Stochastic Model of Evolutionary and Immunological Multi-Agent Systems: Parallel Execution of Local Actions

Article type: Research Article

Authors: Schaefer, Robert | Byrski, Aleksander | Smołka, Maciej

Affiliations: Department of Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland. E-mail: {schaefer,olekb}@agh.edu.pl | Institute of Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland. E-mail: smolka@ii.uj.edu.pl

Abstract: The refined model for the biologically inspired agent-based computation systems EMAS and iEMAS conforming to the BDI standard is presented. Moreover, their evolution is expressed in the form of the stationary Markov chains. This paper generalizes the results obtained by Byrski and Schaefer [7] to a strongly desired case in which some agents' actions can be executed in parallel. In order to find the Markov transition rule, the precise synchronization scheme was introduced, which allows to establish the stepwise stochastic evolution of the system. The crucial feature which allows to compute the probability transition function in case of parallel execution of local actions is the commutativity of their transition operators. Some abstract conditions expressing such a commutativity which allow to classify the agents' actions as local or global are formulated and verified in a very simple way. The above-mentioned Markov model constitutes the basis of the asymptotic analysis of EMAS and iEMAS necessary to evaluate their search possibilities and efficiency.

Keywords: Multi-agent systems, agent-based computation, stochastic modeling

DOI: 10.3233/FI-2009-153

Journal: Fundamenta Informaticae, vol. 95, no. 2-3, pp. 325-348, 2009