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Inequalities for the M/G/∞ queue and related shot noise processes

Published online by Cambridge University Press:  14 July 2016

Fred W. Huffer
Fred W. Huffer*
Affiliation:
Florida State University
*
∗Postal address: Department of Statistics, Florida State University, Tallahassee, Florida 32306-3033, USA.
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Abstract

Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

Keywords

VARIABILITY ORDERINGCONVEX ORDERINGL-SUPERADDITIVE FUNCTIONALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 978 - 989
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported by the Office of Naval Research under contract N00014-76-C-0475.

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