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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Transient behaviour in highly dependable Markovian
systems\, new regimes\, many paths - Reijsbergen\
, D\, de Boer\, P-T\, Scheinhardt\, W (Twente)
DTSTART;TZID=Europe/London:20100622T114000
DTEND;TZID=Europe/London:20100622T120500
UID:TALK25321AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/25321
DESCRIPTION:In recent years\, probabilistic analysis of highly
dependable Markovian systems has received conside
rable attention. Such systems typically consist of
several component types\, subject to failures\, w
ith spare components for replacement while repair
is taking place. System failure occurs when all (s
pare) components of one or several types have fail
ed. In this work we try to estimate the probabilit
y of system failure before some fixed time bound $
au$ via stochastic simulation. Obviously\, in a h
ighly dependable system\, system failure is a rar
e event\, so we apply importance sampling (IS) tec
hniques\, based on knowledge of the behaviour of t
he system and the way the rare event occurs. \n\nI
nterestingly\, we can discern quite a few differen
t situations to explain why system failure is rare
\, each with its own typical way of how the rare e
vent is reached\, namely: (1) low component failur
e rates\, (2) small value of $ au$\, (3) many spar
e components and (4) high component repair rates.
Each of these can be considered as a limiting regi
me in which some model parameter tends to $0$ or i
nfinity. Classifying this parameter as the `mph{r
arity parameter}'\, we can measure the performance
of an IS scheme by how well it does in the asympt
ote involved. We could also combine regimes\, whic
h sometimes leads to new cases and sometimes not (
e.g. the limit in which both failure and repair ra
tes become small is equivalent to $ au$ becoming s
mall).\n\nFor cases (1) and (2)\, a combination of
balanced failure biasing and forcing was proven t
o have bounded relative error in te{shahabuddin19
94importance}. In te{deboer2007estimating} an alt
ernative estimator was proposed\, based on the dom
inant path to failure\, the idea being that when a
n event is rare\, deviations from the most likely
path to this event become even more rare. However\
, in several model checking problems an analysis b
ased on dominant paths fails to identify a well-pe
rforming change of measure. The reason is that the
contribution of some other paths to the probabili
ty of interest is too large to neglect\, or\, more
formally speaking\, that the contribution of thes
e paths does not vanish asymptotically.\n\nIn our
paper\, we first prove that in the asymptote of ca
se (3)\, which is interesting in its own right\, t
he dominant path to failure indeed does determine
the entire rare event\, as in cases (1) and (2). T
hen we demonstrate that this is not true for case
(4). We propose a state- and time-dependent change
of measure for a simple\, yet nontrivial\, model.
Our measure is based on the one in te{deboer2007
estimating} and takes all paths into account that
contribute to the probability of interest. Finall
y\, we empirically verify that our estimators have
good performance.\n \n[1] P.T. de Boer\, P. L'ec
uyer\, G. Rubino\, and B. Tuffin. Estimating the
probability of a rare event over a finite time hor
izon. In Proceedings of the 2007 Winter Simulatio
n Conference\, pages 403-411\, 2007.\n[2] P. Shaha
buddin. Importance \n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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