Weariness and Loyalty Loss in Recurrent Service Models

For recurrent service providers (fast-food, entertainment, medical care,...), retaining loyal customers is obviously a key issue. The customers' loyalty essentially depends on their service satisfaction defined via an ad-hoc utility function. Among several criteria, the utility function strongly depends on the past perceived waiting time. Moreover, the patience that customers consent to allow in waiting does often decrease as a function of the successive utilizations of the service (i.e. weariness). We propose here an idealized queueing model in which the customers' loyalty is determined only by the individual experience gained during the successive visits to a service (i.e. the waiting time and the number of services yet recieved). For regimes where the law of large numbers holds, a deterministic approach enables to analytically discuss the resulting multi-agent dynamics governing the customers' flows. One is able, in particular, to fully calculate, analytically, the characteristics of the emerging complex patterns (i.e. here structured temporal oscillations) which are observed to be strongly structurally stable.