Advances in Applied Probability

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

Alexander Goldenschluger

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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.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 4 (2016), 1117-1138.

Dates
First available in Project Euclid: 24 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1482548431

Mathematical Reviews number (MathSciNet)
MR3595768

Zentralblatt MATH identifier
1356.62125

Subjects
Primary: 62G05: Estimation
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 62M09: Non-Markovian processes: estimation

Keywords
M/G/∞ queue nonparametric estimation minimax risk stationary process covariance function rates of convergence

Citation

Goldenschluger, Alexander. Nonparametric estimation of the service time distribution in the M/G/∞ queue. Adv. in Appl. Probab. 48 (2016), no. 4, 1117--1138. https://projecteuclid.org/euclid.aap/1482548431


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