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In this study, a one‐dimensional cellular automata model is used to represent a self‐organized queueing system with local interaction between captive and boundedly rational customers who repeatedly choose a facility for service. While previous work has focused on decision rules based on adaptive expectations, the present work expands this analysis by explicitly incorporating customers’ attitude toward risk to study the impact of risk aversion on the collective behavior and the average system sojourn time. The customers’ decision process is modeled using adaptive expectations and incorporating the uncertainty involved in these expectations. Customers update their expectations based on their own experience and that of their neighbors. Simulation analysis is used to compare the aggregated behavior for different degrees of customer risk aversion. Risk‐neutral customers base their decisions only on their expected sojourn time, while risk‐averse customers account for uncertainty by estimating an upper bound of the sojourn times. The results indicate that the more risk‐averse the customers, the longer the transient period, and the more slowly the system converges to an almost stable average sojourn time. Systems where customers have an intermediate level of risk aversion achieve the worst average sojourn times.

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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.