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UID:www.tcs.tifr.res.in/event/151
DTSTAMP:20230914T125912Z
SUMMARY:Simulation-based Computation of the Correlation Function in a Levy-
driven Queue
DESCRIPTION:Speaker: Michel Mandjes\nUniversity of Amsterdam\nKorteweg-de V
ries Institute for Mathematics\nScience Park 904\n1098 XH A\n\nAbstract: \
nIn this talk I consider a single-server queue with Levy input\, and in pa
rticular its workload process $Q(t)$\, focusing on its correlation structu
re. With the correlation function defined as $r(t) := {\\\\rm Cov}(Q(0)\,
Q(t))/{\\\\rm Var} Q(0)$ (assuming the workload process is in stationarity
at time 0)\, we first study its transform $\\\\int_0^\\\\infty r(t)e^{-\\
\\theta t} dt\,$ both for the case that the Levy process has positive jump
s\, and that it has negative jumps. These expressions allow us to prove th
at $r(t)$ is positive\, decreasing\, and convex\, relying on the machinery
of completely monotone functions. For the light-tailed case\, we estimate
the behavior of $r(t)$ for $t$ large. We then focus on techniques to esti
mate $r(t)$ by simulation. Naive simulation techniques require roughly $1/
r(t)^2$ runs to obtain an estimate of a given precision\, but we develop a
coupling technique that leads to substantial variance reduction (required
number of runs being roughly $1/r(t)$). If this is augmented with importa
nce sampling\, it even leads to a logarithmically efficient algorithm.\n
URL:https://www.tcs.tifr.res.in/web/events/151
DTSTART;VALUE=DATE:20110118
LOCATION:A-212 (STCS Seminar Room)
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