Revised Chapter 5
نویسندگان
چکیده
There have been two kinds of traffic flow theories presented thus far in this monograph. Chapter 2 discussed the relations among aggregated quantities of flow rate, concentration and mean speeds for stationary vehicular traffic (these relations are also referred to as the equations of state in traffic flow), and Chapter 3 described the dynamic evolution of microscopic quantities of vehicle spacing, headway and speeds in single-lane traffic through the follow-the-leader type of models. In this Chapter we study another kind of traffic flow theory—continuum traffic flow theory— that describes the temporal-spatial evolution of macroscopic flow quantities as mentioned earlier. Continuum theories are natural extensions to the first two kinds of theories because, one one hand, they are closely related to the equations of state and car-following theories, and on the other hand, they overcome some of the drawbacks of the first (stationarity) and second (too much detail and limited observability) kinds of theories. The quantities and features that continuum theories describe, such as traffic concentration and shock waves, are mostly observable with current surveillance technology, which makes it easier to validate and calibrate these models. Many theories exist in the continuum description of traffic flow. All of them share two fundamental relations: one is the conservation of vehicles and the other is the flow-concentration-speed relation q = ku. (1)
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