In this note we prove that the speed of convergence of the workload of a Lévy-driven queue to the quasi-stationary distribution is of order 1/t. We identify also the Laplace transform of the measure giving this speed and provide some examples.
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Keywords Lévy processes, Storage systems, Quasi-stationary distribution, Laplace transforms, Fluctuation theory, Speed of convergence
Palmowski, Z, & Vlasiou, M. (2017). Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues.