Hysteresis and the Unobserved Congestion Branch in the Macroscopic Fundamental Diagram: Theoretical Considerations and Modeling
Bibliographic record
Abstract
The macroscopic fundamental diagram (MFD) is developed to describe traffic operations aggregated over an area. The MFD is defined by network traffic states as a relationship between the accumulation of vehicles and flow or speed of vehicles. The concept of the MFD has been applied to model traffic dynamics and to design control strategies. For various applications (e.g., routing and departure time choices), the MFD is often assumed to be of a particular shape, consisting of two branches—a free-flow branch and a congestion branch. However, empirical observations show some inconsistencies between the theoretical and the empirical MFD. First, the empirical MFD only presents free-flow branch, i.e., the congestion branch is missing. Second, the MFD presents as hysteresis loop(s). This paper explores these differences, providing insights into urban network traffic dynamics. This work takes the travelers’ departure time choices and user equilibrium (UE) as starting points. We consider demand to be in UE in terms of departure time choices. Using this property of the demand profile, the paper proposes a closed-form expression for average density and outflow. Finally, we show some insights in the urban traffic dynamics: (i) an explanation of the hysteresis phenomenon solely from the perspective of departure time choices and UE and (ii) an explanation of why we hardly observe the MFD congestion branch in real life even in heavily congested networks. Our study shows that, for management purposes, the missing of congestion branch is a result of UE, rather than an indicator of congestion severity.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".