Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions
Queueing Systems: Theory and Applications
Random Walk with a Heavy-Tailed Jump Distribution
Queueing Systems: Theory and Applications
Queueing approximation of suprema of spectrally positive Lévy process
Queueing Systems: Theory and Applications
Parallel queueing networks with Markov-modulated service speeds in heavy traffic
ACM SIGMETRICS Performance Evaluation Review - Special issue on the 31st international symposium on computer performance, modeling, measurements and evaluation (IFIPWG 7.3 Performance 2013)
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In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a0, let $\{Y^{(a)}_{n}:n\ge1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_{t}:t\ge0\}$ be a Lévy process such that $X_{1}^{(a)}\stackrel{d}{=}Y_{1}^{(a)}$ , $\mathbb{E}X_{1}^{(a)} and $\mathbb{E}X_{1}^{(a)}\uparrow0$ as a驴0. Let $S^{(a)}_{n}=\sum _{k=1}^{n} Y^{(a)}_{k}$ . Then, under some mild assumptions, , for some random variable and some function Δ(驴). We utilize this result to present a number of limit theorems for suprema of Lévy processes in the heavy-traffic regime.