Hi!

To get a rough overview, I recommend the following review papers:

[1] Bellomo, N. and C. Dogbe. “On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives”. SIAM Rev. 53, no. 3 (2011): 409–463

[2] Chowdhury, D., L. Santen, and A. Schadschneider. “Statistical physics of vehicular traffic and some related systems”. Phys. Rep. 329, no. 4–6 (2000): 199–329

[3] Helbing, D. “Traffic and related self-driven many-particle systems”. Rev. Mod. Phys. 73, no. 4 (2001): 1067–1141

[4] Nagatani, T. “The physics of traffic jams”. Rep. Prog. Phys. 65, no. 9 (2002): 1331–1386

[5] Nagel, K., P. Wagner, and R. Woesler. “Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling”. Op. Res. 51, no. 5 (2003)

These articles offer a good starting point, but most of them [2-5] are more than ten years old.

But this does not mean traffic research has not evolved.The most prominent achievement during the past ten years -- in my opinion -- is the development of the so-called three-phase traffic theory by Boris Kerner. Kerner found that the obvious classification of traffic in free flow and congested flow is too coarse-grained because his studies showed a rich variety of spatiotemporal patterns of congested traffic. According to the three-phase traffic theory, congested traffic subdivides into two phases: “synchronized traffic” and “wide moving jams”. Therefore, this theory is based on and culminates in the identification of distinct spatiotemporal patterns of congested traffic with very characteristic properties. This theory can also explain the physical origin leading to a traffic breakdown. (Yet, it has to be mentioned that this theory is quite controversial among traffic engineers.)

There is a huge amount of literature on this topic itself. A good introduction which is freely available:

[6] Kerner, B. S. “Modern approaches to basic traffic modeling: Three-Phase Traffic Theory”. Transp. Res. Circular E-C 149 (2011): 22–42

and a Wikipedia-article:

https://en.wikipedia.org/wiki/Three-phase_traffic_theory

(There are even two books by Kerner:

[7] Kerner, B. S. “The Physics of Traffic”. Berlin: Springer, 2004

[8] Kerner, B. S. “Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory”. Berlin: Springer, 2009 )

As traffic is studied by engineers and physicists, i finally would like to refer to two text books -- one treating traffic from a physicist's point of view [9] and one treating traffic from a engineer's point of view [10]

[9] Schadschneider, A., D. Chowdhury, and K. Nishinari. “Stochastic Transport in Complex Systems: From Molecules to Vehicles”. Oxford: Elsevier Science, 2010

[10] May, A. D. “Traffic flow fundamentals”. Englewood Cliffs: Prentice-Hall, 1990

Hi, 

since a traffic flow modelling has been studied extensively, can you be more exact about your dominant research objective? In general, three main categories of vehicular traffic flow analysis have been distinguished: microscopic (in my view, the most interesting :-) modelling approach of driver- to-driver interactions in the platoon of vehicles using delay differential equations), macroscopic (modeling in terms of partial differential equations derived from conservation laws) and mesoscopic analysis (combination of both above principles --it lies in defining the probabilistic function of traffic flow state). For more details, see, for instance, a survey by Bellomo and Dogbe -- On the modeling of traffic and crowds: A survey of models, speculations, and perspectives. 

thank you

It is an overview for the current approaches in modeling the traffic flow whatever it is microscopic or macroscopic, sometimes they use finite element to model the traffic flow

just I am searching for good papers that will help my research 

Hi!

To get a rough overview, I recommend the following review papers:

[1] Bellomo, N. and C. Dogbe. “On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives”. SIAM Rev. 53, no. 3 (2011): 409–463

[2] Chowdhury, D., L. Santen, and A. Schadschneider. “Statistical physics of vehicular traffic and some related systems”. Phys. Rep. 329, no. 4–6 (2000): 199–329

[3] Helbing, D. “Traffic and related self-driven many-particle systems”. Rev. Mod. Phys. 73, no. 4 (2001): 1067–1141

[4] Nagatani, T. “The physics of traffic jams”. Rep. Prog. Phys. 65, no. 9 (2002): 1331–1386

[5] Nagel, K., P. Wagner, and R. Woesler. “Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling”. Op. Res. 51, no. 5 (2003)

These articles offer a good starting point, but most of them [2-5] are more than ten years old.

But this does not mean traffic research has not evolved.The most prominent achievement during the past ten years -- in my opinion -- is the development of the so-called three-phase traffic theory by Boris Kerner. Kerner found that the obvious classification of traffic in free flow and congested flow is too coarse-grained because his studies showed a rich variety of spatiotemporal patterns of congested traffic. According to the three-phase traffic theory, congested traffic subdivides into two phases: “synchronized traffic” and “wide moving jams”. Therefore, this theory is based on and culminates in the identification of distinct spatiotemporal patterns of congested traffic with very characteristic properties. This theory can also explain the physical origin leading to a traffic breakdown. (Yet, it has to be mentioned that this theory is quite controversial among traffic engineers.)

There is a huge amount of literature on this topic itself. A good introduction which is freely available:

[6] Kerner, B. S. “Modern approaches to basic traffic modeling: Three-Phase Traffic Theory”. Transp. Res. Circular E-C 149 (2011): 22–42

and a Wikipedia-article:

https://en.wikipedia.org/wiki/Three-phase_traffic_theory

(There are even two books by Kerner:

[7] Kerner, B. S. “The Physics of Traffic”. Berlin: Springer, 2004

[8] Kerner, B. S. “Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory”. Berlin: Springer, 2009 )

As traffic is studied by engineers and physicists, i finally would like to refer to two text books -- one treating traffic from a physicist's point of view [9] and one treating traffic from a engineer's point of view [10]

[9] Schadschneider, A., D. Chowdhury, and K. Nishinari. “Stochastic Transport in Complex Systems: From Molecules to Vehicles”. Oxford: Elsevier Science, 2010

[10] May, A. D. “Traffic flow fundamentals”. Englewood Cliffs: Prentice-Hall, 1990

Thank you Mr Florian I appreciate your help

I would start with:

1. FHWA's Revised Monograph on Traffic Flow Theory. It can be downloaded by chapter at https://www.fhwa.dot.gov/publications/research/operations/tft/.

It is an update to the TRB Special Report 165, "Traffic Flow Theory," published in 1975.  

"The report consists of ten chapters, representing the most updated and unique compilation of knowledge in the field of traffic flow theories. These chapters are: (1) Introduction, (2) Traffic Stream Characteristics, (3) Human Factors, (4) Car Following, (5) Continuum Flow Models, (6) Macroscopic Flow Models, (7) Traffic Impact Models, (8) Unsignalized Intersections, (9) Signalized Intersections, (10) Traffic Simulation. Chapters 3 and 5 are two completely new chapters in this report."

In addition to the above mention of Kerner, I would suggest :

2. Treiber, Martin, and Arne Kesting. 2013. Traffic flow dynamics data, models and simulation. Heidelberg: Springer. http://dx.doi.org/10.1007/978-3-642-32460-4.

Lily Elefteriadou (UF) has a new book out that is somewhat watered-down but may be a good primer and is a short book:

3. Elefteriadou, Lily. 2014. An introduction to traffic flow theory. http://dx.doi.org/10.1007/978-1-4614-8435-6.

As mentioned above if you narrow the question, I can suggest more.  What is the model's application?

https://www.fhwa.dot.gov/publications/research/operations/tft/

Thanks Mr Brian  I appreciate your help 

You're welcome. May I ask what you are working on?

I sent you a message 

Hi,

you can download pdf file on google

"traffic flow theory and modeling " By serge hoogendoorn  and victor knollknoll

Www.victorknoop.eu/paper/chapter_vanwee.pdf