Departure Time Choice Models in Urban Transportation Systems Based on Mean Field Games
Bibliographic record
Abstract
Departure time choice models play a crucial role in determining the traffic load in transportation systems. Most studies that consider departure time user equilibrium (DTUE) problems make assumptions on the user characteristics (e.g., distribution of desired arrival time and trip length) or dynamic traffic model (e.g., classic bathtub or point queue models) in order to analyze the problem. This paper relaxes these assumptions and introduces a new framework to model and analyze the DTUE problem based on the so-called mean field games (MFGs) theory. MFGs allow us to define players at the microscopic level similar to classical game theory models, translating the effect of players’ decisions to macroscopic models. In this paper, we first present a continuous departure time choice model and investigate the equilibria of the system. Specifically, we demonstrate the existence of the equilibrium and characterize the DTUE. Then, a discrete approximation of the system is provided based on deterministic differential game models to numerically obtain the equilibrium of the system. To examine the efficiency of the proposed model, we compare it with the departure time choice models in the literature. We apply our framework to a standard test case and observe that the solutions obtained based on our model are 5.6% better in terms of relative cost compared with the solutions determined based on previous studies. Moreover, our proposed model converges with fewer iterations than the reference solution method in the literature. Finally, the model is scaled up to the real test case corresponding to the whole Lyon metropolis with a real demand pattern. The results show that the proposed framework is able to tackle a much larger test case than usual to include multiple preferred travel times and heterogeneous trip lengths more accurately than existing models.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".