Estimation of Mean Response Time of Multi–Agent Systems Using Petri Nets

Performance analysis of multi–agent system can be done by experiments with real system, simulation or analytic methods. Now, multi–agent technologies, e.g., (Deloach et al., 2001; JADE), are often based on Unified Modeling Lanuage (UML) (Booch et al., 1999; UML, 2007) or its modifications. The following analytical approaches: queuing network models (Kahkipuro, 1999), stochastic automata networks (Steward et al., 1995), stochastic Petri nets (King & Pooley, 1999), stochastic process algebra (Pooley, 1999), Markov chains can be used in performance evaluation of multi–agent systems. In this chapter, an analytical approach, which is based on Petri nets, is developed. This approach is applied to performance evaluation of layered multi–agent system. These layers are associated with the following types of agents: manager, bidder, and searcher ones. Time–out mechanisms are used in communication between agents. Our method is based on approximation using Erlang distribution. Erlang distributions create the family of distributions with different number of stages. In the paper (Babczyński & Magott, 2006a), an approximation method which is based on Erlang distribution has been applied for the above layered multi–agent system. In that paper, there was no bounds for time of waiting for messages from the agents. In present chapter, time–out mechanisms are used in communication between the agents. The chapter is an extension of the paper (Babczyński & Magott, 2006b) where PERT based approach was presented. Accuracy of our approximation method is verified using simulator. This simulator has been previously used in simulation experiments with the following multi–agent systems: personalized information system (Babczyński et al., 2004a), industrial system (Babczyński et al., 2004b), system with static agents and system with mobile agent (Babczyński et al., 2005). These systems have been expressed in standard FIPA (FIPA) which the JADE technology (JADE) is complied with. The chapter is organized as follows. In section 2, the multi–agent system is described. Then our approximation method is presented. In section 4, accuracy of our approximation method is verified by comparison with simulation results. Finally, there are conclusions.