Augmenting Automatic Differentiation for a Single-Server Queue via the Leibniz Integral Rule
arXiv:2604.029002.7h-index: 1
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This work addresses a specific computational challenge in queueing theory, offering incremental improvements for researchers in operations research and simulation.
The paper tackled the problem of computing higher-order derivatives of mean queueing time in a single-server queue by presenting new recursive estimators derived from the Lindley equation and Leibniz integral rule, with illustrative examples provided.
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.