Adaptive Control of Redundant Task Execution for Dependable Volunteer Computing - Cloud, Grid and High Performance Computing: Emerging Applications - page 139

Statistical Resource
Availability Characterizing

Exponential distribution and hyper-exponen-
tial distribution have been used to investigate
the availability behaviors of software, operat-
ing system, workstation, and peer-to-peer file
sharing system in (Goel, 1985; Iyer, 1985; Lee,
1993; Mutka, 1988; Plank, 1998; Tian, 2007). For
the research such as process lifetime estimation
(Harchol-Balter, 1997) and network performance
(Paxson, 1997), Pareto distribution has been used
a lot. Weibull distribution is another distribution
widely used for modeling the resource availabil-
ity. Xu et al.(1999) applied it to the modeling of
network-connected PCs.
Several studies (Schoeder, 2006; Nurmi, 2005;
Iosup, 2007; Nadeem, 2008) compared different
distributions for the modeling. Nurmi (2005)
and Brevik (2004) used exponential, hyper-
exponential, Weibull, and Pareto distributions to
model the TTF availability data gathered from
student lab computers, a cycle-harvesting distrib-
uted computing system - Condor (Litzkow, 1988;
Thain, 2005), and an early survey of Internet hosts
(Long, 1995). Goodness-of-fit analysis indicated
that hyper-exponential and Weibull distributions
fit the empirical data more accurately. Schroeder
et al.(2006) studied the distribution fitting of TTF
in high-performance computing (HPC) systems
with 4750 machines, using Welbull, lognormal,
gamma, and exponential distributions. The results
pointed out that Weibull distribution is a better fit.
Iosup et al.(2007) found Weibull the best fitted
among several distributions for Mean Time Be-
tween Failure (MTBF) and failure duration data of
Grid'5000 (Bolze, 2006; http://www.grid5000.fr).
More recently, Nadeem et al.(2008) also ap-
plied several distributions to the analysis of grid
resource availabilities. It introduced the class
level modeling method by identifying three types
of resources in the Austrian Grid (http://www.
austriangrid.at). Based on the administration
policy, it categorized the resources into three
classes: dedicated resources, temporal resources
and on-demand resources. The distribution fitting
and goodness-of-fit tests are done separately for

There have been a large number of works on the
problem of statistically characterizing resource
availability.

Root Cause Analysis of Failures

Root cause analysis of failures has been stud-
ied in (Gray, 1990; Kalyanakrishnam, 1999;
Oppenheimer, 2003; Schroeder, 2006). The
software-related failure is reported to be around
20% (Oppenheimer, 2003), 50% (Gray, 1990,
Kalyanakrishnam, 1999), and from 5% to 24%
(Schroeder, 2006). The percentage of hardware-
related failure is from 10% to 30% in (Gray, 1990;
Kalyanakrishnam, 1999; Oppenheimer, 2003),
and from 30% to over 60% (Schroeder, 2006).
The network-related failure is significant in some
of those works, while it accounts for around 20%
(Kalyanakrishnam, 1999) and 40% (Oppenheimer,
2003) of the failures. Human errors also lead to
10% - 15% (Gray, 1990) and 14% - 30% (Op-
penheimer, 2003) of the failures. These works
reported different breakdown of failures, because
of the different systems they studied.

Fitting Distribution to
Empirical Availability Data

Some other works studied statistical distributions
of empirical availability data such as Time-to-Fail
(TTF) and Down Time (DT) . Such methods find
the best fitted theoretical distribution for a given
empirical data set, by estimating the parameters
of the theoretical distributions with techniques
such as Maximum Likelihood Estimation (MLE)
(Aldrich, 1997). Several distributions have been
used to model the peer availability, including log-
normal, Weibull, exponential, hyper-exponential,
and Pareto distributions. The detail of these
distributions and their properties can be found in
(Patel, 1976).