EXPONENTIAL APPROXIMATIONS FOR TAIL PROBABILITIES IN QUEUES .2. SOJOURN TIME AND WORKLOAD

We continue to focus on simple exponential approximations for steady-s tate tail probabilities in queues based on asymptotics. For the G/GI/1 model with i.i.d. service times that are independent of an arbitrary stationary arrival process, we relate the asymptotics for the steady-s tate waiting time, sojourn time, and workload. We shaw that the three asymptotic decay rates coincide and that the three asymptotic constant s are simply related. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical results for BMAP/G/1 queues, which h ave batch Markovian arrival processes. Numerical examples show that th e exponential approximations for the tail probabilities are remarkably accurate at the 90th percentile and beyond. Thus, these exponential a pproximations appear very promising for applications.