We continue to focus on simple exponential approximations for steady-state tail probabilities in queues based on asymptotics. For the GI/G/1 model with independent identically distributed service times that are independent of an arbitrary stationary arrival process, we relate the asymptotics for the steady-state waiting time, sojourn time, and workload. We show that the three asymptotic decay rates coincide and that the three asymptotic constants 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 have batch Markovian arrival processes. Numerical examples show that the exponential approximations for the tail probabilities are remarkably accurate at the 90th percentile and beyond. Thus, these exponential approximations appear very promising for applications.
