PA1

PA2

GI

CD

LD LD LD LD LD

CD

SDGI Graphical InterfaceSD Supervisor DaemonCD Cluster DaemonLD Load DaemonPA1 Parallel Application 1 (task allocation)PA2 Parallel Application 2 (task allocation)

!

X

Q1

C

"

"

1! "

1!Q

1#2(1#")#! Q=

2

Q1#! #2µQ

Q2(1#")=2µ

"#! Q=Q#µQ1#!

!Q

1#"=µ Q

C!20

Q1#!

!Q

(1#")=

(1#")#! Q=

!Q

(1#")#! Q=1#!Q!(C!1)

C!1C(1#")=CµQ

1!(C!2) 1!(C!1)Qµ1#!Q!(C!2) Qµ

!Q

1#!

CC(1#")=CµQ

C(1#")#! Q=Q!C 1#!

C(1#")#! Q=Q!C

C+1

Qµ Qµ

(C!1)(C!1) Qµ

0

0.2

0.4

0.6

0.8

1

0 0.01 0.02 0.03 0.04 0.05Uti

lizatio

n fac

torProcesses incoming rate

Linux 2.4.2

measured utilization factortheorical utilization factor

00.5

11.5

22.5

33.5

4

0 0.01 0.02 0.03 0.04 0.05

Expe

ctatio

n num

ber o

f proc

esse

s

Processes incoming rate

Linux 2.4.2

measured theorical

0

0.5

1

1.5

2

0 100 200 300 400 500 600 700

Compar

ison of

X in tra

nsient a

nd stat

ionary s

tate

Time

Comparaison

Approximation of XMarkov chain

Simulation

0200400600800

10001200140016001800

0 200 400 600 800 1000 1200

Averag

e total t

ime of

executi

on of p

rocess

es in se

cond

CPU time requested by a process in second

Prediction of the execution time of 3 processes

simulated time t1predicted time t1simulated time t2predicted time t2simulated time t3predicted time t3