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Inequalities for the M/G/∞ queue and related shot noise processes
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- Journal:
- Journal of Applied Probability / Volume 24 / Issue 4 / December 1987
- Published online by Cambridge University Press:
- 14 July 2016, pp. 978-989
- Print publication:
- December 1987
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- Article
- Export citation
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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.
for all functions 
for all convex functions 
. Various consequences of this result are explored.