Macroscopic traffic models describe the traffic behaviour at a high level of aggregation, i.e. the traffic dynamics is expressed through aggregate variables, such as traffic density, mean speed and flow. Macroscopic models rely on the analogy between the flow of vehicles and the flow of fluids or gases and are based on a limited number of equations that are relatively easy to handle. This chapter is devoted to describe a very relevant class of macroscopic models, i.e. first-order traffic flow models, which capture the dynamics of only one aggregate variable, namely, the traffic density. A very important first-order macroscopic model is the Lighthill–Whitham–Richards model, developed in the 50s, but still of interest nowadays both for theoretical analysis and practical applications. It is a continuous model, which describes the dynamics of the macroscopic variables through partial differential equations. The most famous discretised version of the Lighthill–Whitham–Richards model is the so-called Cell Transmission Model, developed in the 90s and very widespread in the communities of mathematicians and traffic engineers.

### First-order macroscopic traffic models

#### Abstract

Macroscopic traffic models describe the traffic behaviour at a high level of aggregation, i.e. the traffic dynamics is expressed through aggregate variables, such as traffic density, mean speed and flow. Macroscopic models rely on the analogy between the flow of vehicles and the flow of fluids or gases and are based on a limited number of equations that are relatively easy to handle. This chapter is devoted to describe a very relevant class of macroscopic models, i.e. first-order traffic flow models, which capture the dynamics of only one aggregate variable, namely, the traffic density. A very important first-order macroscopic model is the Lighthill–Whitham–Richards model, developed in the 50s, but still of interest nowadays both for theoretical analysis and practical applications. It is a continuous model, which describes the dynamics of the macroscopic variables through partial differential equations. The most famous discretised version of the Lighthill–Whitham–Richards model is the so-called Cell Transmission Model, developed in the 90s and very widespread in the communities of mathematicians and traffic engineers.
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2018
978-3-319-75959-3
978-3-319-75961-6
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11567/964942`