Augmenting Automatic Differentiation for a Single-Server Queue via the Leibniz Integral Rule

TL;DR

This paper introduces new recursive estimators for higher-order derivatives of mean queueing time in a single-server queue, using the Lindley equation and Leibniz integral rule, with illustrative examples.

Contribution

It presents a novel approach to estimate higher-order derivatives in queueing models by combining Lindley's equation with Leibniz's rule, enhancing analytical capabilities.

Findings

New recursive estimators for derivatives are derived.

Estimators are applicable from a single sample path.

Illustrative examples demonstrate the method's effectiveness.

Abstract

New recursive estimators for computing higher-order derivatives of mean queueing time from a single sample path of a first-come, first-served single-server queue are presented, derived using the well-known Lindley equation and applying the Leibniz integral rule of differential calculus. Illustrative examples are provided.