Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload

In this paper, we continue to focus on simple exponential approximations for steady-state tail probabilities in G/GI/1 queues based on large-time asymptotics. The model is quite general because the arrival process can be an arbitrary stationary point process. We relate the large-time asymptotics for the steady-state waiting time, sojourn time and workload. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical results for BMAP/GI/1 queues. Numerical examples show that the exponential approximations for the tail probabilities are remarkably accurate at the 90th percentile and beyond.