Extremal models for the GI∕GI∕K waiting-time tail-probability decay rate

Abstract We identify interarrival-time and service-time distributions that yield tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability in the G I ∕ G I ∕ K queue, given the first two moments of those underlying distributions plus alternative additional information. We apply Tchebycheff systems after providing a concise review.