On a Single Server Queue Fed by a Scheduled Traffic with Pareto Perturbations

TL;DR

This paper analyzes a single server queue with scheduled arrivals perturbed by Pareto-like heavy-tailed delays, deriving tail approximations for workload distribution in critical and heavy-traffic conditions.

Contribution

It introduces tail behavior analysis for queues with Pareto perturbations, focusing on finite-mean heavy-tailed delays and their impact on workload distribution.

Findings

Tail approximations for steady-state workload under heavy tails

Analysis of Bernoulli sums with power-law success probabilities

Insights into queue behavior with Pareto-like perturbations

Abstract

A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of perturbations is assumed to be iid. We describe here the behavior of a single server queue fed by such traffic in which the processing times are deterministic. A particular focus is on perturbation with Pareto-like tails but with finite mean. We obtain tail approximations for the steady-state workload in both cases where the queue is critically loaded and under a heavy-traffic regime. A key to our approach is our analysis of the tail behavior of a sum of independent Bernoulli random variables with success probability following a power law with parameter strictly larger than 1.