A two-stage screening method for nonparametric inference from the M/G/1 workload

2026/07/30 by Royi Jacobovic, Binyamin Kobzantsev
Mathematics · #math.ST #math.PR #stat.TH #msc:62G20 #msc:62M20 #msc:60K25

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arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We study the nonparametric estimation problem posed by Hansen and Pitts (2006) for the service-time distribution of an M/G/1 queue observed through its workload process. Unlike previous work, we assume neither stationarity nor stability, and allow the arrival rate to be unknown. Our main contribution is a two-stage screening procedure that extracts a conditionally independent compound Poisson sample from the dependent workload observations, thereby reducing the original inference problem to a classical decompounding problem. Building on the decompounding methodology of Den Boer and Mandjes (2017), we construct a fully data-driven estimator of the service-time distribution. Under mild smoothness assumptions, we prove that, for every fixed w>0, 𝔼|B_n(w)-B(w)| =O ((log n)/(√ n)). To the best of our knowledge, this is the first estimator for the Hansen--Pitts observation scheme that achieves a nearly parametric convergence rate without requiring stationarity, stability, or knowledge of the arrival rate.

Citations

• Nonparametric estimation of the job-size distribution for an M/G/1 queue with Poisson sampling
• Smoluchowski processes and nonparametric estimation of functionals of particle displacement distributions from count data
• Simple sufficient condition for inadmissibility of Moran's single-split test
• Taylor's Theorem and Mean Value Theorem for Random Functions and Random Variables
• A Survey of Parameter and State Estimation in Queues
• Estimating the input of a L 'evy-driven queue by Poisson sampling of the\n workload process
• On The Asymptotic Efficiency of Selection Procedures for Independent Gaussian Populations
• Convergence rates of Laplace-transform based estimators

Related

• Nonparametric estimation of the job-size distribution for an M/G/1 queue with Poisson sampling
• Queue input estimation from discrete workload observations
• Estimating the input of a L 'evy-driven queue by Poisson sampling of the\n workload process
• Nonparametric estimation of service time distribution in the M/G/∞ queue and related estimation problems
• Bayesian Nonparametric Inference for M/G/1 Queueing Systems