Functional Limit Theorems for the Queue Gi/G/1 in Light Traffic

摘要

A GI/G/1 queueing system in light traffic has the property of returning to the idle state infinitely often. The purpose of the paper is to exploit this property to develop limit theorems for several processes generated by this system. The principal processes of interest are the following: W sub n, the waiting time of the nth customer; Q(t), the number of customers in the system at time t; W(t), the virtual waiting time at time t; B(t), the amount of time the server is busy in (O,t); I(t), the amount of tie the server is idle in (O,t); and D(t), the cumulative number of customers departing the system in (O,t).