Abstract:
Studies of traffic dynamics rely either on macro-scopic models considering the traffic as a fluid, or on micro-scopic models of drivers' behavior. The connection between ...Show MoreMetadata
Abstract:
Studies of traffic dynamics rely either on macro-scopic models considering the traffic as a fluid, or on micro-scopic models of drivers' behavior. The connection between the microscopic and macroscopic scales is often done via empirical relationships such as the fundamental diagram for macroscopic models, relating traffic flow or average velocity and traffic density. In this paper, we consider a microscopic model consisting of a large number of rational, utility-maximizing drivers interacting on a single road. We then use the theory of Mean Field Games (MFG) to deduce a macroscopic model of traffic density emerging from these interactions. We show how to determine a microscopic utility function for the drivers compatible with standard empirical macroscopic fundamental diagrams. In addition to connecting the microscopic and macroscopic models analytically rather than empirically, our approach can offer additional flexibility to model drivers at the macroscopic level, using a Hamilton-Jacobi-Bellman equation coupled with the standard conservation law for the vehicles.
Published in: 2015 American Control Conference (ACC)
Date of Conference: 01-03 July 2015
Date Added to IEEE Xplore: 30 July 2015
ISBN Information:
ISSN Information:
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- IEEE Keywords
- Index Terms
- Mean-field ,
- Traffic Model ,
- Mean-field Game ,
- Game Theory ,
- Traffic Congestion ,
- Traffic Flow ,
- Macroscopic Scale ,
- Microscopic Model ,
- Driver Model ,
- Macroscopic Model ,
- Time And Space ,
- Higher Density ,
- Differential Equations ,
- Partial Differential Equations ,
- System Of Differential Equations ,
- Convergence Of Algorithm ,
- Second-order Model ,
- Nash Equilibrium ,
- Road Segments ,
- Driver Behavior ,
- Evolution Of Density ,
- Traffic Prediction ,
- Backward Equation
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Mean-field ,
- Traffic Model ,
- Mean-field Game ,
- Game Theory ,
- Traffic Congestion ,
- Traffic Flow ,
- Macroscopic Scale ,
- Microscopic Model ,
- Driver Model ,
- Macroscopic Model ,
- Time And Space ,
- Higher Density ,
- Differential Equations ,
- Partial Differential Equations ,
- System Of Differential Equations ,
- Convergence Of Algorithm ,
- Second-order Model ,
- Nash Equilibrium ,
- Road Segments ,
- Driver Behavior ,
- Evolution Of Density ,
- Traffic Prediction ,
- Backward Equation