


Traffic Flow Theory 

Daiheng Ni 
University of Massachusetts Amherst 



Book Front Matter (Preprint) 


A. For Instructors 

Please order a review copy from Elsevier. After you have adopted this textbook, you may contact the author (ni@engin.umass.edu) and request the following supplementary teaching materials: 

 Syllabus and daytoday schedule samples 
 Solution manual to endofchapter problems 
 Lecture slides for each chapter 
 Sample exams with solutions 
 Sample homework assignments with solutions 
 Sample quizzes with solutions 

Please note that, based on the esperiences of a few instructors who adopted this textbook, Elsevier typically handles request for review copy by providing an electronic book rather than a hard copy. 


B. Readership 

This book is best suited for: 
Faculty, researchers, and students in transportation engineering 
Faculty, researchers, and students in applied mathematics 
Traffic engineers and transportation professionals. 


C. Key Features 

The book is selfcontaining. All necessary preparation and background to understand the subject are presented within this book, so the need is minimized for readers to go outside in order to prepare themselves in traffic flow and mathematical modeling. 

The book is easytounderstand. Typical in traffic flow theory is its complicated nature with mathematical modeling and domain knowledge intertwined. Except for the few very knowledgeable researchers, most people especially graduate students and professionals have difficulty understanding traffic flow models and their properties which requires both domain knowledge and ordinary and partial differential equations. The book intends to help them overcome the barrier and ramp up their learning curve. 

The book is inherently coherent as described above in book organization. Basically, the book starts with the “obvious” and go deeper and deeper progressively with each chapter building on the previous. This allows the reader to see an evolving story and is progressively led into the core of the area. 

Perhaps the most distinguishing feature of this book is its unified perspective. Even though they are already logically connected and inherently coherent, all things presented in the first four Parts come together in Part V. In this part, a “family tree” is presented showing the whole picture with models discussed before scattered all over the picture. Then, classification is made and connections are drawn among these models, so readers not only understand how one model relates to another but also find their places in the family tree. 


D. Description 

The book takes a unified perspective on traffic flow modeling and consists of five parts which are coherently connected. 

Part I starts with traffic sensing, observations based on which are used to define traffic flow characteristics. Issues with regular traffic flow definition lead to generalized definition and threedimensional representation. With these preparation, relationships among traffic flow characteristics, in particular equilibrium traffic flow models are introduced. 

Part II builds on previous chapters and talks about dynamic traffic flow models at the macroscopic level aiming at understanding the evolution of traffic flow over time and space. A system of equations is set up for this purpose whose solution requires knowledge of partial differential equations. A special case of the problem, called LWR model, plays a critical role in macroscopic modeling and solutions to this problem were further discussed including graphical and numerical solutions. 

Part III switches gears to microscopic modeling. The focus is on motion and interaction of individual drivervehicle units, especially carfollowing behavior involving operational control in the longitudinal direction. A series of carfollowing models are introduced with varying modeling philosophies and complexity. To enhance understanding of these models, a benchmarking process is used to crosscompared them. 

Part IV extends traffic flow modeling to the picoscopic level. A modeling framework called drivervehicleenvironment closedloop system is introduced to capture ultrafine level of detail of traffic flow. As an example of this modeling framework, a simple engine model, a dynamic interactive vehicle model, and a field theory to model the driver are formulated. 

All things come together in Part V. Using the field theory as the basis, a unified perspective can be casted on traffic flow theory. Macroscopic models and microscopic models introduced thus far can be related to each other, all linked directly or indirectly to the field theory. Hence, a unified diagram is constructed to highlight such relations. In addition, a benchmarking effort is made to crosscompare the performance of some of the macroscopic models and microscopic models in the diagram. Meanwhile, a multiscale modeling approach is presented which involves traffic flow modeling at a spectrum of four levels of detail, namely macroscopic, mesoscopic, microscopic, and picoscopic. The emphasis of multiscale is to ensure modeling consistency, i.e., how less detailed models are derived from more detailed models and, conversely, how more detailed models are aggregated to less detailed models. The proposed approach may establish the theoretical foundation for traffic modeling and simulation at multiple scales seamlessly within a single system. 


E. Table of Contents 


Preface 

I Traffic Flow Characteristics 
Chapter 1 Traffic Sensing Technologies 
Chapter 2 Traffic Flow Characteristics I 
Chapter 3 Traffic Flow characteristics II 
Chapter 4 Equilibrium Traffic Flow Models 

II Macroscopic Modeling 
Chapter 5 Conservation Law 
Chapter 6 Waves 
Chapter 7 Shock and Rarefaction Waves 
Chapter 8 LWR Model 
Chapter 9 Numerical Solutions 
Chapter 10 Simplified Theory of KWaves 
Chapter 11 HighOrder Models 

III Microscopic Modeling 
Chapter 12 Microscopic Modeling 
Chapter 13 Pipes and Forbes Models 
Chapter 14 General Motors Models 
Chapter 15 Gipps Model 
Chapter 16 More SingleRegime Models 
Chapter 17 More Intelligent Models 

IV Picoscopic Modeling 
Chapter 18 Picoscopic Modeling 
Chapter 19 Engine Modeling 
Chapter 20 Vehicle Modeling 
Chapter 21 The Field Theory 
Chapter 22 Longitudinal Control Model 

V The Unified Perspective 
Chapter 23 The Unified Diagram 
Chapter 24 Multiscale Traffic Flow Modeling 





