Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service [sigma]([theta]t[omega]) dt with [integral operator] [sigma]([omega])P(d[omega]) 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 accumulated during the proceding intervals [Tn-1, Tn[ and take a rest of fixed duration D.