Abstract
ABSTRACTThe fundamental diagram of a road, including free-flow capacity and queue discharge rate, is very important for traffic engineering purposes. In the real word, most traffic measurements come from stationary loop detectors. This paper proposes a method to fit Wu's fundamental diagram to loop detector data. Wu's fundamental diagram is characterised by five parameters, being free-flow speed, wave speed, free-flow capacity, queue discharge rate and jam density. The proposed method entails fixing the wave speed and the free-flow speed. The method consists of two steps. We first use a triangular fundamental diagram to separate the congested branch from the free-flow branch. Then, the remaining three parameters of Wu's fundamental diagram are fitted on each branch using a least-square fit. This method is shown to be robust for cases tested in real life, and hence very noisy, data.
Highlights
In traffic flow theory the fundamental diagram is an essential concept
We first use a triangular fundamental diagram to separate the congested branch from the free flow branch
The main innovation of the method proposed in this paper is that we first use a triangular fundamental diagram to separate the congested branch from the free flow branch
Summary
In traffic flow theory the fundamental diagram is an essential concept. The fundamental diagram relates two of the three variables average speed (v), flow (q) and density (k) to each other. Many papers have been written on the shape of the fundamental diagram (see section 2.1), it is remarkable how much spread is present if one plots observed flows versus observed densities This spread can have different causes, for instance:. Use loop detector data from freeways, with the above-mentioned problems If they want to apply theoretical concepts, such as shock wave theory or the method of characteristics, they need to have a fundamental diagram. The parameters of the fundamental diagram should be calibrated for the observed road, as each road has its own characteristics, leading to a unique fundamental diagram Traffic control measures, such as ramp metering (Papamichail et al 2010) or main lane metering (Carlson et al 2010) are exploiting the capacity drop, i.e. the difference between free flow capacity and the queue discharge rate.
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