Qualitative Failure and Error Accumulation of Quasi-Dynamic Equilibrium Induced by the “Travel Time Paradox”*
Bibliographic record
Abstract
The Quasi-Dynamic Traffic Assignment (SDTAQ) model is a crucial tool for balancing the stability of Static Traffic Assignment (STA) with the accuracy of Dynamic Traffic Assignment (DTA). However, the cost calculation formula relied upon by its mainstream framework has been identified as having a “non-separability” defect, known as the “travel time paradox,” which theoretically undermines the uniqueness of the equilibrium solution. Although this paradox has been identified theoretically, its practical impacts have not yet been sufficiently quantified. To address this, this study designs a rigorous comparative experiment in the Sioux Falls network, constructing a time-varying congestion scenario spanning three periods (peak onset, congestion accumulation, and congestion dissipation) to systematically evaluate the performance differences between the “non-separable” formula (Formula A) and a corrected “separable” formula (Formula B) under Stochastic User Equilibrium (SUE) conditions. The results demonstrate that the “travel time paradox” is not merely a theoretical flaw but also leads to severe qualitative errors in practical application. During the congestion accumulation period (T2), Formula A exhibits significant failure when processing multibottleneck paths, calculating an unreasonable travel time of 35.28 hours for a critical alternative route (Path 2162) (compared to 18.92 hours from Formula B). This error further causes Formula A to incorrectly determine the assigned flow on this feasible path as zero. Furthermore, this error possesses characteristics of interperiod propagation and accumulation: the total network delay (VHD) is underestimated by 3.0 % during T2, and due to state dependency, this underestimation widens to 7.0 % in T3. This study is the first to quantitatively reveal the severe impact of the “travel time paradox” on SUE solutions, recommending the adoption of the corrected “separable” cost formula in future SDTAQ model research and application to ensure theoretical consistency and simulation accuracy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.026 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".