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Mining for Availability Models in Large-ScaleDistributed Systems:A Case Study of SETI@home

Bahman Javadi, Derrick Kondo, Jean-Marc Vincent, David P. Anderson

To cite this version:Bahman Javadi, Derrick Kondo, Jean-Marc Vincent, David P. Anderson. Mining for AvailabilityModels in Large-Scale Distributed Systems:A Case Study of SETI@home. [Research Report] 2009.�inria-00375624�

Mining for Availability Models in Large-Scale Distributed Systems:

A Case Study of SETI@home

Bahman Javadi1, Derrick Kondo1, Jean-Marc Vincent2, David P. Anderson3

1INRIA, France, 2University of Joseph Fourier, France, 3UC Berkeley, USA

Abstract

In the age of cloud, Grid, P2P, and volunteer distributed

computing, large-scale systems with tens of thousands of

unreliable hosts are increasingly common. Invariably, these

systems are composed of heterogeneous hosts whose indi-

vidual availability often exhibit different statistical prop-

erties (for example stationary versus non-stationary be-

haviour) and fit different models (for example Exponential,

Weibull, or Pareto probability distributions). In this paper,

we describe an effective method for discovering subsets of

hosts whose availability have similar statistical properties

and can be modelled with similar probability distributions.

We apply this method with about 230,000 host availability

traces obtained from a real large-scale Internet-distributed

system, namely SETI@home. We find that about 34% of

hosts exhibit availability that is a truly random process, and

that these hosts can often be modelled accurately with a

few distinct distributions from different families. We believe

that this characterization is fundamental in the design of

stochastic scheduling algorithms across large-scale systems

where host availability is uncertain.

1 Introduction

With rapid advances in networking technology and dra-

matic decreases in the cost of commodity computing com-

ponents, large-scale distributed computing platforms with

tens or hundreds of thousands of unreliable and heteroge-

neous hosts are common. The uncertainty of host avail-

ability in P2P, cloud, or Grid systems can be due to the

host usage patterns of users, or faulty hardware or software.

Clearly, the dynamics of usage, and hardware and software

stacks are often heterogeneous, spanning a wide spectrum

of patterns and configurations. At same time, within this

spectrum, subsets of hosts with homogeneous properties

can exist.

So one could also expect that the statistical properties

(stationary versus non-stationary behavior for example) and

models of host availability (Exponential, Weibull, or Pareto

for example) to be heterogeneous in a similar way. That is,

host subsets with common statistical properties and avail-

ability models can exist, but differ greatly in comparison to

other subsets.

The goal of our work is to be able to discover host sub-

sets with similar statistical properties and availability mod-

els within a large-scale distributed system. In particular, the

main contributions are as follows:

• Methodology. Our approach is to use tests for random-

ness to identify hosts whose availability is independent

and identically distributed (iid). For these hosts, we

use clustering methods with distance metrics that com-

pare probability distributions to identify host subsets

with similar availability models. We then apply pa-

rameter estimation for each host subset to identify the

model parameters.

• Modelling. We apply this method on one of the largest

Internet-distributed systems in the world, namely

SETI@home. We take availability traces from about

230,000 hosts in SETI@home, and identify host sub-

sets with matching statistical properties and availabil-

ity models. We find that a significant fraction (34%)

of hosts exhibit iid availability, and a few distributions

from several distinct families (in particular Gamma,

Weibull, and Log-Normal) can accurately model the

availability of host subsets.

These results are essential for the design of stochastic

scheduling algorithms for large-scale systems where avail-

ability is uncertain.

In the next section, we describe the application context

that is used to guide our modelling. In Section 3, we define

availability and describe how our availability measurements

were gathered. In Section 4, we contrast this measurement

method and our modelling approach to related work. In Sec-

tion 6, we determine which hosts exhibit random, indepen-

dent, and stationary availability. In Section 7, we describe

the clustering of hosts by their availability distribution. In

Section 8, we describe the implications of our results for

scheduling, and in the last section, we summarize our find-

ings.

2 Application Context

We describe here the context of our application, which

is used to guide what we model. Our modelling is con-

ducted in the context of volunteer distributed computing,

which uses the free resources of Internet-distributed hosts

for large-scale computation and storage. Currently this

platform is limited to embarrassingly parallel applications

where the main performance metric is throughput. One of

the main research goals in this area is to broaden the types

of applications that can effectively leverage this platform.

We focus on the problem of scheduling applications

needing fast response time (instead of high throughput).

This class of applications includes those with batches of

compute-intensive tasks that must be returned as soon as

possible, and also those whose tasks are structured as a di-

rected acyclic graph (DAG).

For these applications, the temporal structure of avail-

ability and resource selection according to this structure is

critical for their performance. The temporal structure of

availability is important because many applications cannot

easily or frequently checkpoint due to complexities of its

state or checkpointing overheads.

Resource selection is important because in our experi-

ence and discussions with application scientists the max-

imum number of tasks in a batch for fast turnaround is

needed is much lower than the number active and available

hosts at a given time point (hundreds of thousands). This

same is true for the maximum number of tasks available in

a DAG application during its execution.

A1

Time

CPU

on host i

A2 An

Figure 1. CPU availability intervals on one

host

Thus our modelling focuses on the interval lengths of

continuous periods of CPU availability for individual hosts.

We term this continuous interval to be an availability inter-

val (see Figure 1). The lengths of the availability intervals

of a particular host over time is the process that we model.

Using these models, a scheduler should then be able to

compute accurately the probability of successful task exe-

cution in some time frame, given a task’s execution time.

Moreover, the scheduler could compute the probability of

success when task replication is used.

3 Measurement Method for CPU Availability

BOINC [5, 2] is a middleware for volunteer distributed

computing. It is the underlying software infrastructure for

projects such as SETI@home, and runs across over 1 mil-

lion hosts over the Internet.

We instrumented the BOINC client to collect CPU avail-

ability traces from about 230,000 hosts over the Internet be-

tween April 1, 2007 to January 1, 2009. We define CPU

availability to be a binary value indicating whether the CPU

was free or not. The traces record the time when CPU starts

to be free and stops.

Our traces were collected using the BOINC server for

SETI@home. The traces are not application dependent nor

specific to SETI@home because they are recorded at the

level of the BOINC client (versus the application it exe-

cutes). In total, our traces capture about 57,800 years of

CPU time and 102,416,434 continuous intervals of CPU

availability.

Artifacts due to a measurement method or middleware

itself are almost inevitable. In our case, artifacts resulted

from a benchmark run periodically every five days by the

BOINC client. As a result, availability intervals longer

than five days were truncated prematurely and separated by

about a one minute period of unavailability before the next

availability interval. Histograms and mass-count graphs

showed that these 5-day intervals were outliers and signifi-

cantly skewed the availability interval mass distribution. As

such, we preprocessed the traces to remove these gaps after

five day intervals artificially introduced by our middleware.

This minimized the effect of these anomalies in the mod-

elling process.

4 Related Work

This work differs from related in terms of what is mea-

sured and what is modelled. In terms of measurements, this

work differs from others by the types of resources measured

(home versus only within an enterprise or university), the

scale and duration (hundreds of thousands over 1.5 years

versus hundreds over weeks), and the type of measurement

(CPU availability versus host availability). Specifically, the

studies [12, 6] focus on host in the enterprise or university

setting and may have different dynamics compare to hosts

primarily on residential broadband networks. Our study in-

cludes both enterprise and university hosts, in addition to

hosts at home.

Also, other studies focus on hundreds of hosts over a

limited time span [12, 7, 15, 1]. Thus their measurements

are of limited breadth and could be biased to a particular

platform. The limited number of samples per host prevents

accurate modelling at the resource level.

Furthermore, while many (P2P) studies of availability

exist [16, 4, 14], these studies focus on host availability,

i.e., a binary value indicating whether a host is reachable.

By contrast, we measure CPU availability as defined in Sec-

tion 3. This is different as a host can clearly be available but

not its CPU. Nevertheless, host availability is subsumed by

CPU availability.

In terms of modelling, most related works [7, 18, 11]

focus on modelling the system as a whole instead of indi-

vidual resources, or the modelling does not capture the tem-

poral structure of availability [3, 11, 13]. Yet this is essen-

tial for effective resource selection and scheduling. For in-

stance, in [7], the authors find that availability in wide-area

distributed systems can be best modelled with a Weibull or

hyperexponential distribution. However, these models con-

sider the system as a whole and are not accurate for indi-

vidual resources. Even the authors note that their best fitted

global distribution is not adequate for modelling individual

hosts.

For another instance, in [11], the author models host

availability as a fraction of time. However, the temporal

structure of availability, which is critical to computational

tasks for example, is not captured in the model. A host with

that is 99% available but in intervals of 1 millisecond may

be of little use to distributed applications.

For a final instance, in our own past work in [13], we

conducted a general characterization of SETI@home. How-

ever, we ignored availability intervals by taking averages

to represent each host’s availability. So we used a differ-

ent data representation with different distance metrics when

clustering. Moreover, the purpose was different because we

intentionally focused on identifying correlated patterns in-

stead of random ones. As such, we did not build statisti-

cal models of availability intervals, and did not address is-

sues such as partitioning hosts according to randomness and

probability distributions.

5 Experimental Setup

We conduct all of our statistical analysis below using

Matlab 2009a on a 32-bit on a Xeon 1.6GHz server with

about 8.3GB of RAM. We use when possible standard tools

provided by the Statistical Toolbox. Otherwise, we imple-

ment or modify statistical functions ourselves.

6 Randomness Testing

A fraction of hosts are likely to exhibit availability inter-

vals that contain trends, periodicity, autocorrelation, or non-

stationarity. For these hosts, modelling their availability us-

ing a probability distribution is difficult given the change of

its statistical properties over time.

Therefore, as the preliminary phase before data analy-

sis and modeling we apply randomness tests to determine

which hosts have truly random availability intervals. There

are several randomness tests which are divided in two gen-

eral categories: parametric and nonparametric. Paramet-

ric tests are usually utilized when there is an assumption

about the distribution of data. As we cannot make any as-

sumption for the underlying distribution of the data set, we

adopted non-parametric randomness tests. We conducted

four well-known non-parametric tests, namely the runs

test, runs up/down test, autocorrelation test and Kendall-tau

test [17, 10]. For all tests, the availability intervals of each

hosts was imported as a given sequence or time series.

We describe intuitively what they measure. The runs test

compares each interval to the mean. The runs up/down test

compare each interval to the previous interval to determine

trends. The autocorrelation test discovers repeated patterns

that differ by some lag in time. The Kendall-tau test com-

pares a interval with all previous ones.

Since the hypothesis for all these tests are based on

the normal distribution, we must make sure that there are

enough samples for each host, i.e., at least 30 samples, ac-

cording to [8] and personal communication with a statis-

tician. About 20% of hosts do not have enough samples

because of a limited duration of trace measurement. (Mea-

surement for a host began only after the user downloaded

and installed the instrumented BOINC client. So some hosts

may have only a few measurements because they began us-

ing the instrumented BOINC client only moments before

we collected and ended the trace measurements.) So we ig-

nored these hosts in our statistical analysis. Finally, we ap-

plied all four test on 168751 hosts with a significance level

of 0.05.

As there is no perfect test for randomness, we decide to

apply all tests and to consider only those hosts that pass all

four tests to be conservative. Table 1 shows the fraction of

hosts that pass each and all four tests.

While iid hosts may not be in the majority (i.e., 34%), to-

gether they still form a platform with significant computing

power. In total, volunteer computing systems, which now

include GPU’s and Cell processors of the Sony PS3, provide

a sustained 6.5 PetaFLOPS. The hosts with iid availability

thus contribute about 2.2 PetaFLOPS, which is significant.

7 Clustering by Probability Distribution

For hosts whose availability is truly random, our ap-

proach was to first inspect the distribution using histograms

and the mass-count disparity (see Figures 2(a) and 2(b)).

We observe significant right skew. For example, the shortest

80% of the availability intervals contribute only about 10%

of the total fraction of availability. The remaining longest

20% of intervals contribute about 90% of the total fraction

Test Runs std Runs up/down ACF Kendall All

# of hosts 101649 144656 109138 101462 57757

Fraction 0.602 0.857 0.647 0.601 0.342

Table 1. Result of Randomness Tests

of availability. The implication for modelling is that we

should focus on the larger availability intervals.

But which hosts can be modelled by which distributions

with which parameters?

7.0.1 Clustering Background

We use two standard clustering methods, in particular k-

means and hierarchical clustering, to cluster hosts by their

distribution. K-means randomly selects k cluster centers,

groups each point to the nearest cluster center, and repeats

until convergence. The advantage is that it is extremely fast.

The disadvantages are that it requires k to be specified a pri-

ori, the clustering results depend in part on the cluster cen-

ters chosen initially, and the algorithm may not converge.

Hierarchical clustering iteratively joins together the two

sub-clusters that are closest together in terms of the average

all-pairs distance. It starts with the individual data points

working its way up to a single cluster. The advantage of

this method is that one can visualize the distance of each

sub-cluster at different levels in the resulting dendrogram,

and that it is guaranteed to converge. The disadvantage is

that we found the method to be 150 times slower than k-

means.

7.0.2 Distance Metrics for Clustering

We tested several distance metrics for clustering, each met-

ric measures the distance between two CDFs [9]. Intu-

itively, Kolmogorov-Smirnov determines the maximum ab-

solute distance between the two curves. Kuiper computes

the maximum distance above and below of two CDFs.

Cramer-von Mises finds the difference between the area

of under the two CDFs. Anderson-Darling is similar to

Cramer-von Mises, but has more weight on the tail.

Using these distance metrics is challenging when the

number of samples is too low or too high. In the former

case, we do not have enough data to have confidence in

the result. In the latter case, the metric will be too sensi-

tive. A model by definition is only an approximation. When

the number of samples is exceedingly high, the distance re-

ported by those metrics will be exceedingly high as well.

This is because the distance is often a multiplicative factor

of the number of samples.

Our situation is complicated even further by the fact that

we have a different number of samples per host. Ideally,

when computing each distance metric we should have the

same number of samples. Otherwise, the distance between

two hosts with 1000 samples will be incomparable to the

distance between two hosts with 100 samples.

Our solution is to select a fixed number of intervals from

each host at random. This method was used also in [7],

where the authors had the same issue. We also discussed

this issues with a statistician, who confirmed that this is an

acceptable approach.

However, if we choose the fixed number to be too high, it

will excluded too large of a portion of hosts from our clus-

tering. If we choose the number to be too low, we will not

have statistical confidence in the result. We choose the fixed

number to be 30 intervals as discussed in Section 6. The test

statistics corresponding to each distance metric is normally

distributed, and so with 30 intervals, one can compute p-

values with enough accuracy.

We performed extensive experiments to compare the dis-

tance metrics for several cases including for different sub-

sets of iid hosts. We also conducted positive and negative

control experiments where the cluster distributions were

generated and known a priori. The following conclusions

were been found to be consistent across all the cases consid-

ered. We found out that Kolmogorov-Smirnov and Kuiper

are not very sensitive in terms of distance as they are only

concerned with extreme bounds. Cramer-von Mises and

Anderson-Darling revealed that they are good candidates of

clustering, but Anderson-Darling is engaged with high time

and memory complexity. Moreover, Cramer-von Mises is

advantageous for right-skewed distributions [9]. Thus we

used the Cramer-von Mises as the distance metric when

clustering.

7.0.3 Cluster Results and Justification

We found that optimal number cluster was 6. We justify

this number of clusters through several means. First, we ob-

served the dendrogram as a result of hierarchical clustering

for a random subset of hosts (due to memory consumption

and scaling issues). As it can be seen in Figure 3(a) the tree

is an unbalanced tree where the height of tree shows the dis-

tance between different (sub)clusters. The good separation

of hosts in this figure confirmed the advantage of Cramer-

von Mises as the distance metric (in comparison to the re-

sult with other metrics). The number of distinct groups in

this dendrogram where the distance threshold is set to one

0 50 100 150 2000

1

2

3

4

5

6

7

8x 10

6

Availability (hours)

Fre

quen

cy

(a) Histogram

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Length of interval (hours)

Cum

ulat

ive

frac

tion

mean: 12.6971

std: 56.757

median: 1.0547

min: 2.7778e−07

max: 13215.9303

MassCount

(b) Mass-count

Figure 2. Distribution of Availability Intervals

reveals that number of clusters should be between 5 to 10.

Second, using the result of hierarchical clustering as

a bootstrap, we run k-means clustering for all iid hosts

and then compute the within-group and between-group dis-

tances for various values of k (see Figure 3(b)). We observe

that the maximum ratio of inter-cluster over intra-cluster

distance is with six clusters. Specifically, for k of 6, the

inter-cluster distance between all clusters was maximized

relative to other values of k. Also, for k of 6, the distance

between all clusters is roughly equal (about 5).

Third, we plotted the EDF corresponding to each cluster

for a range of k. In this way, we can observe convergence

or or divergence of clusters during their formation.

Fourth, we plotted the EDF corresponding to each clus-

ter. Figure 4 shows good separation of these plots.

7.1 Parameter Estimation for Each Clus-ter

After cluster discovery, we conduct parameter fitting for

various distributions, including the Exponential, Weibull,

Log-normal, Gamma, and Pareto. Parameter fitting was

conducted using maximum likelihood estimation (MLE).

Intuitively, MLE maximizes the log likelihood function that

the samples resulted from a distribution with certain param-

eters.

We also considered using moment matching instead of

MLE. However, because the overall distribution is heavily

right-skewed, we were concerned that moment matching,

which is relatively much faster then MLE, would not pro-

duce the most accurate results. Moment matching is also

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Availability (hours)

Cum

ulat

ive

frac

tion

1

4

2

53

6

Cluster 1Cluster 2Cluster 3Cluster 4Cluster 5Cluster 6

Figure 4. EDF of clusters

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8432117320

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Figure 3. Cluster Comparison

very sensitive to outliers [10].

We measured the goodness of fit (GOF) of the result-

ing distributions using standard probability-probability (PP)

plots as a visual method and also quantitative metrics, i.e.,

Kolmogorov-Smirnov (KS) and Anderson-Darling (AD)

tests. The graphical results which are depicted in Figure 5

revealed that in the most cases the Gamma distribution is

a good fit. Also, Exponential distribution has some close

fits, specially in cluster 4. These results could allow an ap-

proximation that would result in a simple analytical model.

Based on the third column of PP-plots, it is obvious that the

Pareto is completely far from our underlying distribution,

so we do not have a heavy-tailed distribution. However, as

in some plots Log-normal and Weibull have a close match,

some cluster distributions are likely to be long-tailed.

To be more quantitative, we also reported the p-values of

two goodness-of-fit tests. We randomly select a subsample

of 30 of each data set and compute the p-values iteratively

for 1000 times and finally obtain the average p-value. This

method is similar to the one used by the authors in [7], and

was suggested to us by a statistician.

The results of GOF tests are listed in Table 2 where in

the each row the best fit is highlighted. These quantitative

results strongly confirm the graphical result of the PP-plots.

(In the PP-plots, the closer the plots are to the line y = x,

the better the fit.) We find that the best-fitting distributions

of each cluster to differ significantly from the overall distri-

bution over all iid hosts. Thus, clustering was essential for

accurate host availability modelling.

To be more precise, Table 3 lists some properties of iid

hosts and clusters as well. The first point is the existing

heterogeneity in the clusters in terms of members and per-

centage of total availability. The biggest cluster (i.e, cluster

6) that includes more than 50% of total iid hosts, only con-

tribute 20% of the total availability and also, cluster 3 that

is behind cluster 6 and 3 in number of hosts has the highest

availability contribution.

One possible question about the distribution fitting re-

sults is why four clusters that follow the Gamma distribu-

tions are not in one cluster. The answer is in the last column

of Table 3 where the shape and scale parameters of fitting

are reported (For Log-normal distribution, the numbers are

µ and σ, respectively). These values revealed that all four

clusters have almost same shape (see Figure 4) but at a dif-

ferent scale which are very far from each other.

Another question that may be raised here is whether or

not we are able to model all hosts as a single distribution,

i.e., Gamma distribution with fixed parameters. The answer

could is no; the shape and scale parameters for the Gamma

distribution fitting for all iid hosts are 0.2442 and 51.9864,

respectively, which does not reflect the properties of differ-

ent distributions listed in Table 3.

However, based on the graphical and quantitative p-value

results, we could say that the Gamma is a good fit for all

clusters, so we can use a unique distribution but with differ-

ent parameters (at least different scales) to model the avail-

ability of different hosts. It is worth nothing that the Gamma

distribution has very interesting properties in terms of flex-

ibility and generalization and can be easily used to propose

an analytical Markov model as well [10].

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Exponential Pareto Weibull Log-Normal Gamma

Data sets AD KS AD KS AD KS AD KS AD KS

All iid hosts 0.004 0.000 0.061 0.013 0.581 0.494 0.568 0.397 0.431 0.359

Cluster 1 0.155 0.071 0.029 0.008 0.466 0.243 0.275 0.116 0.548 0.336

Cluster 2 0.188 0.091 0.020 0.004 0.471 0.259 0.299 0.128 0.565 0.384

Cluster 3 0.002 0.000 0.068 0.023 0.485 0.380 0.556 0.409 0.372 0.241

Cluster 4 0.264 0.163 0.002 0.000 0.484 0.242 0.224 0.075 0.514 0.276

Cluster 5 0.204 0.098 0.013 0.002 0.498 0.296 0.314 0.153 0.563 0.389

Cluster 6 0.059 0.016 0.033 0.009 0.570 0.439 0.485 0.328 0.538 0.467

Table 2. P-value results from GOF tests for all iid hosts and six clusters

Clusters # of hosts % of total avail. Best fit Parameters

shape scale

All iid hosts 57757 1.0 Weibull 0.3787 3.0932

Cluster 1 3606 0.16 Gamma 0.3131 289.9017

Cluster 2 9321 0.35 Gamma 0.3372 161.8350

Cluster 3 13256 0.22 Log-Normal -0.8937 3.2098

Cluster 4 275 0.01 Gamma 0.3739 329.6922

Cluster 5 1753 0.05 Gamma 0.3624 95.6827

Cluster 6 29546 0.20 Weibull 0.4651 1.8461

Table 3. Some properties of clusters and iid hosts

100

101

102

103

104

105

100

101

102

103

104

105

Actual number per cluster

Exp

ecte

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mbe

r pe

r cl

uste

r

VenueTimezoneReference

(a) By venue or timezone

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1

2

3

4

5

6x 10

9

CP

U s

peed

(F

LOP

S)

Cluster index

(b) By CPU speed

Figure 6. Clustering by other criteria

7.2 Significance of Clustering Criteria

Our results in the previous section beg the following

question: could the same clusters have been found using

some other static criteria? In this section we considering

cluster formation by static criteria, namely host venue, time-

zone, and clock rates. (Note that a small fraction of hosts

did not have this information specified, and were thus ex-

cluded from this analysis.)

We define host venue to be whether a host is used at

home, school, or work. This is specified by the user to the

BOINC client (though this is not required). Roughly, 23900

are at home, 5500 are at work, and 772 are at school. If our

clustering results correspond to those categories, we would

expect the distribution of host venue across clusters to be

even more skewed.

To measure this, we computed the expected number of

hosts of a particular venue for each one of the six clus-

ters identified in Section 7.0.3. The expected number is

computed using the global percentage of home, work, and

school hosts. The we counted the actual number of hosts of

each venue in each cluster.

Figure 6(a) shows the expected number versus the actual

number for each venue type over each cluster. The results

for larger cluster sizes are more significant. If the clusters

correspond to host venues, we would expect large devia-

tions from the y = x line. However, this is not the case as

the expected and actual values are similar. Thus, the same

clusters would not have resulted from the host venue.

We conducted the same comparison using host time-

zones. We took counted the number of hosts in each

cluster for each of the six largest timezones (in terms of

hosts). These timezones in corresponded to Central Europe

(17,000 hosts), Eastern North America (11,003 hosts), Cen-

tral North America (6,077 hosts)), Western North America

(4,900 hosts), Western Europe (4280 hosts), and Eastern

Asia (2396 hosts).

We then compared this with the expected number, given

the number of hosts in total for each of the six timezones.

We find again that the corresponding points in Figure 6(a)

are close the the line y = x. This indicates that the clusters

are not a direct result of timezones alone.

We also investigated the relationship between CPU

speeds (in FLOPS) and the clusters. Figure 6(b) shows

a box-and-whisker plot of the CPU speeds for each clus-

ter. The box represents the inter-quartile range. As this

box for each cluster appears in similar ranges, we conclude

that the clusters could not have been formed using CPU

speeds alone, and that there is little correlation between

CPU speeds and the length of intervals.

Nonetheless, one would like an intuition to explain why

there was a formation of six clusters. We do not have a pre-

cise answer to this question. It could depend very much on

the behavior of the user, which is hard to measure. For fu-

ture work, we could like to conduct a survey of volunteers

or to monitor their host processes to classify them by how

they use their computer (for example, for gaming, word pro-

cessing, web surfing). This might shed light on the cause of

these clusters.

8 Scheduling Implications

Our study has pinpointed the exact mixture of iid versus

non-iid hosts, and when iid, the distribution that best mod-

els it and its parameters. The difference between the global

distribution for all iid hosts, and the distributions for each

individual cluster impacts scheduling accuracy greatly. For

example, if one uses the Weibull distribution as the global

model, the probability of a host to successfully complete a

24 hour task is less than 20%. By contrast, for hosts in clus-

ter 4, the probability is about 70%. These differences are

magnified multiplicatively when computing the probability

of task completion with replication or for a series of tasks

with dependencies.

Moreover, in terms of multi-job scheduling, an online

scheduler could create a multi-level priority queue and

channel jobs to hosts depending on their model require-

ments. For example, in typical volunteer computing sys-

tems, there are a mixture of high-throughput and low-

latency jobs. In practice, we have observed that the total

sum of availability across hosts in large numbers to be rel-

atively constant and tends towards a Normal distribution.

High-throughput jobs could then be sent to non-iid hosts as

their lack of randomness likely will not affect the aggregate

system throughput as a whole.

On the other hand, the jobs that need low response time,

such as batches of low-latency tasks or DAG’s, can be

scheduled on hosts that exhibit iid availability, and the prob-

ability of successful task completion can be computed with

the discovered model.

9 Conclusions

We considered the problem of discovering availability

models for host subsets from a large-scale distributed sys-

tem. Our specific contributions were the following:

• With respect to methodology.

– We detected and determined the cause of outliers

in the measurements. We minimize their effect

during the preprocessing phase of the measure-

ments. This is important for others to use the

trace data set effectively.

– We described a new method for partitioning hosts

into subsets that facilitates the design of stochas-

tic scheduling algorithms. We use randomness

tests to identify hosts with iid availability.

– For iid hosts, we use clustering based on dis-

tance metrics that measure the difference be-

tween two probability distributions. We find that

the Cramer-von Mises metric is the most sensi-

tive and computationally efficient compared to

others.

– In the process, we describe how we deal with

with large and variable sample sizes and the hy-

persensitivity of statistical tests by taking a fixed

number (30) of random samples from each host.

• With respect to modelling. We apply the methodology

for the one of the largest Internet-distributed platforms

on the planet, namely SETI@home.

– We find that about 34% of hosts have truly ran-

dom availability intervals.

– These iid hosts have availability that can be

modelled using 6 distributions, in particular, the

Gamma, Weibull, and Log-Normal distributions.

About 51% of the total availability comes from

hosts whose availability follows the Gamma dis-

tribution. This is useful as this distribution is

short-tailed and can be used easily to construct

analytical Markov models.

– The family of Gamma distributions (with differ-

ent scales) could be used to model all iid hosts.

– The discovered distributions from the same fam-

ily differ greatly by scale, which explains their

separation after clustering. The distribution for

all hosts with iid availability also differs signifi-

cant in scale from any of the distributions corre-

sponding to each cluster.

Acknowledgements

We thank Eric Heien for useful discussions. This work

has been supported in part by the ANR project SPADES

(08-ANR-SEGI-025).

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