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November 2019 Estimating the input of a Lévy-driven queue by Poisson sampling of the workload process
Liron Ravner, Onno Boxma, Michel Mandjes
Bernoulli 25(4B): 3734-3761 (November 2019). DOI: 10.3150/19-BEJ1109

Abstract

This paper aims at semi-parametrically estimating the input process to a Lévy-driven queue by sampling the workload process at Poisson times. We construct a method-of-moments based estimator for the Lévy process’ characteristic exponent. This method exploits the known distribution of the workload sampled at an exponential time, thus taking into account the dependence between subsequent samples. Verifiable conditions for consistency and asymptotic normality are provided, along with explicit expressions for the asymptotic variance. The method requires an intermediate estimation step of estimating a constant (related to both the input distribution and the sampling rate); this constant also features in the asymptotic analysis. For subordinator Lévy input, a partial MLE is constructed for the intermediate step and we show that it satisfies the consistency and asymptotic normality conditions. For general spectrally-positive Lévy input a biased estimator is proposed that only uses workload observations above some threshold; the bias can be made arbitrarily small by appropriately choosing the threshold.

Citation

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Liron Ravner. Onno Boxma. Michel Mandjes. "Estimating the input of a Lévy-driven queue by Poisson sampling of the workload process." Bernoulli 25 (4B) 3734 - 3761, November 2019. https://doi.org/10.3150/19-BEJ1109

Information

Received: 1 August 2018; Revised: 1 January 2019; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110154
MathSciNet: MR4010971
Digital Object Identifier: 10.3150/19-BEJ1109

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4B • November 2019
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