Time and customer processes in queues with stationary inputs

Abstract

Two types of processes occurring in queues with stationary inputs are considered. They are called ‘time processes’ and ‘customer processes’. Sufficient conditions for the convergence of sample averages and the existence of limiting distributions for each type of processes are given. The results generalize those of Loynes (1962). The results are applied to three queueing processes and the Little's formula L = λW is obtained under rather general conditions.