Graph Cellular Automata with Relation-Based Neighbourhoods of Cells for Complex Systems Modelling: A Case of Traffic Simulation

A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to analyse applications of graph structures together with cellular automata. It proposes a graph cellular automaton with a variable configuration of cells and relation-based neighbourhoods (r–GCA). The developed mechanism enables modelling of phenomena found in complex systems (e.g., transport networks, urban logistics, social networks) taking into account the interaction between the existing objects. As an implementation example, modelling of moving vehicles has been made and r–GCA was compared to the other cellular automata models simulating the road traffic and used in the computer simulation process.

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