Nonparametric Estimation of the Probability of a Long Delay in the M/G/1 Queue
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Authors
Gaver, D.P.
Jacobs, P.A.
Subjects
M/G/1 Queue
virtual waiting time distribution
terminating renewal process
asymptotic exponential tail
jackknife
domain of attraction of a stable law
central limit theorem
virtual waiting time distribution
terminating renewal process
asymptotic exponential tail
jackknife
domain of attraction of a stable law
central limit theorem
Advisors
Date of Issue
1988
Date
Publisher
Royal Statistical Society
Language
Abstract
A Poisson stream of customers with known arrival rate ʎ approaches a single server having
independent identically distributed service times with unknown distribution. A nonpara-
metric estimator of the probability of a long customer delay is obtained from an asymptotic
renewal theoretic result giving an exponential approximation to the tail of the virtual waiting
time distribution for a stable M/G/1 queue. Asymptotic properties of the estimator are
obtained. Results of a simulation study of the small sample size behaviour are given.
Type
Article
Description
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Probability and Statistics Program of the Mathematical Sciences Division of the Office of Naval Research.
Funder
Format
12 p.
Citation
Gaver, Donald P., and Patricia A. Jacobs. "Nonparametric estimation of the probability of a long delay in the M/G/1 queue." Journal of the Royal Statistical Society: Series B (Methodological) 50.3 (1988): 392-402.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.