"Special issue on Selected papers from the Twenty-eighth International Symposium on Graph Drawing and Network Visualization, GD 2020" Parameterized Algorithms for Queue Layouts Vol. 26, no. 3, pp. 335-352, 2022. Regular paper. Abstract An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ sets, called queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$-queue layout is the queue number of $G$. We present two fixed-parameter tractable algorithms that exploit structural properties of graphs to compute optimal queue layouts. As our first result, we show that deciding whether a graph $G$ has queue number $1$ and computing a corresponding layout is fixed-parameter tractable when parameterized by the treedepth of $G$. Our second result then uses a more restrictive parameter, the vertex cover number, to solve the problem for arbitrary $h$.  This work is licensed under the terms of the CC-BY license. Submitted: October 2020. Reviewed: May 2022. Revised: June 2022. Accepted: June 2022. Final: June 2022. Published: June 2022. Communicated by David Auber and Pavel Valtr article (PDF) BibTeX