An extension of Osuna's model to observable queues

In his seminal work, Osuna (1985) defines the psychological cost of waiting as the psychological stress accumulated during the waiting period. He contends that after having to wait for a certain amount of time, anxiety and stress start to build up in individuals, due both to the sense of waste and the uncertainty in the time that they still have to wait. We build on the works of Osuna (1985) and Suck and Holling (1997) that show how psychological costs build up in a single wait situation. We consider waiting in observable queues and model how the progress and the static waits in a queue affect the accumulation of stress. This modeling approach allows for the representation of the expected total accumulated stress of waiting in an observable queue in terms of the queue characteristics, the queue length, L, and the mean and variance of the total waiting time in the queue E[Tq] and V[Tq], respectively (or the mean and variance of the associated service time distribution, E[t] and V[t], respectively). We propose that, in evaluating and comparing the psychological costs of waiting in alternative queue designs, researchers can focus on the final dissatisfaction as represented by the total stress accumulated during the waiting period.