In this paper we use an agent-based modelling and simulation approach to model a queuing system with autonomous customers who routinely choose a facility for service. We propose a Cellular Automata model to represent the customers' interactions and study how customers use their own experience and that of their neighbours in order to update their memory and decide what facility to join the next period. We use exponential smoothing to update the customers' expected sojourn time. We incorporate uncertainty regarding these expectations into the customers' decision. We compare the resulting behaviour when customers take into account uncertainty to the case where they ignore uncertainty at both the individual and the system level.