Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty

Daniel Zhuoyu Long; Viet Anh Nguyen; Zikun Lin

arxiv: 2605.23378 · v1 · pith:Z4NHDQADnew · submitted 2026-05-22 · 🧮 math.OC · cs.LG

Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty

Zikun Lin , Daniel Zhuoyu Long , Viet Anh Nguyen This is my paper

Pith reviewed 2026-05-25 04:36 UTC · model grok-4.3

classification 🧮 math.OC cs.LG

keywords ambulance dispatchtravel-time uncertaintydual dispatchOHCA responsebilevel optimizationuncertainty modelingHong Kong emergency servicesoptimistic gap

0 comments

The pith

IDEAL dispatches a second ambulance only when the optimistic travel-time gap exceeds a learned threshold, yielding better response-resource trade-offs than static or map-based methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops IDEAL, a selective dual-dispatch framework for ambulances responding to out-of-hospital cardiac arrest. It learns context-specific edge travel times from historical dispatch records, including routes never observed before, and uses those times plus quantified uncertainty to decide in real time whether sending a second unit is justified. This matters because always sending two units wastes scarce fleet capacity while static territories or deterministic estimates break down under changing congestion. The approach casts the decision as an optimistic-gap computation solvable by a difference-of-convex program and tests it in real-time adaptive simulations on Hong Kong records. The results show improved balance between arrival speed and resource use compared with region-based and Google-based baselines.

Core claim

IDEAL learns context-specific edge travel times from trip-level dispatch records, including unobserved routes, via a weakly supervised bilevel representation network; it models uncertainty through Burg-divergence perturbations around a shared metric to induce correlated changes and learns context-specific radii from historical underprediction errors; the optimistic gap is then computed as a difference-of-convex program with an efficient oracle, enabling selective dual dispatch that produces stronger response-time and resource trade-offs in real-time adaptive simulations on historical OHCA data.

What carries the argument

The weakly supervised bilevel representation network that infers context-specific edge travel times from dispatch records, combined with Burg-divergence perturbations that create correlated uncertainty and context-specific radii derived from historical underprediction errors.

Load-bearing premise

The bilevel network accurately infers travel times for unobserved routes from limited dispatch data, and the radii taken from historical underprediction errors correctly quantify the uncertainty needed for real-time optimistic-gap decisions.

What would settle it

Running the real-time adaptive simulations on the Hong Kong OHCA records and finding that IDEAL does not produce a stronger response-time and resource trade-off than the region-based and Google-based baselines would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2605.23378 by Daniel Zhuoyu Long, Viet Anh Nguyen, Zikun Lin.

**Figure 1.** Figure 1: (Left) Two depots respond to one demand. The heart marks the incident; crosses mark MOU (west) and MOR (east). (Right) Segment-by-segment evolution of Google Routes’ total predicted travel time, defined as elapsed time plus the current predicted remainder. Each marker is recorded when a segment completes, and the API is re-queried. The horizontal axis is cumulative elapsed time; the vertical axis is total … view at source ↗

**Figure 2.** Figure 2: illustrates IDEAL as a three-step flow. In the scenario set construction step, the bilevel representation learning network maps static edge information and call-time context to learned representation vectors and a nominal edge-travel-time vector, while the radius prediction network maps the learned contextual representation vector to an uncertainty radius; together, these outputs define the scenario set. I… view at source ↗

**Figure 3.** Figure 3: Representation-learning architecture for edge travel time prediction. The static edge representation learning network embeds edge information. The dynamic contextual representation learning network embeds contextual information. The cross representation learning network fuses both embeddings to produce context-dependent edge representation vectors and edge travel time estimates. A shortest-path problem ag… view at source ↗

**Figure 4.** Figure 4: Candidate-optimal rates across strategies. The figure marks the alwaysdual IDEAL operating point and another IDEAL operating point that exceeds the strongest baseline with a lower average dispatch volume [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗

**Figure 5.** Figure 5: Mean-regret and tail-risk trade-offs for the same threshold sweep. Left: mean regret versus average dispatch volume. Right: CVaR0.95 regret versus average dispatch volume. value. The IDEAL (dual) curve rises faster than the baseline curves, indicating lower regret in both typical incidents and the high-regret tail. The numerical summaries in [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

**Figure 6.** Figure 6: Empirical CDF of regret. For each regret x, the curve reports the fraction of incidents with regret at most x. We also test for consistent per-incident improvements against baselines using one-sided paired Wilcoxon signed-rank tests on Regi (b) − Regi (IDEAL dual) [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗

**Figure 7.** Figure 7: Candidate-optimal rates in the Sha Tin transfer test. The figure marks the always-dual IDEAL operating point and another IDEAL operating point that exceeds the strongest baseline with a lower average dispatch volume [PITH_FULL_IMAGE:figures/full_fig_p054_7.png] view at source ↗

**Figure 8.** Figure 8: shows the regret–dispatch-volume trade-off. At a¯ = 2, IDEAL lowers mean regret from 8.28 seconds under Google dual dispatch to 0.33 seconds, and lowers CVaR0.95 regret from 126.5 seconds to 6.5 seconds [PITH_FULL_IMAGE:figures/full_fig_p054_8.png] view at source ↗

**Figure 9.** Figure 9: Empirical CDF of regret in the Sha Tin transfer test. For each regret x, the curve reports the fraction of incidents with regret at most x [PITH_FULL_IMAGE:figures/full_fig_p055_9.png] view at source ↗

read the original abstract

Ambulance response is time-critical in out-of-hospital cardiac arrest (OHCA), where dispatchers must balance timely arrivals with limited fleet capacity. Static territories and deterministic travel-time estimates are vulnerable to dynamic congestion, while always-dual dispatch adds redundancy but consumes fleet capacity. We propose IDEAL (Intelligent Dual dispatch of Emergency AmbuLances), a selective dual-dispatch framework that sends a second ambulance only when the optimistic gap between primary and secondary paths exceeds a threshold. IDEAL learns context-specific edge travel times from trip-level dispatch records, including unobserved routes, using a weakly supervised bilevel representation network. We train the nonsmooth model with mini-batch conservative gradients and prove an asymptotic convergence guarantee. IDEAL models uncertainty via Burg-divergence perturbations to a shared metric in the learned representation space, thereby inducing correlated changes in edge travel times and learning context-specific radii from historical underprediction errors. For real-time decisions, IDEAL casts optimistic-gap computation as a difference-of-convex program and derives an efficient oracle with complexity guarantees. In collaboration with the Hong Kong Fire Services Department, we evaluate IDEAL using historical OHCA records and real-time adaptive simulations. The results achieve a stronger response-time/resource trade-off relative to all region-based and Google-based baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper puts together bilevel learning, Burg-divergence uncertainty, and a DC oracle for selective ambulance dispatch, but the accuracy of the learned travel times on unobserved routes is not checked in a way that supports the performance claims.

read the letter

The main takeaway is a selective dual-dispatch rule that sends a second ambulance only when an optimistic gap in travel time exceeds a threshold. The method learns context-specific edge times from trip-level records via a weakly supervised bilevel network, perturbs them with Burg-divergence to capture correlated uncertainty, fits radii from historical underprediction errors, and solves the gap computation as a difference-of-convex program with claimed complexity bounds and asymptotic convergence for training. The evaluation uses Hong Kong OHCA records in real-time adaptive simulations and reports better response-resource trade-offs than region-based and Google baselines. The collaboration with the fire department and the attempt to handle unobserved routes are the practical strengths. The formal pieces on convergence and oracle efficiency are also concrete. The central weakness is that the bilevel network's accuracy on edges never seen in the dispatch data is not directly verified. No hold-out MAE on observed edges or coverage check on prediction errors is described, so it is hard to know whether the optimistic-gap decisions are driven by faithful travel-time estimates or by artifacts of the fitting process. The radii are also derived from the same historical records used for evaluation, which adds circularity even if the authors label it as learning. These issues sit at the foundation of the reported gains. The work is aimed at operations researchers and emergency-services modelers who already work on robust dispatch or ML-augmented optimization. A reader looking for an end-to-end applied example with some theory will get value, but anyone needing tight empirical grounding on the learned metric will have to ask for more checks. It deserves a serious referee because the problem is real, the formal claims are stated, and the data source is external, even though the validation of the representation network will need scrutiny.

Referee Report

3 major / 2 minor

Summary. The paper proposes IDEAL, a selective dual-dispatch policy for OHCA ambulance response that dispatches a second unit only when the optimistic gap between primary and secondary paths exceeds a threshold. It learns context-specific edge travel times (including unobserved routes) via a weakly supervised bilevel representation network trained on trip-level dispatch records, models uncertainty through Burg-divergence perturbations around a shared metric with radii fitted from historical underprediction errors, casts the optimistic-gap computation as a difference-of-convex program with an efficient oracle and complexity guarantees, proves asymptotic convergence of the nonsmooth training procedure, and reports superior response-time/resource trade-offs versus region-based and Google-based baselines in real-time adaptive simulations on historical Hong Kong Fire Services Department OHCA records.

Significance. If the central claims hold, the work offers a principled optimization-based approach to selective dual dispatch under contextual travel-time uncertainty, with potential practical value for emergency services given the collaboration with the Hong Kong Fire Services Department. The DC-oracle formulation and convergence guarantee for the bilevel network training are technical strengths that could advance contextual uncertainty modeling in network optimization. The empirical trade-off improvement, if independently validated, would be a meaningful contribution to operations research applications in emergency logistics.

major comments (3)

[uncertainty modeling and evaluation sections] The context-specific radii are derived directly from historical underprediction errors on the training records and then used in the same records for the real-time adaptive simulations; this circularity (detailed in the uncertainty modeling and evaluation sections) means the reported superiority over baselines may reflect post-hoc fitting rather than out-of-sample performance, undermining the load-bearing claim of a stronger response-time/resource trade-off.
[bilevel network training and real-time decision sections] No quantitative validation (e.g., hold-out MAE on observed edges, coverage probability of prediction errors, or accuracy metrics on a validation set of routes) is provided for the weakly supervised bilevel representation network's inferences on unobserved edges, yet this accuracy is foundational to attributing the simulation improvements to the optimistic-gap policy rather than to the learned metric itself (see the bilevel network training and real-time decision sections).
[methods section on training and convergence] The asymptotic convergence guarantee for mini-batch conservative gradient training of the nonsmooth bilevel model is stated in the abstract and methods, but the manuscript provides no explicit statement of the assumptions (e.g., on the Burg-divergence perturbation or the representation space) under which the guarantee holds, making it impossible to assess whether the proof supports the claimed reliability of the learned travel times.

minor comments (2)

[abstract and introduction] Notation for the optimistic gap threshold and the context-specific radii should be introduced with explicit symbols and distinguished from free parameters in the abstract and introduction to improve readability.
[evaluation section] The description of the Google-based baseline lacks detail on how real-time queries are emulated in the historical-record simulations; a short clarification would help readers replicate the comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. We address each major comment below and indicate the revisions that will be made to strengthen the manuscript.

read point-by-point responses

Referee: [uncertainty modeling and evaluation sections] The context-specific radii are derived directly from historical underprediction errors on the training records and then used in the same records for the real-time adaptive simulations; this circularity (detailed in the uncertainty modeling and evaluation sections) means the reported superiority over baselines may reflect post-hoc fitting rather than out-of-sample performance, undermining the load-bearing claim of a stronger response-time/resource trade-off.

Authors: We acknowledge the concern about potential circularity. The radii are fitted from underprediction errors to reflect context-specific uncertainty, and the adaptive simulations apply the resulting policy sequentially. To address out-of-sample validity, we will revise the evaluation to use a temporal hold-out: fit radii on earlier records and evaluate the full pipeline on later records. This change will be reflected in the uncertainty modeling and results sections. revision: yes
Referee: [bilevel network training and real-time decision sections] No quantitative validation (e.g., hold-out MAE on observed edges, coverage probability of prediction errors, or accuracy metrics on a validation set of routes) is provided for the weakly supervised bilevel representation network's inferences on unobserved edges, yet this accuracy is foundational to attributing the simulation improvements to the optimistic-gap policy rather than to the learned metric itself (see the bilevel network training and real-time decision sections).

Authors: We agree that additional validation would help attribute improvements to the policy. Because the setting is weakly supervised, direct ground truth for unobserved edges is unavailable. We will add indirect validation in the revised manuscript, including consistency metrics on observed edges, sensitivity analysis of the learned metric, and ablation studies isolating the effect of the optimistic-gap threshold. revision: partial
Referee: [methods section on training and convergence] The asymptotic convergence guarantee for mini-batch conservative gradient training of the nonsmooth bilevel model is stated in the abstract and methods, but the manuscript provides no explicit statement of the assumptions (e.g., on the Burg-divergence perturbation or the representation space) under which the guarantee holds, making it impossible to assess whether the proof supports the claimed reliability of the learned travel times.

Authors: The convergence proof appears in the supplementary material. We agree that the main text should state the assumptions explicitly (compactness of the representation space and continuity of the Burg-divergence). We will add this statement to the methods section on training. revision: yes

Circularity Check

1 steps flagged

Radii fitted from underprediction errors on training records reduce uncertainty model to evaluation data

specific steps

fitted input called prediction [Abstract]
"IDEAL models uncertainty via Burg-divergence perturbations to a shared metric in the learned representation space, thereby inducing correlated changes in edge travel times and learning context-specific radii from historical underprediction errors."

The radii are explicitly learned from underprediction errors on the historical dispatch/OHCA records. These same records supply the training data for the weakly supervised network and the testbed for the real-time adaptive simulations that demonstrate superiority over baselines. Consequently the uncertainty quantification used to trigger selective dual dispatch is a fitted quantity on the evaluation distribution rather than an independent bound.

full rationale

The paper's uncertainty modeling step derives context-specific radii directly from historical underprediction errors on the dispatch records used both to train the bilevel network and to run the real-time adaptive simulations. This matches the fitted_input_called_prediction pattern: the radii parameter is computed from the same data that later serves as the benchmark for claiming superior response-time/resource trade-offs. The bilevel network and DC oracle are presented as independent, but the load-bearing optimistic-gap threshold inherits its calibration from the evaluation set, creating partial circularity in the performance claims. No self-citation chains or self-definitional equations are evident from the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the ability of the bilevel network to learn unobserved routes and on the Burg-divergence radii fitted from historical errors; these are domain modeling choices rather than independently verified quantities.

free parameters (2)

optimistic gap threshold
The threshold that triggers dual dispatch is a tunable parameter whose value affects the reported trade-off.
context-specific radii
Radii are learned from historical underprediction errors and directly shape the uncertainty model used in decisions.

axioms (2)

standard math Mini-batch conservative gradients yield asymptotic convergence for the nonsmooth bilevel model
Invoked to justify training the representation network.
domain assumption The difference-of-convex formulation admits an efficient oracle with complexity guarantees
Required for real-time deployment claims.

pith-pipeline@v0.9.0 · 5752 in / 1497 out tokens · 35565 ms · 2026-05-25T04:36:32.659738+00:00 · methodology

discussion (0)

Reference graph

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When t0 =t nominal(T),λ(tnominal(T);T)measures how sensitive clinical risk is to small changes in travel time for the current demand. Under this linear approximation, an improvement of∆tunits in travel time reduces clinical risk by approximatelyλ(t0;T)·∆t. We want the threshold function to compare this optimistic reduction with the operational cost of sen...

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Feature name Dim

SELECTIVE AMBULANCE DISPATCH UNDER CONTEXTUAL TRA VEL-TIME UNCERTAINTY 34 Table 4.Environmental features for each OHCA record. Feature name Dim. Description Weather variables 5 Temperature, rainfall, relative humidity, wind speed, sea-level pressure Hour 1 Hour of day (0–23) Day of week 7 One-hot indicators for Monday to Sunday Month 12 One-hot indicators...

work page 2022