Open Access
February 2020 Heavy-tailed random walks, buffered queues and hidden large deviations
Harald Bernhard, Bikramjit Das
Bernoulli 26(1): 61-92 (February 2020). DOI: 10.3150/18-BEJ1081


It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such random walks in the large deviations scale which we call hidden large deviations. Our results are illustrated using two examples. First, we apply this idea in the context of queueing processes with heavy-tailed service times and study approximations of probabilities of severe congestion times for (buffered) queues. We exhibit our techniques by using limit measures from different large deviation regimes to provide a unified estimate of rare event probabilities in a simulated queue. Furthermore, we use our result to provide probability estimates of rare events governed by more than one jump in case the innovations of a random walk have infinite mean.


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Harald Bernhard. Bikramjit Das. "Heavy-tailed random walks, buffered queues and hidden large deviations." Bernoulli 26 (1) 61 - 92, February 2020.


Received: 1 January 2017; Revised: 1 May 2018; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140493
MathSciNet: MR4036028
Digital Object Identifier: 10.3150/18-BEJ1081

Keywords: buffered queues , heavy-tails , large deviations , regular variation

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 1 • February 2020
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