Abstract
We provide a complete large and moderate deviations asymptotic for the steady-state waiting time of a class of subexponential M/G/1 queues under heavy traffic. The asymptotic is uniform over the positive axis, and reduces to heavy-traffic asymptotics and heavy-tail asymptotics on two ends, both of which are known to be valid over restricted asymptotic regimes. The link between these two well-known asymptotics is a transition term that is expressible as a convolution-type integral. The class of service times that we consider includes regularly varying and Weibull tails in particular.
It is our pleasure to contribute to this special issue dedicated to the International Year of Statistics. In response to the request of the editors of this special issue we briefly overview the research topics that we have investigated recently. Our research group has pursued several themes in recent years. All of them lie under the scope of applied probability. Some of our projects deal with computational probability. In this context, our goal is to enable efficient computation in stochastic systems using (and often developing) theory of probability to inform the design of algorithm that are optimal and robust in certain sense (see Blanchet and Glynn (2008)). Most of the computations that we study relate to stochastic simulation (also known as Monte Carlo) methods (see Blanchet and Lam (2012)). Other projects that we pursue relate to classical analysis in probability, such as asymptotic approximations, large deviations, and heavy-traffic limits (Blanchet and Glynn (2006) and Lam et al (2011)). All of our research efforts are motivated by models and problems in areas such as: Finance …
Authors
Jose Blanchet, Henry Lam
Publication date
2013
Journal
Bull. of the Mex. Math. Soc.(3)
Volume
19
