Generally, swarm models and algorithms consider synchronous agents, i.e., they act simultaneously. This hypothesis does not fit multi-agent simulators nor robotic systems. In this paper, we consider such issues on a patrolling ant algorithm. We examine how different execution hypotheses influence self-organization capabilities and patrolling performances of this algorithm. We consider the mono and multiagent cases, the synchronism and determinism hypotheses, and the execution of the model with real robots.