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

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 a...

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Bibliographic Details
Published inAdvances in applied probability Vol. 48; no. 4; pp. 1117 - 1138
Main Author Goldenshluger, Alexander
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2016
Applied Probability Trust
Subjects
Estimation
Markov analysis
Nonparametric statistics
Probability
Queues
Queuing theory
Upper bounds
Primary 62G05
Secondary 60K25
stationary process
nonparametric estimation
minimax risk
62M09
M/G/∞ queue
covariance function
rates of convergence
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ISSN0001-8678
1475-6064
DOI10.1017/apr.2016.67

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Summary: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.
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content type line 14
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2016.67