Stationary queues with one autonomous server
Given a stationary stochastic continuous demand of service \(\sigma (\theta_ t\omega)dt\) with \(\int \sigma (\omega)P(d\omega)<1\), the author constructs a real stationary point process \((T_ n, n\in Z)\), \(T_ n<T_{n+1}\), \(\lim_{n\to \pm \infty}T_ n=\pm \infty\), such that \(T_{n+1}-T_ n=D+\int^{T_ n}_{T_{n-1}}\sigma \theta_ t dt\), for a given constant \(D>0.\) These point processes correspond to a service discipline for which a single server services during the time \([T_ n,T_{n+1})\) the demand of service accumulated during the preceding interval \([T_{n-1},T_ n)\) and takes a rest of fixed duration D.
stationary stochastic continuous demand of service
scientific article; zbMATH DE number 3905606
scientific article