shown below.
![Typical DTA model flow Typical DTA model flow](https://tfresource.org/Dta-flowchart.png)
As with static assignment models, the process shown above is iteratively solved until a stable solution is reached. The memory and computing requirements of DTA, however, are orders of magnitude larger than for static assignment, reducing the number of iterations and paths that can be kept in memory. Instead of a single time period, as with static assignment, DTA models must store data for each time interval as well. A three-hour static assignment would involve only one time interval. A DTA model of the same period, however, might require 12 intervals, each 15 minutes in duration. These are all in addition to the memory requirements imposed by the number of user classes and zones.
# Early Experiences
Research into DTA dates back several decades, but was largely limited to academics working on its formulation and theoretical aspects. DTA overcomes the limitations of static assignment models, although at the cost of increased data requirements and computational burden. Moreover, software platforms capable of solving the DTA problem for large urban systems and experience in their use are recent developments.
(opens new window) has been successfully applied to a large subarea of Calgary and to analyses of the Rue Notre-Dame in Montreal. Although user group presentations of both applications have been made, and reported very encouraging results, the work is currently unpublished and inaccessible except through contact with the developers.
(opens new window) . The network from the Atlanta Regional Commission (ARC) regional travel model formed the starting point for the DTA network. Intersections were coded, centroid connectors were re-defined, and network coding errors were corrected. A signal synthesizer derived locally optimal timing parameters for more than 2,200 signalized intersections in the network. Trip matrices from the ARC model were divided into 15-minute intervals for the specification of demand. Approximately 40 runs of the model were required to diagnose coding and software errors. Unfortunately, the execution time for the model was approximately one week per run. The resulting model eventually validated well to observed conditions; however, the length of time required to render it operational and the run time required prevented it from being used in studies as originally intended. Subsequent work by the developer has resulted in substantial reductions in run time, but this remains a significant issue that must be overcome before such models can be more widely used.
# Current Practices
# research needs.
A number of cities are currently testing DTA models, but are not far enough along in their work to share even preliminary results. At least a dozen such cases are known to be in varying stages of planning or execution, suggesting that the use of DTA models in planning applications is about to expand dramatically. However, in addition to the issue of long run times, a number of other issues must be addressed before such models are likely to be widely adopted:
- Criteria for the validation of such models have not been widely accepted. The paucity of traffic counts in most urban areas, and especially at 15, 30, or 60 minute intervals, is a significant barrier to definitive assessment of these models.
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Using the General Link Transmission Model in a Dynamic Traffic Assignment to Simulate Congestion on Urban Networks
This article presents two new models of Dynamic User Equilibrium that are particularly suited for intelligent transportation systems (ITS) applications, where the evolution of vehicle flows and travel times must be simulated on large road networks, possibly in real-time. The key feature of the proposed models is the detail representation of the main congestion phenomena occurring at nodes of urban networks, such as vehicle queues and their spillback, as well as flow conflicts in mergins and diversions. Compared to the simple word of static assignment, where only the congestion along the arc is typically reproduced through a separable relation between vehicle flow and travel time, this type of dynamic traffic assignment (DTA) models are much more complex, as the above relation becomes non-separable, both in time and space. Traffic simulation is here attained through a macroscopic flow model, that extends the theory of kinematic waves to urban networks and non-linear fundamental diagrams: the General Link Transmission Model (GLTM). The sub-models of the GLTM, namely the Node Intersection Model, the Forward Propagation Model of vehicles and the Backward Propagation Model of spaces, can be combined in two different ways to produce arc travel times starting from turn flows. The first approach is to consider short time intervals of a few seconds and process all nodes for each temporal layer in chronological order. The second approach allows to consider long time intervals of a few minutes and for each sub-model requires to process the whole temporal profile of involved variables. The two resulting DTA models are here analyzed and compared with the aim of identifying their possible use cases. A rigorous mathematical formulation is out of the scope of this paper, as well as a detailed explanation of the solution algorithm. The dynamic equilibrium is anyhow sought through a new method based on Gradient Projection, which is capable to solve both proposed models with any desired precision in a reasonable number of iterations. Its fast convergence is essential to show that the two proposed models for network congestion actually converge at equilibrium to nearly identical solutions in terms of arc flows and travel times, despite their two diametrical approaches wrt the dynamic nature of the problem, as shown in the numerical tests presented here.
- Record URL: https://doi.org/10.1016/j.trpro.2015.01.011
- Record URL: http://www.sciencedirect.com/science/article/pii/S2352146515000125
- Find a library where document is available. Order URL: http://worldcat.org/issn/23521465
- © 2013 Guido Gentile. Published by Elsevier B.V.
- Gentile, Guido
- Publication Date: 2015
- Media Type: Digital/other
- Features: Figures; References; Tables;
- Pagination: pp 66-81
- Transportation Research Procedia
- Issue Number: 0
- Publisher: Elsevier
- ISSN: 2352-1465
- Serial URL: http://www.sciencedirect.com/science/journal/23521465/
Open Access (libre)
Subject/Index Terms
- TRT Terms: Dynamic traffic assignment ; Intelligent transportation systems ; Macroscopic traffic flow ; Traffic assignment ; Traffic congestion ; Traffic forecasting ; Traffic simulation ; Travel time
- Uncontrolled Terms: Dynamic user equilibrium
- Subject Areas: Highways; Operations and Traffic Management; Planning and Forecasting; I72: Traffic and Transport Planning;
Filing Info
- Accession Number: 01554671
- Record Type: Publication
- Files: TRIS
- Created Date: Feb 26 2015 9:53AM
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A dynamic traffic assignment model for highly congested urban networks
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World's Worst Traffic In Moscow, TomTom Says
July 22, 2014 • Staff • Bookmark +
![dynamic traffic assignment congestion Photo of Moscow congestion from 2012 via Sergey Ivanov/Flickr.](https://fleetimages.bobitstudios.com/upload/automotive-fleet/content/news/_migrated/m-cc-moscow-traffic.jpg)
Photo of Moscow congestion from 2012 via Sergey Ivanov/Flickr.
Drivers in Moscow during the most congested periods will spend an average of 74 percent more time getting to their destination in a city TomTom has ranked as the most congested around the globe.
That would equate to an average delay of 76 minutes per hour during peak travel times. The finding came in the annual global traffic index from the Amsterdam-based navigation and traffic services company.
Commuters spend an average of eight days per year stuck in traffic jams. Traffic on secondary routes can be more congested, the study found.
The annual traffic index covers 180 global cities, and compares travel times during non-congested hours to those in peak hours. The index takes into consideration major highways and local roads.
Only one U.S. city, Los Angeles, made the list of the 10 most congested cities, according to TomTom. Here's the full list with the average percent increase in traffic times:
- Moscow, Russia: 74 percent
- Istanbul, Turkey: 62 percent
- Rio de Janeiro, Brazil: 55 percent
- Mexico City, Mexico: 54 percent
- São Paulo, Brazil: 46 percent
- Palermo, Italy: 39 percent
- Warsaw, Poland: 39 percent
- Rome, Italy: 37 percent
- Los Angeles, USA: 36 percent
- Dublin, Ireland: 35 percent
For the full report, click here .
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Data-Driven Traffic Assignment: A Novel Approach for Learning Traffic Flow Patterns Using Graph Convolutional Neural Network
- Published: 24 July 2023
- Volume 5 , article number 11 , ( 2023 )
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- Rezaur Rahman 1 &
- Samiul Hasan 1
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We present a novel data-driven approach of learning traffic flow patterns of a transportation network given that many instances of origin to destination (OD) travel demand and link flows of the network are available. Instead of estimating traffic flow patterns assuming certain user behavior (e.g., user equilibrium or system optimal), here we explore the idea of learning those flow patterns directly from the data. To implement this idea, we have formulated the traditional traffic assignment problem (from the field of transportation science) as a data-driven learning problem and developed a neural network-based framework known as Graph Convolutional Neural Network (GCNN) to solve it. The proposed framework represents the transportation network and OD demand in an efficient way and utilizes the diffusion process of multiple OD demands from nodes to links. We validate the solutions of the model against analytical solutions generated from running static user equilibrium-based traffic assignments over Sioux Falls and East Massachusetts networks. The validation results show that the implemented GCNN model can learn the flow patterns very well with less than 2% mean absolute difference between the actual and estimated link flows for both networks under varying congested conditions. When the training of the model is complete, it can instantly determine the traffic flows of a large-scale network. Hence, this approach can overcome the challenges of deploying traffic assignment models over large-scale networks and open new directions of research in data-driven network modeling.
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The data that support the findings of this study are available from the corresponding author, [[email protected]], upon reasonable request.
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Appendix A: modeling traffic flows using spectral graph convolution
In spectral graph convolution, a spectral convolutional filter is used to learn traffic flow patterns inside a transportation network in response to travel demand variations. The spectral filter is derived from spectrum of the Laplacian matrix, which consists of eigenvalues of the Laplacian matrix. So to construct the spectrum, we must calculate the eigenvalues of` the Laplacian matrix. For a symmetric graph, we can compute the eigenvalues using Eigen decomposition of the Laplacian matrix. In this problem, we consider the transportation network as a symmetric-directed graph, same number of links getting out and getting inside a node, which means the in-degree and out-degree matrices of the graph are similar. Thus, the Laplacian matrix of this graph is diagonalizable as follows using Eigen decomposition
where \(\boldsymbol{\Lambda }\) is a diagonal matrix with eigenvalues, \({\lambda }_{0},{\lambda }_{1},{\lambda }_{2}, . . . ,{\lambda }_{N}\) and \({\varvec{U}}\) indicates the eigen vectors, \({u}_{0},{u}_{1},{u}_{2}, . . . ,{u}_{N}\) . Eigen values represent characteristics of transportation network in terms of strength of a particular node based on its position, distance between adjacent nodes, and dimension of the network. The spectral graph convolution filter can be defined as follows:
where \(\theta\) is the parameter for the convolution filter shared by all the nodes of the network and \(K\) is the size of the convolution filter. Now the spectral graph convolution over the graph signal ( \({\varvec{X}})\) is defined as follows:
According to spectral graph theory, the shortest path distance i.e., minimum number of links connecting nodes \(i\) and \(j\) is longer than \(K\) , such that \({L}^{K}\left(i, j\right) = 0\) (Hammond et al. 2011 ). Consequently, for a given pair of origin ( \(i\) ) and destination ( \(j)\) nodes, a spectral graph filter of size K has access to all the nodes on the shortest path of the graph. It means that the spectral graph convolution filter of size \(K\) captures flow propagation through each node on the shortest path. So the spectral graph convolution operation can model the interdependency between a link and its \(i\) th order adjacent nodes on the shortest paths, given that 0 ≤ i ≤ K .
The computational complexity of calculating \({{\varvec{L}}}_{{\varvec{w}}}^{{\varvec{k}}}\) is high due to K times multiplication of \({L}_{w}\) . A way to overcome this challenge is to approximate the spectral filter \({g}_{\theta }\) with Chebyshev polynomials up to ( \(K-1\) )th order (Hammond et al. 2011 ). Defferrard et al. (Defferrard et al. 2016 ) applied this approach to build a K -localized ChebNet, where the convolution is defined as
in which \(\overline{{\varvec{L}} }=2{{\varvec{L}}}_{{\varvec{s}}{\varvec{y}}{\varvec{m}}}/{{\varvec{\uplambda}}}_{{\varvec{m}}{\varvec{a}}{\varvec{x}}}-{\varvec{I}}\) . \(\overline{{\varvec{L}} }\) represents a scaling of graph Laplacian that maps the eigenvalues from [0, \({\uplambda }_{max}\) ] to [-1,1]. \({{\varvec{L}}}_{{\varvec{s}}{\varvec{y}}{\varvec{m}}}\) is defined as symmetric normalization of the Laplacian matrix \({{{\varvec{D}}}_{{\varvec{w}}}}^{-1/2}{{\varvec{L}}}_{{\varvec{w}}}{{\boldsymbol{ }{\varvec{D}}}_{{\varvec{w}}}}^{-1/2}.\) \({T}_{k}\) and θ denote the Chebyshev polynomials and Chebyshev coefficients. The Chebyshev polynomials are defined recursively by \({T}_{k}\left(\overline{{\varvec{L}} }\right)=2x{T}_{k-1}\left(\overline{{\varvec{L}} }\right)-{T}_{k-2}\left(\overline{{\varvec{L}} }\right)\) with \({T}_{0}\left(\overline{{\varvec{L}} }\right)=1\) and \({T}_{1}\left(\overline{{\varvec{L}} }\right)=\overline{{\varvec{L}} }\) . These are the basis of Chebyshev polynomials. Kipf and Welling (Kipf and Welling 2016 ) simplified this model by approximating the largest eigenvalue \({\lambda }_{max}\) of \(\overline{L }\) as 2. In this way, the convolution becomes
where Chebyshev coefficient, \(\theta ={\theta }_{0}=-{\theta }_{1}\) , All the details about the assumptions and their implications of Chebyshev polynomial can be found in (Hammond et al. 2011 ). Now the simplified graph convolution can be written as follows:
Since \({\varvec{I}}+{{{\varvec{D}}}_{{\varvec{w}}}}^{-1/2}{{\varvec{A}}}_{{\varvec{w}}}{{\boldsymbol{ }{\varvec{D}}}_{{\varvec{w}}}}^{-1/2}\) has eigenvalues in the range [0, 2], it may lead to exploding or vanishing gradients when used in a deep neural network model. To alleviate this problem, Kipf et al. (Kipf and Welling 2016 ) use a renormalization trick by replacing the term \({\varvec{I}}+{{{\varvec{D}}}_{{\varvec{w}}}}^{-1/2}{{\varvec{A}}}_{{\varvec{w}}}{{\boldsymbol{ }{\varvec{D}}}_{{\varvec{w}}}}^{-1/2}\) with \({{\overline{{\varvec{D}}} }_{{\varvec{w}}}\boldsymbol{ }\boldsymbol{ }}^{-1/2}{\overline{{\varvec{A}}} }_{{\varvec{w}}}{{\boldsymbol{ }\overline{{\varvec{D}}} }_{{\varvec{w}}}}^{-1/2}\) , with \({\overline{{\varvec{A}}} }_{{\varvec{w}}}={{\varvec{A}}}_{{\varvec{w}}}+{\varvec{I}}\) , similar to adding a self-loop. Now, we can simplify the spectral graph convolution as follows:
where \({\varvec{\Theta}}\in {{\varvec{R}}}^{{\varvec{N}}\times {\varvec{N}}}\) indicates the parameters of the convolution filter to be learnt during training process. From Eq. 21 , we can observe that spectral graph convolution is a special case of diffusion convolution (Li et al. 2018 ), but the only difference is that in spectral convolution, we symmetrically normalized the adjacency matrix.
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Rahman, R., Hasan, S. Data-Driven Traffic Assignment: A Novel Approach for Learning Traffic Flow Patterns Using Graph Convolutional Neural Network. Data Sci. Transp. 5 , 11 (2023). https://doi.org/10.1007/s42421-023-00073-y
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DOI : https://doi.org/10.1007/s42421-023-00073-y
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