Optimal departure time choices as quantiles and expectiles of the travel time distribution
Bibliographic record
Abstract
We consider two alternative preference specifications for optimal departure time choices: the classical asymmetric linear loss for early and late delays, and a new specification based on asymmetric quadratic loss. We demonstrate that the resulting optimal choices correspond to the tail indices of the travel time distribution—quantiles for the asymmetric linear specification and expectiles for the asymmetric quadratic specification. Additionally, we establish a correspondence between the choices induced by these two utility specifications, showing that the asymmetric quadratic preference class is a valid alternative with favorable properties, as demonstrated through examples and applications. For both utility specifications, we derive travel time reliability ratios and present a straightforward computation method using the concepts of τ -deviation and τ -variance. Moreover, we test both specifications using departure time choice data, finding that the quadratic loss specification more accurately represents actual departure time choices. Finally, using Montreal travel time data for two alternative routes, we fit a mixture of gamma distributions and compare the behavior of the optimal departure time choices and travel time reliability ratio curves induced by the different utility specifications.
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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 | 0.004 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".