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Convergence and rate of convergence of a simple ant model

We present a simple ant model that solves a discrete foraging problem. We provide simulations and a convergence analysis. We argue that the ant population computes the solutions of some optimal control problems and converges in some well defined sense. We also discuss the rate of convergence with respect to the number of ants: we give experimental and theoretical arguments that suggest that this rate is superlinear with respect to the number of agents.