Mariana Olvera-Cravioto. Jose Blanchet. Peter Glynn. “On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case.” Ann. Appl. Probab. 21 (2) 645 – 668, April 2011. https://doi.org/10.1214/10-AAP707
Abstract
Two of the most popular approximations for the distribution of the steady-state waiting time, W∞, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic intensity, ρ, is close to 1 and the processing times have finite variance, the heavy-traffic approximation states that the distribution of W∞ is roughly exponential at scale O((1 − ρ)−1), while the heavy tailed asymptotic describes power law decay in the tail of the distribution of W∞ for a fixed traffic intensity. In this paper, we assume a regularly varying processing time distribution and obtain a sharp threshold in terms of the tail value, or equivalently in terms of (1 − ρ), that describes the point at which the tail behavior transitions from the heavy-traffic regime to the heavy-tailed asymptotic. We also provide new approximations that are either uniform in the traffic intensity, or uniform on the positive axis, that …
Authors
Mariana Olvera-Cravioto, Jose Blanchet, Peter Glynn
Publication date
2011/4/1
Volume
21
Issue
2
Pages
645-668
