Asymptotic stationarity of queues in series and the heavy traffic approximation
For a sequence of single server queues with infinite waiting rooms under FCFS the joint departure processes, waiting time processes, and sojourn time processes are considered with respect to asymptotic behaviour in the sense of weak and strong convergence and convergence in variation of the random sequences, as well as that of Cesàro type limits. It is proved that if the input sequences (interarrival and service times) for the system are asymptotically stationary in one sense of the above definitions, then the process of the functionals mentioned above is asymptotically stationary in the same sense. Certain refinements of this are derived and heavy traffic results are obtained providing diffusion approximations.
scientific article; zbMATH DE number 4199219