Source-linked AI summary
Dynamic Active Fleet Sizing of Heterogeneous UAV Relays for Post-Disaster Communication Networks
Jimin Choi, Max Z. Li
TL;DR
Disaster recovery changes ground communication capacity and demand, so aerial support needs can change over time. The paper uses MPC to size and allocate heterogeneous UAV relays under operational constraints; fleet needs vary across recovery, and backhaul affects service.
Problem
Disaster outages can be severe and prolonged, while ground capacity recovers and communication demand varies, changing the need for aerial support.
Source: §1 · p. 3, §4.1.1 · p. 9Method
An MPC framework dynamically sizes and allocates Mobile and Tethered UAV relays, accounting for demand, ground recovery, backhaul, and Mobile UAV energy.
Source: §4.1.3 · p. 11, §6.3 · p. 47Results
12.03% lower overall backlog when backhaul constraints are accounted for than with planning that ignores them; active UAV needs also vary substantially across recovery.
Source: §6.3 · p. 47Takeaways & Limitations
Dynamic fleet sizing should account for both aerial resource availability and supporting communication infrastructure as recovery conditions change.
Source: §6.3 · p. 47The model assumes the same backhaul type and capacity for every zone in each scenario, with independent zone connections.
Source: §6.2 · p. 46
Abstract
from arXiv · showhide
Uncrewed aerial vehicle (UAV) communication systems are increasingly used to provide temporary connectivity when ground communication infrastructure is damaged by disasters such as hurricanes and wildfires. However, the amount of aerial support required changes as ground networks recover and communication demand evolves. We focus on dynamically adjusting the number and allocation of actively deployed UAVs within a fixed available fleet. We develop a model predictive control (MPC) framework for dynamic fleet sizing of heterogeneous UAV relays during post-disaster communication recovery. The framework accounts for communication demand, ground network recovery, heterogeneous UAV operation, UAV energy availability, and backhaul capacity, which limits how much relayed traffic can be transmitted to the external communication network. The resulting formulation is a convex quadratic program that supports efficient online fleet sizing and deployment decisions. We evaluate the framework using seven historical disaster recovery case studies based on Federal Communications Commission reports, together with four backhaul scenarios and sensitivity analyses. Results show that required active UAV fleet size varies considerably throughout recovery, while backhaul capacity and fleet composition affect communication performance, highlighting the value of adapting active fleet size over time.
1. Introduction
Disasters can leave communication infrastructure severely damaged while demand and ground capacity change during recovery. The paper frames temporary UAV support as a fleet-sizing problem that must adapt over time and develops an MPC approach to do so.
1. Introduction
- Ground communication outages can be severe and prolonged, and restoration can vary significantly across disasters.At the worst point after Hurricane Maria, more than 95% of Puerto Rico cell sites were out of service.Source: §1 · p. 3
- UAV relays provide temporary communication support when disaster damage leaves ground infrastructure unavailable.Deployments described include support during the Maui wildfires, Hurricane Beryl, and Hurricane Helene.Source: §1 · p. 3
- The required number and allocation of active UAVs change as ground capacity and communication demand evolve during recovery.Battery endurance and recharge needs, as well as backhaul capacity, further shape fleet requirements.Source: §1 · pp. 3–4
- A convex MPC framework dynamically sizes heterogeneous UAV relay fleets while incorporating backhaul, energy, demand, and ground-network recovery.A piecewise affine relay-model approximation keeps the formulation a convex quadratic program for repeated optimization.Source: §1 · p. 4
- This study extends a preliminary version presented at the AIAA AVIATION 2026 Forum through a more comprehensive operational model and broader numerical evaluation.Source: §1 · p. 4
2. Literature Review
Prior work spans post-disaster UAV communication, fleet sizing, dynamic allocation, and operational constraints. The review distinguishes these strands and describes how UAV capabilities, energy, and backhaul affect communication service.
2.1. UAVs for Post-Disaster Recovery
- Post-disaster UAV research covers recovery operations, communication architectures, deployment, and network design, including placement, trajectory planning, and scheduling.Source: §2.1 · p. 5
2.2. UAV Fleet Sizing
- UAV fleet-sizing studies address delivery and persistent-service needs, considering battery endurance, stochastic demand, service decisions, and spare vehicles for recharging.Source: §2.2 · pp. 5–6
2.3. Dynamic Fleet Sizing and Resource Allocation
- Dynamic resource-allocation research updates capacity or vehicle assignments as demand and system conditions change, including stochastic MPC for heterogeneous rail fleets.Source: §2.3 · pp. 6–7
2.4. Operational Constraints in UAV Communication Systems
- Heterogeneous UAVs combine differing mobility and endurance, while energy limits and recharge cycles affect service availability.Source: §2.4 · p. 7
- Backhaul capacity and link structure constrain how much UAV-relayed communication service reaches the wider network.Source: §2.4 · p. 7
3. Research Gaps and Contribution
The paper identifies limited attention to dynamic UAV fleet sizing and to jointly accounting for operational constraints. It formulates an MPC approach and evaluates it across historical recovery cases and backhaul scenarios.
3. Research Gaps and Contribution
- Prior work often fixes UAV fleet size in advance, while heterogeneous capabilities, energy and recharge limits, and backhaul capacity are often studied separately.The paper motivates dynamic sizing as sequential decisions responding to changing communication conditions and system state.Source: §3 · pp. 7–8
- The paper formulates post-disaster UAV fleet sizing as an MPC problem whose convex quadratic program supports repeated decisions as recovery conditions change.Source: §3 · p. 8
- The framework incorporates heterogeneous UAV operation, energy and recharge dynamics, and backhaul capacity limitations.Source: §3 · p. 8
- Evaluation uses seven historical disaster recovery cases, multiple backhaul scenarios, component ablations, and sensitivity analyses.The experiments examine how recovery conditions and operational constraints affect fleet requirements and communication service.Source: §3 · p. 8
4. Methodology
The methodology section covers the post-disaster communication system, the dynamic active fleet-sizing formulation, and the MPC solution approach.
4. Methodology
- The methodology is organized around the communication system, fleet-sizing formulation, and MPC solution approach.Source: §4 · p. 8
4.1. System Model
The system model combines recovering ground networks, changing zone-level demand, heterogeneous UAV relays, and local backhaul links. UAV deployments respond to unmet demand and resource availability, while backhaul capacity limits delivered service.
4.1.1. Post-Disaster Communication System
- The communication system divides the affected area into service zones, where UAV relays supplement ground networks and send traffic through local backhaul links.Demand, ground recovery, and resource availability change over time, prompting the controller to update deployments across zones.Source: §4.1.1 · p. 9, Figure 1 · p. 9
4.1.2. Ground Network Recovery and Demand
- Aerial support serves demand exceeding available ground capacity; that load changes as demand varies and the ground network recovers.The model represents ground recovery with a logistic trajectory fitted separately for each historical disaster case.Source: §4.1.1 · p. 9, §4.1.2 · pp. 10–11
4.1.3. Heterogeneous UAV Relay Fleet
- The fleet combines mobile UAVs, which can be reassigned but require battery recharge and face deployment ramp limits, with tethered UAVs that provide persistent support at fixed sites.Tethered UAVs cannot move between zones, while mobile UAV availability depends on energy and charging cycles.Source: §4.1.3 · pp. 11–12
4.1.4. Backhaul Infrastructure
- The model converts effective backhaul capacity in Mbps into a service rate used by the optimization model.The resulting rate represents the maximum service supported by a zone’s backhaul endpoint.Source: §4.1.4 · p. 12
- Each service zone has an independent backhaul endpoint shared by its UAVs, and delivered service cannot exceed that endpoint’s capacity.Experiments use the same backhaul type and endpoint capacity across zones within each scenario.Source: §4.1.4 · p. 12
4.2. Mathematical Formulation
The formulation tracks communication backlog and Mobile UAV energy while choosing UAV deployment and service over a prediction horizon. Its constraints jointly account for relay and backhaul capacity, fleet availability, energy, and operational limits.
4.2.1. States and Decision Variables
- Backlog and total Mobile UAV energy are the system states; Tethered UAVs need no energy state because they receive continuous ground power.Backlog records unserved communication demand, while one energy unit represents the energy of a fully charged Mobile UAV.Source: §4.2.1 · p. 13
- Mobile UAV allocation and Tethered UAV active-time fractions determine fleet size and its distribution across service zones.Mobile deployment is modeled as a continuous average number of active UAVs during each control interval.Source: §4.2.1 · pp. 13–14
4.2.2. System Dynamics and Constraints
- Delivered service is bounded by aerial relay capacity, local backhaul capacity, and demand waiting to be served.Backhaul capacity is zone-specific, shared by relays in that zone, and cannot be transferred between zones.Source: §4.2.1 · p. 13, §4.2.2 · pp. 14–15
- Tethered UAVs operate only at fixed sites, while increases in Mobile UAV deployment are constrained between control steps and decreases are unrestricted.Tethered UAV sites serve only their assigned zones, without explicit modeling of tether length or overlapping coverage.Source: §4.2.2 · pp. 15–16
- Mobile UAV deployment is limited by available fleet size and energy, with ground recharging represented through transitions in the aggregate energy state.The model does not track each Mobile UAV’s battery level or charger use individually.Source: §4.2.2 · pp. 15–16
4.2.3. MPC Formulation
- At each update, the MPC uses current backlog and Mobile UAV energy plus predicted residual load to choose Mobile deployment, Tethered activation, and service across the horizon.Decisions adapt fleet size and zone allocation as demand, ground recovery, backhaul capacity, and Mobile UAV energy availability change.Source: §4.2.3 · pp. 17–18
- The MPC balances backlog service, active deployment, deployment changes, terminal backlog, and remaining Mobile UAV energy over its prediction horizon.The deployment penalty encourages meeting demand with fewer active UAVs, while the variation penalty discourages large changes between control steps.Source: §4.2.3 · p. 17
4.3. Solution Approach
The solution uses receding-horizon control, applying only the first optimized deployment decision before updating the system and solving again. A conservative piecewise affine relay approximation keeps the optimization convex while simulations evaluate the nonlinear service model.
4.3.1. Receding Horizon Control
- Only the first deployment decision from the horizon optimization is applied; the controller then updates actual backlog and energy and solves again.The optimization uses current system states and a forecast of residual communication load over H steps.Source: §4.3.1 · pp. 18–19
4.3.2. Piecewise Affine Relay Approximation
- The relay model’s increasing, concave saturation function is conservatively approximated with piecewise affine segments for the MPC.The approximation remains below the original function, so its service limit does not overestimate nonlinear aerial service capacity.Source: §4.3.2 · pp. 19–20
- The MPC solves a convex quadratic program using the approximation, while closed-loop simulation evaluates realized service with the original nonlinear saturation function.Only the optimization uses the approximation; realized service is calculated after the first deployment action is implemented.Source: §4.3.2 · p. 20
5. Numerical Experiments
The numerical study evaluates dynamic fleet sizing across historical disaster recovery cases and backhaul scenarios, alongside model-component, sensitivity, robustness, and computational analyses.
5. Numerical Experiments
- The experiments assess historical recovery and backhaul scenarios alongside fleet sizing, model components, sensitivity, robustness, and computational performance.The setup specifies the cases, parameters, Monte Carlo design, metrics, and implementation used in the numerical study.Source: §5 · p. 20, §5.1 · p. 21
5.1.1. Historical Disaster Recovery Cases
- Seven disaster-region cases use separately fitted logistic recovery models based on historical outage and recovery observations reported through FCC disaster records.Table 1 summarizes observations and fitted recovery parameters for cases including West Maui and Hurricanes Maria, Helene, and Michael.Source: §5.1.1 · p. 21, Table 1 · p. 21
- Recovery-model fit quality is high, with R² values ranging from 0.947 to 0.997, while the seven cases span markedly different recovery trajectories.Maria PR and USVI recover slowly, Helene NC transitions within the evaluation period, and Helene SC, Helene VA, and Michael start at more advanced recovery levels.Source: §5.1.1 · pp. 21–22, Figure 2 · p. 22
5.1.2. Backhaul Scenarios
- Four backhaul scenarios assume a common capacity and independent, non-transferable backhaul for each of six service zones.The scenario capacities are Fiber 1000 Mbps, Microwave 500 Mbps, Mobile Gateway 200 Mbps, and Satellite 100 Mbps.Source: §5.1.2 · p. 23, Table 2 · p. 23
5.1.3. Model and Experimental Parameters
- The baseline case uses 30 Mobile and three Tethered UAVs across six zones, with a one-hour control step and an eight-step prediction horizon.The evaluation lasts 168 hours; baseline demand and ground capacity settings are held common across primary comparisons.Source: Table 3 · p. 24, §5.1.3 · p. 25
5.1.4. Monte Carlo Experiment Setup
- The Monte Carlo design compares an integrated model with five ablations across 840 matched scenarios, yielding 5,040 model-scenario simulation runs.The scenarios combine seven disaster cases, four backhaul settings, and 30 matched Monte Carlo runs; the ablations remove or alter model components.Source: §5.1.4 · pp. 25–26, Table 4 · p. 26
5.1.5. Evaluation Metrics
- Performance measures include served ratio, backlog integral, and total relay hours, with paired model differences calculated using the same Monte Carlo samples.Served ratio captures demand ultimately served; backlog integral captures the duration and magnitude of temporary delay, while relay hours measure aerial resource use.Source: §5.1.5 · pp. 26–27
5.1.6. Computational Implementation
- The MPC is implemented in Python as convex quadratic programs, using CLARABEL primarily and OSQP or SCS as fallback solvers.Solver outputs are checked for constraint violations before simulation use.Source: §5.1.6 · pp. 27–28
5.2. Dynamic Fleet Sizing Across Disasters
System performance and active UAV use vary with both ground recovery and backhaul capacity. Across representative disasters, the fleet’s service, deployment, and energy trajectories differ substantially as terrestrial networks recover.
5.2.1. System Performance
- West Maui’s served ratio falls from 68.8% under Fiber to 28.2% under Satellite, while backlog rises from 56,460 to 118,180 service units · hours.Table 5 averages results over 30 Monte Carlo samples; performance depends on both recovery trajectory and backhaul capacity.Source: §5.2.1 · p. 28, Table 5 · p. 29
- West Maui and Maria PR use more than 2,500 relay hours under Fiber and Microwave, whereas Michael uses about 112 and Helene SC about 197 across tested backhauls.More restrictive backhaul reduces relay use because additional aerial capacity cannot always translate into delivered service.Source: §5.2.1 · p. 30
- Backlog generally falls as ground disruption decreases, but backhaul capacity affects how much remains, and the same recovery trajectory can yield different backlog levels.Fiber and Microwave produce nearly the same performance across the seven disaster cases; the backhaul effect shrinks as recovery reduces residual demand.Source: §5.2.1 · pp. 30–31, Figure 3 · p. 31
5.2.2. Service, Backlog, and Fleet Trajectories
- Maria PR sustains unmet demand and exceeds 450 backlog units; Helene NC clears a 41.4-unit peak as Mobile deployment falls to 2.9, while Michael remains low-use.Figures 4 and 5 show service, backlog, and active fleet composition for these three representative cases.Source: Figure 4 · p. 32, Figure 5 · p. 32, §5.2.2 · pp. 32–33
5.2.3. Energy Trajectories
- Mobile UAV utilization stays near 40% in Maria PR, energy remains low, and Helene NC’s energy availability recovers as deployment declines; Michael’s energy stays near full.The phase trajectories distinguish Maria’s stable operation, Helene’s transition, and Michael’s low-use, high-energy state.Source: §5.2.3 · pp. 33–34, Figure 6 · p. 34
5.3. Component Ablation and Bottleneck Analysis
Component ablations show that backhaul information has the largest overall effect on service performance, while fleet composition, energy modeling, and ground recovery information affect different aspects of operation. The size of these effects changes with available backhaul capacity.
5.3.1. Component Ablation Results
- Compared with No Backhaul, the Integrated model reduces backlog by 12.0%, raises served ratio by 2.6 percentage points, and uses about 321 fewer relay hours.Across the tested scenarios, backhaul information has the largest effect on service performance.Source: Table 6 · p. 35, §5.3.1 · pp. 35–36
- Compared with All Mobile, the Integrated mixed fleet reduces backlog by 7.9% and raises served ratio by 1.2 percentage points, while using about 71 more relay hours.Explicit energy modeling reduces backlog by 0.6% versus Duty Limit and raises served ratio by 0.04 percentage points, with 5.9 more relay hours.Source: §5.3.1 · pp. 35–36
- Ground recovery information reduces backlog by only 0.2% versus No Recovery but saves about 800 relay hours; future recovery adds little backlog reduction at the baseline horizon.Against Persistence, backlog and served ratio are nearly identical, while the Integrated model uses 4.6 fewer relay hours.Source: §5.3.1 · p. 36
5.3.2. Effect of Backhaul Capacity
- Under Fiber, the Integrated model reduces backlog by 22.7% versus All Mobile; under Mobile Gateway and Satellite, it reduces backlog by 27.6% and 9.1% versus No Backhaul.Fleet composition matters more with high backhaul capacity, while backhaul information matters more when capacity is limited and extra UAV capacity has limited benefit.Source: §5.3.2 · pp. 36–37, Figure 8 · p. 37
5.4. Sensitivity and Robustness Analysis
Sensitivity analyses vary fleet architecture, energy and demand conditions, prediction horizon, and forecast errors. The resulting effects differ by operating condition, with forecast errors affecting UAV use more than backlog in the tested cases.
5.4.1. Fleet Architecture
- With equal fleet counts, All Mobile produces 7.9% higher backlog than the mixed fleet; matching steady aerial availability makes the 38-Mobile fleet’s backlog 1.1% lower.The results point to longer operating time as the main benefit of Tethered UAVs.Source: Table 7 · p. 38, §5.4.1 · p. 38
5.4.2. Energy and Demand Scale
- At demand scale 0.35, explicit energy modeling reduces backlog by 10.4%, versus 2.1% at the 0.50 baseline; its relative benefit increases from 2.0% at 1-hour recharge to 2.7% at 3 hours.Absolute backlog reductions rise from 248 to 516 service units · hours as demand increases, and from 288 to 1,308 service units · hours as recharge time increases.Source: §5.4.2 · pp. 38, 40, Figure 9 · p. 39, Table 8 · p. 39
5.4.3. Planning Horizon
- Across 4- to 24-hour horizons, backlog remains effectively unchanged, while fleet decisions differ more often and relay-hour savings increase.Under Fiber, savings rise from 1.09 to 4.69 UAV hours and differing decisions from 3.8% to 22.1%; under Mobile Gateway, they rise from 0.42 to 2.54 UAV hours and 18.0% to 44.0%.Source: §5.4.3 · pp. 40, 42, Table 9 · p. 41, Figure 10 · p. 41
5.4.4. Forecast Error
- With 30% joint demand and recovery forecast errors, backlog increases by only 0.043%, while relay use rises by 39.1% and mean fleet-decision difference reaches 3.47 UAVs.The synthetic error distributions are for sensitivity analysis and are not intended as empirically calibrated forecast errors.Source: §5.4.4 · p. 43, Table 10 · p. 43
5.5. Computational Performance and Numerical Reliability
The MPC simulations run well within the one-hour control interval used in the experiments. All runs completed successfully, and accepted solutions met numerical tolerance.
5.5. Computational Performance and Numerical Reliability
- All simulation runs completed successfully, and all accepted solutions satisfied the numerical tolerance.Action projection and energy balance errors were also small.Source: §5.5 · pp. 43–44
- Mean solution time per MPC update is 0.013 ± 0.004 s, with an overall 95th-percentile solution time of 0.027 s.Across 5,040 simulation runs, mean complete-simulation wall-clock time is 11.9 ± 1.2 s, with a maximum of 18.5 s.Source: §5.5 · p. 43, Table 11 · p. 44
- Solution times were much shorter than the one-hour control interval used in the numerical experiments.The results indicate solvability within the available control time for the tested problem size.Source: §5.5 · pp. 43–44
6. Discussion and Conclusion
The results show that active UAV fleet requirements change with recovery conditions, while backhaul capacity and fleet composition shape communication performance. The framework’s conclusions are bounded by simplifying assumptions about backhaul, UAV operation, and forecast errors.
6.1. Operational Insights
- A mixed fleet outperforms an All Mobile fleet with the same total UAV count, but the difference narrows when All Mobile can provide similar continuous aerial support.Mobile UAVs can be reassigned across zones, while Tethered UAVs provide long-duration support at fixed locations; deployment costs and site constraints are not modeled.Source: §6.1 · p. 45
- Current ground recovery information reduces UAV use with only a small backlog change, while added future-recovery information provides little further benefit at the baseline prediction horizon.Longer horizons change fleet decisions but yield limited additional savings in UAV use.Source: §6.1 · pp. 45–46
- At the largest tested joint forecast error, backlog changes by less than 0.05% while relay use increases by 39.1%.Forecast accuracy should be assessed using both communication performance and UAV resource use.Source: §6.1 · p. 46
6.2. Limitations and Future Work
- Backhaul scenarios assume every zone has an independent connection of the same type and capacity, leaving shared networks and time-varying availability for future study.The results identify backhaul capacity as a constraint on the benefit of additional UAVs.Source: §6.2 · p. 46
- Mobile UAV energy is modeled at fleet level, Tethered UAV locations are fixed, routes are not optimized, and deployment and operating costs are omitted.Future work could include site selection, individual scheduling and routing, charging resources, travel time, and costs.Source: §6.2 · p. 46
- Forecast sensitivity uses assumed error levels rather than errors estimated from real disaster data, so the backlog effects under observed forecast uncertainty remain to be evaluated.The authors identify observed demand and recovery forecast errors as a direction for future analysis.Source: §6.2 · pp. 46–47
6.3. Conclusion
- A convex quadratic program supports repeated fleet-sizing decisions, and experiments across seven recovery trajectories show that persistent shortages require sustained UAV deployment while returning ground capacity allows the active fleet to decrease.The required fleet is not fixed throughout disaster recovery.Source: §6.3 · p. 47
6.1. Operational Insights
- Accounting for backhaul constraints reduces overall backlog by 12.03% versus planning that ignores them; explicit Mobile UAV energy modeling has a smaller baseline effect that increases with recharge time.Backhaul can limit how much additional aerial capacity translates into service.Source: §6.1 · p. 45, §6.3 · p. 47