@inbook{cb4d65ec582b4e0a9fa74d7a3aae9b45,

title = "Traffic flow theory",

abstract = "This chapter presents the basic traffic flow theory which is used in the following chapters for control problem formulations. The theory develops the Lighthill–Whitham–Richards (LWR) model that uses the conservation law for traffic. Additionally, a density-dependent speed formula is used. There are many relationships available for this fundamental diagram, the chapter uses Greenshields{\textquoteright} formula for further analysis. Elementary partial differential equations (PDE) theory is also presented including the method of characteristics needed for the analysis of the traffic model. Shockwaves and weak solutions are discussed followed by a brief discussion of traffic measurements.",

author = "Pushkin Kachroo and {\"O}zbay, {Kaan M.A.}",

year = "2018",

doi = "10.1007/978-3-319-69231-9_3",

language = "English (US)",

series = "Advances in Industrial Control",

publisher = "Springer International Publishing",

number = "9783319692296",

pages = "57--87",

booktitle = "Advances in Industrial Control",

edition = "9783319692296",

}