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. Keywords Agent Cooperation::Biologically-inspired approaches and methods, Agent-based simulations::Simulation techniques, tools and environments