We consider a single-server GI / GI / 1 queueing system with feedback. We assume the service time distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer’s sojourn time in two cases: the customer arrives in an empty system, and the customer arrives in the system in the stationary regime. In particular, in the case of Poisson input we obtain more explicit formulae than those in the general case. As auxiliary results, we find the tail asymptotics for the busy period distribution in a single-server queue with an intermediate varying service times distribution and establish the principle-of-a-single-big-jump equivalences that characterise the asymptotics.
- Heavy-tailed and intermediate regularly varying distributions
- Principle of a single big jump
- Single-server queue
- Sojourn time
- Tail asymptotics