# Heavy-tailed random walks, buffered queues and hidden large deviations

## TL;DR

This paper explores the complex behavior of heavy-tailed random walks and queues, revealing hidden large deviations beyond the well-known principle of one large jump, with applications to queue congestion analysis and simulation verification.

## Contribution

It introduces the concept of hidden large deviations in heavy-tailed random walks and applies it to queueing processes, providing new insights into severe congestion time approximations.

## Key findings

- Hidden large deviations exist beyond the principle of one large jump.
- Approximate severe congestion times in heavy-tailed queues.
- Simulation results verify theoretical predictions.

## Abstract

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 deviation scale which we call hidden large deviation. We apply this idea in the context of queueing processes with heavy-tailed service times and study approximations of severe congestion times for (buffered) queues. We conclude with simulated examples to verify our results.