Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime

We consider a first–come first–served multiserver queue in the Quality– and Efficiency–Driven (QED) regime. In this regime, which was first formalized by Halfin and Whitt, the number of servers N is not small, servers' utilization is 1–O(1/√N;) (Efficiency–Driven) while waiting time is O(1/√N;)(Quality–Driven). This is equivalent to having the number of servers N being approximately equal to R+β√R, where R is the offered load and β is a positive constant.