In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a s...

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known Markov chains and mixing sequences by another common possibility to measure allow additional time dependence. main result is central limit theorem processes. Moreover, maximal inequalities expectations sums are developed. show applicability our in...