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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
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