Introduction of First Passage Time (FPT) Analysis for Software Reliability and Network Security
Author
Ma, Zhanshan (Sam)
Krings, Axel W.
Millar, Richard C.
Date
2009Metadata
Show full item recordAbstract
The study of the First Passage Time (FPT) problem (also known
as first passage problem, FPP) started more than a century ago,
but its diverse applications in science and engineering mostly
emerged in the last two to three decades. Assuming that X(t) is a
one-dimensional stochastic process, the First Passage Time is
defined as the time (T) when X(t) first crosses a threshold.
Engineering reliability is obviously a suitable application domain,
and indeed applications such as optimal dam design in hydrology
and analysis of structural failure in civil and mechanical
engineering are typical examples. Although we envision that the
FPT problem has great potential in network and software
reliability, it should be more useful for network security and
survivability because the approaches developed for the FPT
problem are mostly analytical. The assumption for this inference
is that in reliability analysis, experimental or historical data are
often more readily available, which makes statistical approaches
such as survival analysis more convenient and likely more
realistic. In contrast, data is generally more difficult to obtain in
security and survivability analyses, and analytical approaches can
be leveraged to play more important roles. Furthermore, security
and survivability often have to deal with malicious actions that
may be driven by sophisticated cognition and behavioral
processes, which are highly variable over time and very difficult
to detect with short term data. If the behavior of an intruder can
be characterized with some stochastic process such as Brownian
motion, then the FPT approach may be applied to find the closedform
solution of the probability density function (PDF) of the first
passage time, which can be the time when the system breaks
down or when the hacker is successful in compromising a
network. In addition, the solutions to FPT depend on boundary
and initial conditions of the corresponding partial differential
equations, and they also describe the evolution of PDF over time.
This may suggest that it is possible to model the behavior changes
of an intruder over time and circumstances. Another advantage of
FPT analysis is that it may help solve some non-Markov
stochastic process problems in reliability analysis and survival
analysis. In this article, we first briefly introduce the FPT problem
with Brownian motion as an example, and then suggest its
potential applications in software reliability and network security.
Description
The Fifth CSIIRW '2009, April 13-15, Oak Ridge National Lab, Oak Ridge, Tennessee, USA. Includes a powerpoint presentation.
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