Dynamic computation of population protocols

Abstract

Population protocols provide theoretical foundations for mobile tiny device networks in which global behavior emerges from a set of simple interactions between anonymous agents. The works in this area mostly focus on studying the computational power of the model. Results hold as long as a fair scheduler, which governs the interactions between nodes, ensures that all reachable system states may eventually happen. This paper studies for the first time the impact of the agents' mobility model on the convergence speed of population protocols, emphasizing the dynamic of the computation. We propose an augmented population protocol model where each edge of the interaction graph is weighted, representing the probability of two agents to interact. This model enables to define the behavior of the scheduler under various mobility models. We have empirically shown that mobility models have a significant impact on the convergence speed of the protocols. In fact, we observed that the uniform distribution always provides the best convergence time. Such a model is representative of the well-known Random Way Point model used to evaluate most of mobile ad-hoc network protocols. In this paper, we formally prove that a uniform distribution of weights provides the lowest bound of average convergence speed for a large class of population protocols. Therefore, this analysis reveals that the Random Way Point model, following this distribution, provides the best case scenario questioning its relevance as a reference model.