We address a service facility problem with captive interacting customers and service providers. This problem is modelled as a deterministic queuing system. Customers must routinely decide which facility to join for service, whereas service providers must decide how much to adjust the service capacity of their facilities. Both service providers and customers base their decisions on their perceptions about the system. Customers use their previous experience and that of their neighbours to update their perceptions about the average sojourn time, while service providers form their perceptions based on the queue length. We use cellular automata (CA) to model the interaction between customers and service providers. We perform a simulation to assess the way the customers' and service providers' decisions evolve and affect the system behaviour. Our results show that the more conservative the service providers, the larger the market share they achieve and the lower probability that their facility closes down.