Convexity of Workload Autocorrelation in a Stationary Single Server Queue with Independent Increment Input

TL;DR

This paper introduces a probabilistic method to analyze the convexity of workload autocorrelation functions in stationary single-server queues, demonstrating its application to GI/GI/1 queues and Lévy-driven fluid queues.

Contribution

It presents a novel probabilistic approach for studying autocorrelation convexity in workload processes, applicable to various queue models.

Findings

Convexity properties established for workload autocorrelation functions.

Method successfully applied to GI/GI/1 queues and Lévy-driven fluid queues.

Provides new insights into workload process behaviors.

Abstract

We propose a method based on probabilistic arguments to study the convexity of the autocorrelation function of processes associated with a single server queue. To illustrate the power of the method we apply it in two cases: to the workload process seen by the customers of a GI/GI/1 queue, and to the workload process of a fluid queue fed by a general L\'evy process.