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Bounds for the variance of the busy period of the M/G/∞ queue

Published online by Cambridge University Press:  01 July 2016

M. F. Ramalhoto
M. F. Ramalhoto*
Affiliation:
Instituto Superior Técnico, Lisbon
*
∗Postal address: Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1000 Lisboa, Portugal.
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Abstract

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Some bounds for the variance of the busy period of an M/G/∞ queue are calculated as functions of parameters of the service-time distribution function. For any type of service-time distribution function, upper and lower bounds are evaluated in terms of the intensity of traffic and the coefficient of variation of the service time. Other lower and upper bounds are derived when the service time is a NBUE, DFR or IMRL random variable. The variance of the busy period is also related to the variance of the number of busy periods that are initiated in (0, t] by renewal arguments.

Keywords

LOWER AND UPPER BOUNDSSTOCHASTIC ORDER RELATIONSVARIANCE OF NUMBER OF BUSY PERIODS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 929 - 932
Copyright
Copyright © Applied Probability Trust 1984 

Footnotes

Research partially supported by the Centro de Estatística e Aplicaçõ es do INIC under the Applied Stochastic Processes Research Project.

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