Traditional queueing research has concentrated mainly on design, performance and running of the service facility with customers arriving following a stochastic process. In this paper we develop a behavioral model of a queueing system including repeat (returning) customers using a combination of Cellular Automata models (CA) and Genetic Algorithms (GA). An agent based evolutionary approach using simulation is adopted where agents' structural properties are defined using a CA and evolutionary strategies are implemented with the help of a GA.