Continuum Approximation Model for Transit Service Design with Stochastic Demand
Bibliographic record
Abstract
Travel demand is commonly predefined as a constant during the planning period in transit service design, but it varies daily with many factors, for example, weather, vacation, and social activity. Under the uncertain demand, the transit system operates in two states, that is, unsaturation and saturation, distinguished by whether or not the capacity of transit vehicle satisfies the possible demand. Thus, we propose a continuum approximation (CA) model for transit service design, including headway and station location, to account for the effects of the stochastic demand via a penalty cost, a service-reliability constraint, and equilibrium. The penalty cost is utilized to describe the saturation state. The service-reliability constraint is applied to ensure the robustness of the transit system. The equilibrium is introduced to allocate the household location where trip demand is generated in a corridor. Furthermore, we build a bilevel framework to find the solutions to the proposed model. In the numerical experiment, the proposed model is applied in the impact analyses of the service-reliability constraint, as well as the sensitivity analyses of the household numbers and value of time. The impact analyses indicate that the transit service design integrated with the effect of housing location choice is necessary under the stochastic demand. The sensitivity analyses show that the number of households and the value of time play a significant role in the performance of transit systems accounting for service reliability. The proposed model and findings serve to improve the design of the transit system under stochastic demand.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".