Capacity provisioning for evacuation on path networks
Bibliographic record
Abstract
Abstract Designing an appropriate evacuation plan in the event of large scale disasters is extremely important. A considerable research effort has been invested in effective mathematical models and algorithms for the evacuation of densely populated areas. Dynamic networks and flows, and the closely related sink location and evacuation problems are research directions that are being actively pursued at the moment. In this work, we propose an extension of the sink location problem in dynamic networks that is suitable for planning the evacuation of remote and sparsely populated communities. We exploit the connection between the capacity of a transportation network and the amount of resources allocated to the rescue operation, and we introduce a new objective function for the problem of evacuation in a dynamic network. Given a network with known edge lengths and with a known number of evacuees located at the vertices, we would like to assign capacities to the edges of the network, from a fixed capacity budget, in such a way that the evacuation time of all evacuees to the set of fixed sink nodes in the network is minimized. We consider a simple path network with one fixed sink node and observe that the solution can be obtained numerically from a non‐linear program. However, by exploiting two useful properties of the optimal capacity allocation, we propose a combinatorial algorithm that returns a parametric solution, that is, a solution that depends on a single parameter, namely the capacity assigned to one edge of the path. Our algorithm runs in time where is the budgeted capacity, is the precision to which the solution is computed, and is the number of vertices occupied by evacuees in an ‐vertex path. This work is the first to consider the capacity allocation problem in the context of sink location problems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".