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SUMMARY:Simulation-based computation of the workload correlation function 
 in a Levy-driven queue - Michel Mandjes\, Universiteit van Amsterdam and E
 urandom\, Eindhoven
DTSTART:20100222T150000Z
DTEND:20100222T160000Z
UID:TALK22742@talks.cam.ac.uk
CONTACT:Sarah Lilienthal
DESCRIPTION:We consider a single-server queue with Levy input\, and in\npa
 rticular its workload process Q(t)\, focusing on its correlation structure
 .\nWith the correlation function defined as r(t) := Cov(Q(0)\, Q(t))/Var Q
 (0)\n(assuming the workload process is in stationarity at time 0)\, we fir
 st study its\ntransform\n  int_0^\\infty r(t)e^{-theta t} dt\,\nboth for t
 he case that the Levy process has positive jumps\, and that it has\nnegati
 ve jumps. These expressions allow us to prove that r(t) is positive\,\ndec
 reasing\, and convex\, relying on the machinery of completely monotone\nfu
 nctions. For the light-tailed case\, we estimate the behavior of r(t) for 
 t\nlarge. We then focus on techniques to estimate r(t) by simulation. Naiv
 e\nsimulation techniques require roughly 1/r(t)^2 runs to obtain an estima
 te of a\ngiven precision\, but we develop a coupling technique that leads 
 to substantial\nvariance reduction (required number of runs being roughly 
 1/r(t)). If this is\naugmented with importance sampling\, it even leads to
  a logarithmically\nefficient algorithm.\n
LOCATION:Seminar Room 1\, Isaac Newton Institute for Mathematical Sciences
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