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Nonparametric estimation of the service time distribution in the M/G/∞ queue

Part of: Nonparametric inference Inference from stochastic processes Special processes

Published online by Cambridge University Press:  11 January 2017

Alexander Goldenshluger
Alexander Goldenshluger*
Affiliation:
University of Haifa
*
* Postal address: Department of Statistics, University of Haifa, Haifa 31905, Israel. Email address: goldensh@stat.haifa.ac.il
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Abstract

The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well.

Keywords

M/G/∞ queuenonparametric estimationminimax riskstationary processcovariance functionrates of convergence

MSC classification

Primary: 62G05: Estimation
Secondary: 60K25: Queueing theory 62M09: Non-Markovian processes
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 4 , December 2016 , pp. 1117 - 1138
Copyright
Copyright © Applied Probability Trust 2017 

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