Abstract
In this paper, the area swept under the workload graph is analyzed: with {Q(t): t=0} denoting the stationary workload process, the asymptotic behavior of
p_{T(u)} (u):=P(\int^T(u)_0 Q(r)dr > u)
is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of pT(u)(u) are given for the case that T(u) grows slower than vu, and then logarithmic asymptotics for (i) T(u)=Tvu (relying on sample-path large deviations), and (ii) vu=o(T(u)) but T(u)=o(u). Finally, the Laplace transform of the residual busy period are given in terms of the Airy function.
Original language | English |
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Pages (from-to) | 395-415 |
Number of pages | 21 |
Journal | Bernoulli |
Volume | 20 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2014 |