Modeling Drone Deliveries Using Petri Nets: An Evaluation on Collision Recovery and Energy Efficiency

IEEE SMC talk on autonomous drone deliveries, drone fleets

1. Leonel Feitosa, Vandirleya Barbosa, Luiz Guilherme, Iure Fé, Fabíola Oliveira, Luiz
Bittencourt, Huber Flores and Francisco Airton Silva
E-mail: [email protected]
Homepage: https://huberflores.com
ModelingDrone Deliveries Using Petri Nets:
An Evaluation on Collision Recovery and
Energy Efficiency
October 8, 2025, Vienna, Austria

2. SMC 2025, Vienna, Austria
[email protected]
Edge deployment of LLMs
Example: Healthcare
#2
Importance
Practical drone delivery is a reality
[Source] Drone charging pad https://www.skycharge.de/drone-charging-pad

3. SMC 2025, Vienna, Austria
[email protected]
Edge deployment of LLMs
Example: Healthcare
#3
Importance
Practical drone delivery is a reality
[Source] Walmart drone delivery https://makeagif.com/gif/walmart-drone-delivery-by-
wing-Ksm9u5

4. SMC 2025, Vienna, Austria
[email protected]
Edge deployment of LLMs
Example: Healthcare
#4
Importance
Practical drone delivery is a reality
[Source] https://gizmodo.com/drones-emergency-landing-steep-roofs-house-rooftops-
1849445310
Flying collision
Several possible failures
Landing crash

5. SMC 2025, Vienna, Austria
[email protected]
#5
Modelling drone deliveries
Main Challenge: How can the performance of delivery drones be accurately predicted in complex urban
environments considering collisions and the interaction of multiple dynamic factors?
Several factors
•Package arrival rate for delivery;
•Probability of collision of drones in route;
•Battery recharge time at strategic points;
•Number of drones available for operation;
•Time to repair and replace crashed drones;
•Interactions between factors such as recharge, collision and replacement;
Existing methods
-Simulation
-Heuristics
Difficult to implement

6. Our contributions
•Modelling using Petri Nets: Predict the performance of drone
delivery architecture considering collisions, recharging and
arrival of demands, using SPN.
•New insights: Considering different characteristics of drones
and scenarios
•Simultaneous integration of recharging, continuous delivery and collision;
•Inclusion of drone replacement and repair logistics;
•Evaluation of metrics such as MMT, utilization, delivery rate, energy consumed and
carbon footprint.
SMC 2025, Vienna, Austria
[email protected]
#6

7. Stochastic Petri Nets (SPN)
●Models parallel/concurrent processes;
●Allows you to model the system in detail;
●It is equivalent to CTMC.
SMC 2025, Vienna, Austria
[email protected]
#7
Place
Direction
Token
Transitions
TimeDeterministicImmediate
CTMC = Continuous-time Markov Chain

8. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
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#8
Start
End

9. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#9
Start
End

10. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#10
Start
End

11. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#11
Start
End

12. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#12
Start
End

13. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#13
Start
End

14. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#14
Start
End

15. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#15
Start
End

16. Stochastic Petri Nets (SPN)
SMC 2025, Vienna, Austria
[email protected]
#16
Start
End

17. Architecture
#17SMC 2025, Vienna, Austria
[email protected]

18. SPN model
#18SMC 2025, Vienna, Austria
[email protected]

19. SPN model
#19SMC 2025, Vienna, Austria
[email protected]

20. SMC 2025, Vienna, Austria
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#20
Evaluation
Mean mission time
Increasing the number of
drones cuts delivery time
drastically.
•100 drones → ~26 hours at
high demand
•500 drones → ~6 hours
With 500 drones, even heavy
traffic (164 packages/h) takes
only ~2.7 hoursto complete.

21. SMC 2025, Vienna, Austria
[email protected]
#21
Evaluation
Utilization
Smaller fleets get overloaded
quickly:
100 drones reach 85%
utilizationbelow 50
packages/h.
500 drones stay around
22%, handling more
demand smoothly.
Larger fleets balance workload
betterand prevent service
delays.

22. SMC 2025, Vienna, Austria
[email protected]
#22
Evaluation
Delivery rate x Drone Collision prob.
When collision risk is low (1%),
performance differences are huge:
500 drones → 3.13 packages/h
100 drones → 0.81 packages/h
When collisions rise above 5%, all
configurations lose performanceand
converge.
The benefits of larger fleets
disappear if collision control is poor
—reliable navigation is essential.

23. SMC 2025, Vienna, Austria
[email protected]
#23
Evaluation
Energy consumption
and
Carbon footprint
More drones deliver faster, but
also consume much more
energy

24. SMC 2025, Vienna, Austria
[email protected]
#24
Take aways
•Proposed Stochastic Petri Net model for drone delivery performance.
•More drones improve delivery speed only if the system can safely
coordinate them.
•Scaling up the fleet requires smarter collision-avoidance and traffic
management to prevent performance collapse.
•Larger fleets also increase energy use and carbon footprint.

25. Thanks for listening!
Huber Flores
[email protected]