Stochastic Modelling of Free-Floating Car-Sharing Systems
Bibliographic record
Abstract
Car-sharing systems (CSSs) have gained popularity during the last decade as a flexible, efficient and ecological alternative mode of transportation. But for the operator, managing such systems is far to be simple. Due to heterogeneity of demand and also randomness, the user may face a lack of resources: no car or no parking space available. And the operator has to design the system in order to improve it. The total number of cars impact the performance of the system. We address the dimensioning issue. For that, mathematical models are needed. In many cities, two systems coexist: station-based and free-floating. The latter gives more flexibility to the user both to take or return the car. But he can reserve only the car for a short period, and not the parking space, as the car is parked on public space with no specific parking spaces. The car reservation is here to help the user. The aim of the paper is to study its influence on the system behavior. This study focuses on Communauto's Montreal free-floating car-sharing system (FFCSS). Data analysis investigates the main features of the system based on user preferences. It allows proposing a mathematical modelling. Then we present two analytical approaches. First the mean-field method could be used for different variants, and w gives first insights on the optimal fleet size in a homogeneous framework. Second the general inhomogeneous model is described as a closed Jackson network with blocking-rerouting policy. We prove that its state at stationarity is given by a product-form distribution. It allows in future work to obtain an explicit large-scale representation of the system which can be used both theoretically or numerically for optimization purposes.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| 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".