Tail Asymptotics for the Waiting Time in an M/G/1/ROS Vacation Queue with Regularly-Varying Service

Abstract

We study the asymptotic behavior of tail probability for the waiting time in the steady-state M/G/1/ROS multiple-vacation queue with regularly-varying service time and vacation time distributions. Conditioning on the server being busy or on vacation, the asymptotic conditional tail probabilities are obtained explicitly. We also verify that the waiting-time tail for M/G/1/ROS queue with multiple-vacation is asymptotically equivalent to that for the standard M/G/1/ROS queue (without vacation), as long as the vacation time has a tail probability lighter than the service time.