Limits and approximations for the M/G/1 LIFO waiting-time distribution

We provide additional descriptions of the steady-state waiting-time distribution in the M/G/1 queue with the last-in first-out (LIFO) service discipline. We establish heavy-traffic limits for both the cumulative distribution function (cdf) and the moments. We develop an approximation for the cdf that is asymptotically correct both as the traffic intensity ρ →1 for each time t and as t →∞ for each ρ. We show that in heavy traffic the LIFO moments are related to the FIFO moments by the Catalan numbers. We also develop a new recursive algorithm for computing the moments.