In this paper, we incorporate decision rules based on adaptive behaviour in order to analyze the impact of customers' decisions on queue formation. We deviate from most of the literature in that we model dynamic queuing systems with deterministic and endogenous arrivals. We apply a one-dimensional cellular automata in order to model the research problem. We describe a self organizing queuing system with local interaction and locally rational customers. They decide which facility to use considering both their expected sojourn time and their uncertainty regarding these expectations. These measures are updated each period applying adaptive expectations and using customers' experience and that of their local neighbours. This paper illustrates how the average sojourn time of customers in the system depends on their characteristics. These characteristics define how risk-averse customers are as well as how conservative they are regarding new information.