Modeling Robot Swarms Using Integrals of Birth-Death Processes

This article investigates the use of the integral of linear birth-death processes in the context of analyzing swarm robotics systems. We show that when a robot swarm can be modeled as a linear birth-death process, well-established results can be used to compute the expected value and/or the distribution of important swarm performance measures, such as the swarm activity time or the swarm energy consumption. We also show how the linear birth-death model can be used to estimate the long-term value of such performance measures and design robot controllers that satisfy constraints on these measures.