Rebalancing the Rebalancers: Optimally Routing Vehicles and Drivers in\n Mobility-on-Demand Systems
Bibliographic record
Abstract
In this paper we study rebalancing strategies for a mobility-on-demand urban\ntransportation system blending customer-driven vehicles with a taxi service. In\nour system, a customer arrives at one of many designated stations and is\ntransported to any other designated station, either by driving themselves, or\nby being driven by an employed driver. The system allows for one-way trips, so\nthat customers do not have to return to their origin. When some origins and\ndestinations are more popular than others, vehicles will become unbalanced,\naccumulating at some stations and becoming depleted at others. This problem is\naddressed by employing rebalancing drivers to drive vehicles from the popular\ndestinations to the unpopular destinations. However, with this approach the\nrebalancing drivers themselves become unbalanced, and we need to "rebalance the\nrebalancers" by letting them travel back to the popular destinations with a\ncustomer. Accordingly, in this paper we study how to optimally route the\nrebalancing vehicles and drivers so that stability (in terms of boundedness of\nthe number of waiting customers) is ensured while minimizing the number of\nrebalancing vehicles traveling in the network and the number of rebalancing\ndrivers needed; surprisingly, these two objectives are aligned, and one can\nfind the optimal rebalancing strategy by solving two decoupled linear programs.\nLeveraging our analysis, we determine the minimum number of drivers and minimum\nnumber of vehicles needed to ensure stability in the system. Interestingly, our\nsimulations suggest that, in Euclidean network topologies, one would need\nbetween 1/3 and 1/4 as many drivers as vehicles.\n
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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) | 0.002 | 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 | 0.002 | 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".