traffic assignment in transportation

The Geography of Transport Systems

The spatial organization of transportation and mobility

A.8 – Route Selection and Traffic Assignment

Author: dr. jean-paul rodrigue.

Transportation seeks to minimize the effort of moving passengers and freight between locations. A component of this effort involves route selection.

1. Route Selection

Human beings are natural effort minimizers , notably when it involves moving around. When given the opportunity, they will always try to choose the shortest path to go from one place to another. This behavior commonly characterizes pedestrians. When possible, a pedestrian will walk over a lawn, zigzag by cars in a parking lot, or cross a street sideways between intersections if the route selected enables them to reach a destination faster.

Transportation, as an economic activity, replicates this process of minimization, notably by trying to minimize the friction of distance between locations. Shorter times and lower costs are looked upon by all transport users, from individuals managing their own mobility to multinational corporations managing complex supply chains. For an individual, it is often only a matter of convenience, but for a corporation, it is strategically important as a direct monetary cost is involved. Under such circumstances, numerous methods have been developed to deal with the complex issue of route selection. One such classic application is the “ traveling salesperson ” problem, where the shortest route has to be selected from a set of possible paths.

Route selection has two major dimensions:

• Construction . Involves activities related to the setting of transport networks, such as road and rail construction where a physical path has to be traced. Among the primary considerations are factors such as distance and topography.
• Operation . Concerns the management of flows in a network. This is the most common route selection activity since it considers routes as fixed entities and seeks an optimal path considering existing constraints.

2. Evaluating the Route Selection Process

The choice of linking a location to another, and more importantly, the path selected, is part of a route selection process that respects a set of constraints. Although route selection varies by mode, the underlying principles remain similar; in its most simple form, a route selection process (R) tries to respect these general constraints:

R = f(min C : max E)

Route selection tries to find or use a path minimizing costs (C) and maximizing efficiency (E). There are two major dimensions of this function:

• Cost minimization . A good route selection should minimize the overall costs of the transport system. This implies construction as well as operating costs. The most direct route is not necessarily the least expensive, notably if rugged terrain is concerned, but a direct route is usually selected. It also implies that route selection must be the least damageable to the environment if environmental consequences are considered.
• Efficiency maximization . A route must support economic activities by providing a level of accessibility, thus fulfilling the needs of regional development. Even if a route is longer and thus more expensive to build and operate, it might provide better services for an area. Its efficiency is thus increased at the expense of higher costs. In numerous instances, roads were constructed more for political reasons than for meeting economic considerations.

Route selection is consequently a compromise between the cost of a transport service and its efficiency. Sometimes, there are no compromises, as the most direct route is the most efficient. At other times, a compromise is very difficult to establish as cost and efficiency are inversely proportional.

3. Traffic Assignment

Contemporary transportation networks are intensively used and congested to various degrees, notably road transportation systems in urban areas. Less known is the spatial logic behind the generation, attraction, and distribution of traffic on a network. There are two important concepts related to understanding traffic in transport systems:

• The transport demand between places must either be known or estimated. For instance, the gravity model offers a methodology to assess potential flows between locations if a set of attributes are known, such as respective distances and emission and attraction variables.
• The transport supply between places must also either be known or estimated. This involves establishing a set of paths between places that are generating and attracting movements. This includes the geometric definition of transport networks with the graph theory.

However, a fundamental concept is absent: how traffic is distributed in a transport network when its structure, capacity, and spatial demand are known.

A traffic assignment problem is traffic distribution in a network considering a demand between a set of locations and the transport supply of the network. Assignment methods are looking to model the distribution of traffic in a network according to a set of constraints, notably related to transport capacity, time, and cost.

Purchasing an airplane ticket is a classic traffic assignment example. For instance, a potential traveler wishes to go from city A to city B at a specific date and time. A query to a reservation system will offer a set of choices (paths) along with a price quote for each path. The traveler will likely choose the least expensive path, which may not necessarily be a direct path and may involve a transfer at an intermediate airport C. When tens of thousands of travelers make these daily decisions, assigning passengers to paths (air service) becomes a very complex task for airlines and their reservation (traffic assignment) system. On the other hand, airline companies use these decisions to adjust their transport supply (mainly flights) to match the demand as closely as possible. This type of problem can be solved using optimization methods.

4. Traffic and its Properties

Traffic is the number of units passing on a link in a given period of time, and it is commonly represented by Q(a,b), that is, the amount of traffic passing on the a,b link (between a and b). Units can be vehicles, passengers, tons of freight, etc. Because of the characteristics of transportation networks, there are two major types of traffic flows:

• Uninterrupted traffic . Traffic regulated by vehicle-vehicle interactions and interactions between vehicles and the transport infrastructure. The most common example of uninterrupted traffic is a highway.
• Interrupted traffic . Traffic regulated by an external means, such as a traffic signal, often creates queuing. Under interrupted flow conditions, vehicle-vehicle interactions and vehicle-infrastructure interactions play a less important part. The most common example of interrupted traffic in urban circulation is regulated by traffic signals such as lights and stop signs.

Traffic is not a spatial interaction as an interaction represents movements between locations (origins and destinations), while traffic represents movements on network links. Traffic could be similar to an interaction when the transport network is equal to the set of Origin / Destination (O/D) pairs, but this is very unlikely.

• Traffic is represented in a graph (network) by its value ; the number of any units flowing (cars, people, tons, etc.). The intensity of the traffic is proportional to the load of the network.
• Traffic is also represented in a graph by its assignment ; how the traffic is distributed on a graph according to supply and demand.

Traffic is assigned on a network according to a sequence of links where every link has its value and direction where several conditions must be satisfied:

• The graph must have nodes where traffic can be generated and attracted. These nodes are generally associated with centroids in an O-D matrix.
• The minimal (l(a,b)) and maximal (k(a,b)) capacities of every link must be respected. k(a,b) is the transport supply on the link (a,b).
• Transport demand must be respected. The O/D matrix has equal inputs and outputs (closed system).
• There is a conservation of the traffic at every node that is not an origin or a destination.

There are also two general network traffic measures: maximum load and load.

Maximum Load (ML): Number of traffic units a network can support at any time. The maximal load is the summation of the capacity of all links.

Load (L): Number of traffic units that a network supports while fulfilling a transport demand. Load is the summation of the traffic of all links.

When the load of a network reaches the maximum load, congestion is reached.

5. Traffic Maximization and Costs Minimization

Traffic in a transportation network can be represented from two perspectives, traffic maximization and costs minimization . Traffic maximization involves the determination of the maximal transport demand that a network or a section of a network can support between its nodes.

It involves maximizing traffic for all links, where the traffic on links must be equal to or lower than the link’s capacity. For simple networks, this procedure can be solved heuristically .

Cost minimization involves determining the minimal transport costs considering a known demand. Transport costs on a link are expressed by g(Q(a,b)) and the minimization function by:

This equation aims to minimize the summation of transport costs (global cost) of each link subject to capacity constraints. Again, for simple networks, the procedure can be solved heuristically . Several types of costs are involved in the minimization procedure:

• The global cost is the sum of transport costs for every link of a network, considering the demand.
• The average cost expresses the transport cost per unit in a network considering the demand (global cost/load). It often varies with the demand.
• The marginal cost expresses the costs incurred to transport a supplementary unit in a network considering an existing demand. The more a network is congested, the higher the marginal cost.

Bibliography

• Cambridge Systematics (2019) Quick Response Freight Methods, USDOT, Federal Highway Administration, Office of Planning and Environment Technical Support Services for Planning Research.

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Transportation Networks for Research

bstabler/TransportationNetworks

Folders and files.

Repository files navigation

Transportation networks.

Transportation Networks is a networks repository for transportation research.

If you are developing algorithms in this field, you probably asked yourself more than once: where can I get good data? The purpose of this site is to provide an answer for this question! This site currently contains several examples for the traffic assignment problem. Suggestions and additional data are always welcome.

Many of these networks are for studying the Traffic Assignment Problem, which is one of the most basic problems in transportation research. Theoretical background can be found in “The Traffic Assignment Problem – Models and Methods” by Michael Patriksson, VSP 1994, as well as in many other references.

This repository is an update to Dr. Hillel Bar-Gera's TNTP . As of May 1, 2016, data updates will be made only here, and not in the original website.

How To Download Networks

Each individual network and related files is stored in a separate folder. There are a number of ways to download the networks and related files:

• Click on a file, click view as Raw, and then save the file
• Clone the repository to your computer using the repository's clone URL. This is done with a Git tool such as TortoiseGit . Cloning will download the entire repository to your computer.

How To Add Networks

There are two ways to add a network:

• Create a GitHub account if needed
• Fork (copy) the repo to your account
• Make changes such as adding a new folder and committing your data
• Issue a pull request for us to review the changes and to merge your changes into the master
• Create an issue, which will notify us. We will then reply to coordinate adding your network to the site.

Make sure to create a README in Markdown for your addition as well. Take a look at some of the existing README files in the existing network folders to see what is expected.

All data is currently donated. Data sets are for academic research purposes only. Users are fully responsible for any results or conclusions obtained by using these data sets. Users must indicate the source of any dataset they are using in any publication that relies on any of the datasets provided in this web site. The Transportation Networks for Research team is not responsible for the content of the data sets. Agencies, organizations, institutions and individuals acknowledged in this web site for their contribution to the datasets are not responsible for the content or the correctness of the datasets.

How to Cite

Transportation Networks for Research Core Team. Transportation Networks for Research . https://github.com/bstabler/TransportationNetworks . Accessed Month, Day, Year.

This repository is maintained by the Transportation Networks for Research Core Team. The current members are:

• Ben Stabler
• Hillel Bar-Gera
• Elizabeth Sall

This effort is also associated with the TRB Network Modeling Committee . If you are interested in contributing in a more significant role, please get in touch. Thanks!

Any documented text-based format is acceptable. Please include a README.MD that describes the files, conventions, fields names, etc. It is best to use formats that can be easily read in with technologies like R, Python, etc. Many of the datasets on TransportationNetworks are in TNTP format.

TNTP Data format

TNTP is tab delimited text files, with each row terminated by a semicolon. The files have the following format:

• First lines are metadata; each item has a description. An important one is the <FIRST THRU NODE> . In the some networks (like Sioux-Falls) it is equal to 1, indicating that traffic can move through all nodes, including zones. In other networks when traffic is not allow to go through zones, the zones are numbered 1 to n and the <FIRST THRU NODE> is set to n+1.
• Comment lines start with ‘~’.
• Link travel time = free flow time * ( 1 + B * (flow/capacity)^Power ).
• Link generalized cost = Link travel time + toll_factor * toll + distance_factor * distance
• The network files also contain a "speed" value for each link. In some cases the "speed" values are consistent with the free flow times, in other cases they represent posted speed limits, and in some cases there is no clear knowledge about their meaning. All of the results reported below are based only on free flow travel times as described by the functions above, and do not use the speed values.
• Free Flow Time
• Speed limit
• Trip tables (must be named <network>_trips.tntp ) – An Origin label and then Origin node number, followed by Destination node numbers and OD flow

Import scripts

The networks' formatting has been harmonized to facilitate programatic imports, and import scripts are provided inside the folder _scripts :

Summary of Networks

Publications

A partial list of publications where datasets from this repository have been used. All website users are kindly requested to add their publications to this list.

• Bar-Gera, H.(2002), Origin-based algorithm for the traffic assignment problem, Transportation Science 36(4), 398-417. Bar-Gera, H. & Boyce, D. (2003), Origin-based algorithms for combined travel forecasting models, Transportation Research Part B - Methodological 37 (5), 405-422.
• Boyce, D. & Bar-Gera, H. (2003), Validation of urban travel forecasting models combining origin-destination, mode and route choices, Journal of Regional Science, 43, 517-540.
• Boyce, D., Ralevic-Dekic, B. & Bar-Gera, H. (2004), Convergence of Traffic Assignments: How Much Is Enough? The Delaware Valley Region Case Study, ASCE Journal of Transportation Engineering, 130 (1), 49-55.
• Boyce, D. & Bar-Gera, H. (2004), Multiclass Combined Models for Urban Travel Forecasting, Networks and Spatial Economics, 4 (1), 115-124.
• Bar-Gera, H. & Boyce D. (2006), Solving a non-convex combined travel forecasting model by the Method of Successive Averages with constant step sizes, Transportation Research Part B - Methodological, 40 (5), 351-367.
• Bar-Gera, H. (2006), Primal Method for Determining the Most Likely Route Flows in Large Road Networks, Transportation Science, 40 (3), 269-286.
• Bar-Gera, H., Mirchandani, P.B. & Wu, F.ST (2006), Evaluating the assumption of independent turning probabilities, Transportation Research Part B - Methodological, 40 (10), 903-916.
• Bar-Gera, H. & Luzon, A. (2007), Differences among route flow solutions for the user-equilibrium traffic assignment problem, ASCE Journal of Transportation Engineering, 133 (4), 232-239.
• Bar-Gera, H. & Luzon, A. (2007), Non-unique route flow solutions for user-equilibrium assignments. Traffic Engineering and Control, 48 (9), 408-412.
• Bar-Gera, H. (2010), Traffic assignment by paired alternative segments, Transportation Research Part B - Methodological, 44 (8-9), 1022-1046.
• Bar-Gera, H., Boyce, D. & Nie, Y. (2012), User-equilibrium route flows and the condition of proportionality. Transportation Research Part B - Methodological 46 (3), 440–462.
• Bar-Gera, H., Hellman, F. & Patriksson, M. (2013), Efficient design and pricing of equilibrium traffic networks precise calculations of equilibria and sensitivities. Transportation Research Part B - Methodological, 57, 485-500.
• Rey, D.PI, Bar-Gera, H.PI, Dixit, V.PI, Waller, S.T.PI (2019). A Branch and Price Algorithm for the Work-zone Scheduling Problem. Accepted for publication in Transportation Science.

Other Related Projects

• TRB Network Modeling Committee
• InverseVIsTraffic is an open-source repository that implements some inverse Variational Inequality (VI) formulations proposed for both single-class and multi-class transportation networks. The package also implements algorithms to evaluate the Price of Anarchy in real road networks. Currently, the package is maintained by Jing Zhang .
• Frank-Wolfe algorithm that demonstrates how to read these data formats and runs a FW assignment. The header file "stdafx.h" is for Microsoft Visual C (MSVC) compiler. On Unix and other compilers it can be simply omitted.
• seSue is an open source tool to aid research on static path-based Stochastic User Equilibrium (SUE) models. It is designed to carry out experiments to analyze the effects of (1) different path-based SUE models associated with different underlying discrete choice models (as well as hybrid models), and (2) different route choice set generation algorithms on the route choice probabilities and equilibrium link flows. For additional information, contact Ugur Arikan
• TrafficAssignment.jl is an open-source, Julia package that implements some traffic assignment algorithms. It also loads the transportation network test problem data in vector/matrix forms. The packages is maintained by Changhyun Kwon .
• DTALite-S - Simplified Version of DTALite for Education and Research
• NeXTA open-source GUI for visualizing static/dynamic traffic assignment results
• Transit Network Design Instances - transit network design instances for research repository
• Fast-Trips - open source dynamic transit assignment software, data standards, and research project
• AMS Data Hub is an FHWA research project to develop a prototype data hub and data schema for transportation simulation models
• GTFS-PLUS - GTFS-based data transit network data standard suitable for dynamic transit modeling
• Open matrix - Open matrix standard for binary matrix data management that is supported by the major commercial travel demand modeling packages and includes code for R, Python, Java, C#, and C++.
• AequilibraE - Python package for transportation modeling
• General Modeling Network Specification - GMNS defines a common human and machine readable format for sharing routable road network files. It is designed to be used in multi-modal static and dynamic transportation planning and operations models.

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Traffic Assignment: A Survey of Mathematical Models and Techniques

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• Kaan M. A. Özbay 15  

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This chapter presents the fundamentals of the theory and techniques of traffic assignment problem. It first presents the steady-state traffic assignment problem formulation which is also called static assignment, followed by Dynamic Traffic Assignment (DTA), where the traffic demand on the network is time varying. The static assignment problem is shown in a mathematical programming setting for two different objectives to be satisfied. The first one where all users experience same travel times in alternate used routes is called user-equilibrium and another setting called system optimum in which the assignment attempts to minimize the total travel time. The alternate formulation uses variational inequality method which is also presented. Dynamic travel routing problem is also reviewed in the variational inequality setting. DTA problem is shown in discrete and continuous time in terms of lumped parameters as well as in a macroscopic setting, where partial differential equations are used for the link traffic dynamics. A Hamilton–Jacobi- based travel time dynamics model is also presented for the links and routes, which is integrated with the macroscopic traffic dynamics. Simulation-based DTA method is also very briefly reviewed. This chapter is taken from the following Springer publication and is reproduced here, with permission and with minor changes: Pushkin Kachroo, and Neveen Shlayan, “Dynamic traffic assignment: A survey of mathematical models and technique,” Advances in Dynamic Network Modeling in Complex Transportation Systems (Editor: Satish V. Ukkusuri and Kaan Özbay) Springer New York, 2013. 1-25.

This chapter is taken from the following Springer publication and is reproduced here, with permission and with minor changes: Pushkin Kachroo, and Neveen Shlayan, “Dynamic traffic assignment: A survey of mathematical models and techniques,” Advances in Dynamic Network Modeling in Complex Transportation Systems (Editor: Satish V. Ukkusuri and Kaan Özbay) Springer New York, 2013. 1–25.

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Dynamic Traffic Assignment: A Survey of Mathematical Models and Techniques

Traffic Assignments to Transportation Networks

Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation

Gazis DC (1974) Traffic science. Wiley-Interscience Inc, New York, NY

MATH   Google Scholar  

Potts RB, Oliver RM (1972) Flows in transportation networks. Elsevier Science

Google Scholar  

Stouffer SA (1940) Intervening opportunities: a theory relating mobility and distance. Am Sociol Rev 5:845–867

Article   Google Scholar  

Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230

Article   MathSciNet   Google Scholar  

Voorhees AM (2013) A general theory of traffic movement 40:1105–1116. https://doi.org/10.1007/s11116-013-9487-0

Wilson AG (1967) A statistical theory of spatial distribution models. Transp Res 1:253–269

Ben-Akiva ME, Lerman SR (1985) Discrete choice analysis: theory and application to travel demand. MIT Press series in transportation studies, MIT Press

Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc Inst Civil Eng PART II 1:325–378

Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall

Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Netw Spat Econ 1(3/4):233–265

Kachroo P, Sastry S (2016a) Travel time dynamics for intelligent transportation systems: theory and applications. IEEE Trans Intell Transp Syst 17(2):385–394

Kachroo P, Sastry S (2016b) Traffic assignment using a density-based travel-time function for intelligent transportation systems. IEEE Trans Intell Transp Syst 17(5):1438–1447

Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Natl Bur Stan 73B:91–118

Beckmann MJ, McGuire CB, Winsten CB (1955) Studies in the economics of transportation. Technical report, Rand Corporation

Dafermos S (1980) Traffic equilibrium and variational inequalities. Transp Sci 14:42–54

Dafermos S (1983) An iterative scheme for variational inequalities. Math Prog 26:40–47

Kinderlehrer D, Stampacchia G (2000) An introduction to variational inequalities and their applications, vol 31. Society for Industrial Mathematics

Avriel M (2003) Nonlinear programming: analysis and methods. Dover Publications

Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming: theory and algorithms. John Wiley & Sons

Mangasarian OL (1994) Nonlinear programming, vol 10. Society for Industrial Mathematics. https://doi.org/10.1137/1.9781611971255

Nugurney A (2000) Sustainable transportation networks. Edward Elgar Publishing, Northampton, MA

Facchinei F, Pang JS (2007) Finite-dimensional variational inequalities and complementarity problems. Springer Science & Business Media

Nagurney A, Zhang D (2012) Projected dynamical systems and variational inequalities with applications, vol 2. Springer Science & Business Media

Zhang D, Nagurney A (1995) On the stability of projected dynamical systems. J Optim Theory Appl 85(1):97–124

Nagurney A, Zhang D (1997) Projected dynamical systems in the formulation, stability analysis, and computation of fixed-demand traffic network equilibria. Transp Sci 31(2):147–158

Zhang D, Nagurney A (1996) On the local and global stability of a travel route choice adjustment process. Transp Res Part B: Methodol 30(4):245–262

Dafermos S (1988) Sensitivity analysis in variational inequalities. Math Oper Res 13:421–434

Dupuis P, Nagurney A (1993) Dynamical systems and variational inequalities. Ann Oper Res 44(1):7–42

Skorokhod AV (1961) Stochastic equations for diffusion processes in a bounded region. Theory Probab Appl 6:264–274

Chiu Y-C, Bottom J, Mahut M, Paz A, Balakrishna R, Waller T, Hicks J (2010) A primer for dynamic traffic assignment. Trans Res Board, 2–3

Ran B, Boyce DE (1996) Modeling dynamic transportation networks: an intelligent transportation system oriented approach. Springer

Chapter   Google Scholar  

Friesz TL (2001) Special issue on dynamic traffic assignment. Netw Spat Econ Part I 1:231

Merchant DK, Nemhauser GL (1978a) A model and an algorithm for the dynamic traffic assignment problems. Transp Sci 12(3):183–199

Merchant DK, Nemhauser GL (1978b) Optimality conditions for a dynamic traffic assignment model. Transp Sci 12(3):183–199

Boyce D, Lee D, Ran B (2001) Analytical models of the dynamic traffic assignment problem. Netw Spat Econ 1:377–390

Friesz TL, Luque J, Tobin RL, Wie BW (1989) Dynamic network traffic assignment considered as a continuous time optimal control problem. Oper Res 37:893–901

Friesz TL, Bernstein D, Smith TE, Tobin RL, Wie BW (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper Res 41:179–191

Chen HK (2012) Dynamic travel choice models: a variational inequality approach. Springer Science & Business Media

Carey M (1992) Nonconvexity of the dynamic traffic assignment problem. Transp Res Part B: Methodol 26(2):127–133

Lighthill MJ, Whitham GB (1955) On kinematic waves II. A theory of traffic on long crowded roods. Proc Roy Soc London A Math Phys Sci 229:317–345. https://doi.org/10.1098/rspa.1955.0089

Richards PI (1956) Shockwaves on the highway. Oper Res 4:42–51

Greenshields B, Channing W, Miller H (1935) A study of traffic capacity. In: Highway Research Board Proceedings. National Research Council (USA), Highway Research Board

LeVeque RJ (1990) Numerical methods for conservation laws. Birkhäuser Verlag

Bressan A (2000) Hyperbolic systems of conservation laws: the one-dimensional Cauchy problem. Oxford University Press

Strub I, Bayen A (2006) Weak formulation of boundary conditions for scalar conservation laws: an application to highway modeling. Int J Robust Nonlinear Control 16:733–748

Garavello M, Piccoli B (2006) Traffic flow on networks. American Institute of Mathematical Sciences, Ser Appl Maths 1:1–243

Holden H, Risebro NH (1995) A mathematical model of traffic flow on a network of unidirectional roads. SIAM J Math Anal 26:999–1017

Lebacque JP (1996) The godunov scheme and what it means for first order traffic flow models. In: Transportation and Traffic Theory, Proceedings of The 13th International Symposium on Transportation and Traffic Theory, Lyon, France, pp 647–677

Coclite GM, Piccoli B (2002) Traffic flow on a road network. Arxiv preprint math/0202146

Garavello M, Piccoli B (2005) Source-destination flow on a road network. Commun Math Sci 3(3):261–283

Gugat M, Herty M, Klar A, Leugering G (2005) Optimal control for traffic flow networks. J Optim theory Appl 126(3):589–616

Lebacque JP, Khoshyaran MM (2002) First order macroscopic traffic flow models for networks in the context of dynamic assignment. In: Patriksson M, Labbé M (eds) Transportation, Planning: State of the Art. Springer US, Boston, MA, pp 119–140. https://doi.org/10.1007/0-306-48220-7_8

Buisson C, Lebacque JP, Lesort JB (1996) Strada, a discretized macroscopic model of vehicular traffic flow in complex networks based on the godunov scheme. In: CESA’96 IMACS Multiconference: computational engineering in systems applications, pp 976–981

Mahmassani HS, Hawas YE, Abdelghany K, Abdelfatah A, Chiu YC, Kang Y, Chang GL, Peeta S, Taylor R, Ziliaskopoulos A (1998) DYNASMART-X; Volume II: analytical and algorithmic aspects. Technical report ST067 85

Ben-Akiva M, Bierlaire M, Koutsopoulos H, Mishalani R (1998) DynaMIT: a simulation-based system for traffic prediction. In: DACCORS short term forecasting workshop, vol TRANSP-OR-CONF-2006-060

Kachroo P, Özbay K (2012) Feedback control theory for dynamic traffic assignment. Springer Science & Business Media

Kachroo P, Özbay K (2011) Feedback ramp metering in intelligent transportation systems. Springer Science & Business Media

Kachroo P, Özbay K (1998) Solution to the user equilibrium dynamic traffic routing problem using feedback linearization. Transp Res Part B: Methodol 32(5):343–360

Kachroo P, Özbay K (2006) Modeling of network level system-optimal real-time dynamic traffic routing problem using nonlinear \(\text{ h }{\infty }\) feedback control theoretic approach. J Intell Transp Syst 10(4):159–171

Kachroo P, Özbay K (2005) Feedback control solutions to network level user-equilibrium real-time dynamic traffic assignment problems. Netw Spat Econ 5(3):243–260

Spiess H (1990) Conical volume-delay functions. Transp Sci 24(2):153–158

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Kachroo, P., Özbay, K.M.A. (2018). Traffic Assignment: A Survey of Mathematical Models and Techniques. In: Feedback Control Theory for Dynamic Traffic Assignment. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-69231-9_2

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