On the Transition from Heavy-traffic to Heavy-tails for the M/G/1 Queue: The Regularly Varying Case (with M. Olvera-Cravioto and P. Glynn)

Summary:

This paper reconciles the diffusion approximation to the maximum of a random walk with negative drift (which takes an exponential form) with the heavy-tailed approximation (which shows a power-law decay behavior). It is shown that the there is a sharp transition threshold which is given by the maximum of these two approximations. The paper fits within the body of theory on uniform large deviations results for heavy-tailed random variables pioneered by Nagaev and Rozovskii.

Bibtex:

@Article{OCBG09,

author = {M. Olvera-Cravioto and J. Blanchet and P. Glynn},

title = {On the transition from heavy-traffic to heavy-tails for the M/G/1 queue: The regularly varying case},

journal = {Annals of Applied Probability},

year = {2011},

volume = {21},

pages = {645-668}

}