Volume Over Lethality: A Matrix-Exponential Framework for Defending Drone Swarms

Abstract

We study large, heterogeneous drone swarms composed of both threat and decoy drones. The defender's engagement is modelled as a multi-stage stochastic process that captures uncertainty and variability in response times. A non-discriminatory defender is considered in which threat and decoy drones are treated identically. We adopt a matrix-exponential framework that yields tractable, closed-form expressions for key performance measures. The results indicate that swarm size has a substantially stronger impact on defence success than threat-decoy composition. For a typical defender, swarms exceedingly roughly ten drones may exceed single-defender swarm-size capacity under the baseline modelling assumptions, even with high decoy fractions. While a typical defender can reliably handle seven threat drones, augmenting the swarm with seven decoys reduces the probability of successful defence from 0.93 to 0.09. From a cost perspective, heterogeneous drone swarms can reduce overall cost by up to 67% when decoy drones are priced at approximately one tenth of the cost of threat drones. Finally, performance depends not only on aggregate rates but also on individual stage bottlenecks. Under idealised conditions where each engagement stage completes in approximately one second on average, single-defender capacity increases to approximately 35-40 drones.