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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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LWR and shockwave analysis - Failures under a concave fundamental diagram and unexpected induced disturbances
This paper undertakes a detailed empirical study of traffic dynamics on a freeway. The results show the traffic dynamics that systematically determine the shape of the fundamental diagram, FD, can also violate the stationarity assumptions of both shockwave analysis and Lighthill, Whitham and Richard's models, thereby inhibiting the applicability of these classical macroscopic traffic flow theories. The outcome is challenging because there is no way to identify the problem using only the macroscopic detector data. The research examines conditions local to vehicle detector stations to establish the FD while the single vehicle passage method is used to analyze the composition of vehicles underlying the aggregate samples. Then, traffic states are correlated between successive stations to measure the actual signal velocities and show they are inconsistent with the classical theories. This analysis also revealed that conditions in one lane can induce signals in another lane. Rather than exhibiting a single signal passing a given point in time and space, the induced and intrinsic signals are superimposed on one another in the given lane. We suspect the subtle dynamics revealed in this research have gone unnoticed because they are far below the resolution of conventional traffic monitoring. The findings could have implications to other traffic flow models that rely on the FD, so care should be taken to assess if a given model is potentially sensitive to the non-stationary dynamics presented herein. The results have a direct impact on practice. Traffic flow theory is a critical input to many aspects of surface transportation, e.g., traffic management, traffic control, network design, vehicle routing, traveler information, and transportation planning all depend on models or simulation software that are based upon traffic flow theory. If the underlying traffic flow theory is flawed it puts the higher level applications at risk. So, the findings in this paper should lead to caution in accepting the predictions from traffic flow models and simulation software when the traffic exhibits a concave FD.
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- Award ID(s):
- 2023857
- PAR ID:
- 10560097
- Publisher / Repository:
- https://www.sciencedirect.com/science/article/abs/pii/S0965856423001866
- Date Published:
- Journal Name:
- Transportation Research Part A: Policy and Practice
- Volume:
- 175
- Issue:
- C
- ISSN:
- 0965-8564
- Page Range / eLocation ID:
- 103766
- Subject(s) / Keyword(s):
- Traffic flow theory fundamental relationship fundamental diagram Lighthill Whitham and Richards loop detectors highway traffic
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.tra.2023.103766
