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Hydrodynamic and continuum traffic flow models usually require that traffic states are stationary for the model assumptions to hold. The reproducibility of a concave fundamental diagram, FD, is typically assumed to also demonstrate that the underlying states are sufficiently near stationary. This paper uses loop detector data from five locations to empirically demonstrate that the microscopic traffic dynamics giving rise to a concave FD can also invalidate the stationarity assumptions required by the traffic flow models. Specifically, this work develops the exclusionary vehicle aggregation, EVA, method to evaluate conditions underlying conventional fixed time average state measurements. The shape of the FD is shown to be highly correlated with the standard deviation of headways, stdev(h), within the underlying samples: low stdev(h) corresponding to triangular FD and high stdev(h) to concave FD. Furthermore, high stdev(h) is shown to correspond to the presence of large voids within the given sample. These voids are inherently non-stationary because different regions of the sample are perceptively distinct. With these new insights in mind, a review of the earliest FD literature reveals evidence supporting the loop detector-based findings. Collectively, the loop detector and historical FD results span over 75 years of empirical traffic data. Meanwhile, a driver behind a large void can act independent of their leader. From the kinematic wave, KW, perspective, a void creates an ill posed problem: if a driver acts independent of their leader there are no KW from the boundaries that reach the driver during their independence, and thus, there is no way to predict how the driver should act. Generally, this type of ill posed problem is avoided in theoretical developments by requiring stationary conditions for the given model, but as this paper shows, real traffic does not necessarily provide stationary conditions. Although the voids are large enough to disrupt stationarity, their duration remains far below the resolution of fixed time averaging to be perceived. As a result, whenever a traffic flow model depends on stationarity and the shape of the FD, it is imperative to check the data to make sure they support the assumptions placed on the FD, e.g., via the EVA method developed herein. Finally, the empirical results in this paper should facilitate the development of macroscopic models that better capture the dynamics of real traffic.
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Microscopic Discontinuities Disrupting Hydrodynamic and Continuum Traffic Flow Models
This paper explores short duration disturbances in the traffic stream that are large enough to impact the traffic dynamics and disrupt stationarity when establishing the fundamental diagram, FD, but small enough that they are below the resolution of conventional vehicle detector data and cannot be seen using conventional methods. This empirical research develops the Exclusionary Vehicle Aggregation method (EVA) to extract high fidelity time series data from conventional loop detectors and then extends the method to measure the standard deviation of headways in a given fixed time sample, stdevh. Using loop detector data spanning 18 years and five sites, all of the sites show that samples with low stdevh tend towards a triangular FD while samples with high stdevh tend towards a concave FD that falls inside the triangular FD. The stdevh is also shown to be strongly correlated with the duration of the longest headway within the sample. The presence of a long headway means the state is perceptively different over the sample and thus, the measurement is non-stationary. A review of the earliest FD literature by Greenshields finds strong supporting evidence for these trends. Collectively, the loop detector and historical FD results span over 75 years of empirical traffic data. Based on the EVA analysis, this work offers the following insights: the shape of equilibrium FD appears to be triangular and that conventional detector data mask critical features needed by hydrodynamic traffic flow models, HdTFM. Because the driver behind a long headway can act independent of their leader, the long headways can correspond to unobserved boundary conditions that generate kinematic waves. If these boundaries were detected many HdTFM could accommodate them, especially multi-class models. But the stochastic nature of the long headways also challenges the predictive abilities of deterministic HdTFM. Perhaps the largest of these challenges is driver agency- the driver behind a long headway can maintain it, resulting in signals propagating downstream or they can close the gap, resulting in signals propagating upstream. Meanwhile, this work provides a test for stationary conditions to help ensure an empirical FD supports the assumptions placed upon it.
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- Award ID(s):
- 2023857
- PAR ID:
- 10560105
- Publisher / Repository:
- https://www.sciencedirect.com/science/article/pii/S0191261524001929
- Date Published:
- Journal Name:
- Transportation Research Part B: Methodological
- Volume:
- 189
- Issue:
- C
- ISSN:
- 0191-2615
- Page Range / eLocation ID:
- 103068
- Subject(s) / Keyword(s):
- Fundamental diagram Vehicle detection Traffic flow theory Hydrodynamic traffic flow model Continuum traffic flow model
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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