Formal Modeling of Temporal Interaction Aspects in Multi-Agent Systems

Multi-agent interaction protocols play a crucial role in multi-agent systems (MAS) development. They are used to manage and to control interactions among several autonomous agents in a MAS. Their formal specification, as well as their verification, constitute an essential task for the design of MAS applications. Several approaches have been proposed to formally represent agent interaction protocols, but there still lacks a formalism for representing temporal interaction constraints. This time dimension is an essential parameter in the protocol modeling seeing that most real world applications they support are time-sensitive. This paper proposes to use Timed Colored Petri Nets (TCPN) to model correctly and formally this temporal issue often defined as interaction duration and message deadlines. We then take the well-known Contract Net protocol (CNP) as an example to show that interaction protocols with time constraints can be modeled naturally and efficiently with this formalism. Finally, thanks to simulation techniques and state space analysis we will prove that the most important keys namely model correctness, deadline respect, absence of deadlocks and livelocks, absence of dead code, agent terminal states consistency, concurrency and validity are met. Keywords-Interaction protocols, Contract net protocol, Multiagent systems, Timed Colored Petri Nets.