Comparison of Morning and Evening Commutes in the Vickrey Bottleneck Model
Bibliographic record
Abstract
Dynamic user equilibrium has received considerable theoretical attention for morning peak-period travel but very little for the evening peak. In an attempt to redress this imbalance, morning and evening travel are characterized and compared by using Vickrey’s bottleneck model. To focus ideas, it is assumed that morning and evening travel differ in just one respect: scheduling preferences for the morning are defined in terms of arrival time at work, whereas preferences for the evening are defined in terms of departure time from work. Sufficient conditions are identified for the existence and uniqueness of a deterministic dynamic user equilibrium in terms of departure times for the morning and evening peaks. These conditions, which go well beyond previous work, involve relatively general assumptions about the schedule delay cost functions for morning and evening and essentially no restrictions on the degree of heterogeneity in trip-timing preferences of travelers. Plausibility of the conditions is examined in light of the limited empirical evidence. A numerical example is developed at length to illustrate the importance of traveler heterogeneity and the extent of differences between morning and evening in the time pattern of departures and aggregate travel costs.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".