Estimating the input of a Lévy-driven queue by Poisson sampling of the workload process

Liron Ravner, Onno Boxma, Michel Mandjes

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3734-3761
Number of pages28
Issue number4 B
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 ISI/BS.


  • Lévy-driven queue
  • Nonparametric estimation
  • Poisson probing
  • Queue input estimation
  • Transient queueing

ASJC Scopus subject areas

  • Statistics and Probability


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