Given a stationary stochastic continuous demand of service [sigma]([theta]t[omega]) dt with [integral operator] [sigma]([omega])P(d[omega]) < 1, we construct real stationary point processes such that for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [Tn, Tn+1[ the demand of service...</1,>