an integer programming representation for data center power-aware management - slides
DESCRIPTION
Slides for CANO (Communication Networks Optimization) projectTRANSCRIPT
ILP model and Heuristic
Authors: Josep Subirats
Arinto Murdopo
Ioanna Tsalouchidou
Problem Description
The ILP model
Heuristic Design
Data-Set Generation
Results
Conclusions
ContentResult
Grid data-center scheduling problem
Optimal solution
economic revenue
power saving
QoS
Set of elements
machines
processors
jobs
Problem Description
Problem Description
Revenue
QoS Health
Power
Migration
Problem Description
Job allocation in data-grid
• Power consumption based on used CPUs
• CPUs in each host
• Min CPUs required by each job
• Max CPUs required by each job
ILP
Objective Function
Max:
Benefit of
Execution
QoS Penalty
Power
Consumption
Migration
Cost
ILP
S.T: Processor switched on/off in order: keep consistency
Relaxation: job scheduled or not scheduled
Available CPUs in each host not exceed
Output: Max. Benefit
Placement of each job in the infrastracture
CPU assignment for each job
CPUs used in each host
ILP
Generate an array of numHosts components:
cpus[]: CPUs in each host, each with 1, 2, 4 or 8 CPUs (random).
Generate two arrays of numJobs components:
consMin[]: minimum CPU required, between 1 and 10 (random).
consMax[]: maximum CPU required, randomly between consMin[j] + 1 to 2 extra CPUs (random).
Data Generation
CPU : Intel i7 @ 2.8 GHz OS: Windows 7 RAM: 8 GB CPLEX: IBM ILOG CPLEX Optimization Studio 12.4 Heuristic: Java in JRE 1.6.0_24-b07
Multiple Alpha: 0, 0.1, 0.2 … 1 Multiple Problem Sizes: 5H10J, 15H30J, 20H40J, 30H40J, 40H80J, 100H200J Multiple Iterations: 10, 100, 1000, 10000, 100000
0
50
100
150
200
250
5H10J 10H20J 15H30J 20H40J
Tim
e (
s)
Problem Size
CPLEX Execution Time
Execution Time
0
50
100
150
200
250
300
350
10 100 1000 10000 100000
Tim
e (
s)
Number of Iteration
Heuristic Random 100H200J - Time (s)
Time (s)
165
170
175
180
185
190
195
0 0.5 1 1.5
Be
nef
it
Alpha
Alpha vs Benefit 40H 80J NR
10
100
1000
10000
100000
480
500
520
540
560
580
0 0.5 1
Be
nef
it
Alpha
Alpha vs Benefit 100H 200J NR
10
100
1000
10000
100000
81
86
91
96
101
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit 20H40J NR
10
100
1000
10000
100000
110
120
130
140
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit 30H60J NR
10
100
1000
10000
100000
81
83
85
87
89
91
93
95
97
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Be
nef
it
Alpha
Alpha vs Benefit 20H40J NR
10
100
1000
10000
100000
490
500
510
520
530
540
550
560
570
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit 100H 200J NR
10
100
1000
10000
100000
7
11
14 17
24
69
683
12377 133566
97
97.5
98
98.5
99
99.5
100
No
rmal
ize
d B
en
efit
(%
)
Time (mili seconds)
Solution Quality - Alpha 0.1 - 100H - 200J - 100000 Iterations
NormalizedBenefit (%)
7
11
14 17
24
69
97
97.5
98
98.5
99
99.5
100
No
rmal
ize
d B
en
efit
(%
)
Time (mili-seconds)
Solution Quality - Zoomed In - Alpha 0.1 - 100H - 200J - 100000 Iterations
NormalizedBenefit (%)
160
180
200
220
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit 40H80J R
10
100
1000
10000
100000
470
520
570
620
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit H100 J200 R
10
100
1000
10000
100000
80
85
90
95
100
105
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit 20H40J R
10
100
1000
10000
100000
110
130
150
170
0 0.2 0.4 0.6 0.8 1
Be
nef
it
Alpha
Alpha vs Benefit 30H60J R
10
100
1000
10000
100000
80
85
90
95
100
105
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Be
nef
it
Alpha
Alpha vs Benefit 20H40J R
10
100
1000
10000
100000
470
490
510
530
550
570
590
610
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Be
nef
it
Alpha
Alpha vs Benefit H100 J200 R
10
100
1000
10000
100000
3
9
13
2012
8813 112341
224536
86
88
90
92
94
96
98
100
No
rmal
ize
d B
en
efit
(%
)
Time (mili-seconds)
Solution Quality - Alpha 0.0 - 100H - 200J - 100000 Iterations
NormalizedBenefit (%)
3
9
13 292 617 693
85
87
89
91
93
95
97
99
No
rmal
ize
d B
en
efit
(%
)
Time(mili-seconds)
Solution Quality - Zoomed In -Alpha 0.0 - 100H - 200J - 100000 Iterations
NormalizedBenefit (%)
0
100
200
300
400
500
600
700
Be
nef
it
Problem Size
Problem Size vs Methodology vs Benefit
CPLEX
Heuristic Non-Random InitialSelection (NR)
Heuristic RandomInitial Selection(R) -10000 Iter
Heuristic RandomInitial Selection(R) -100000 Iter
Datacenter job scheduling and management can be optimized using ILPs.
Complex ILP restrictions can be translated into easy heuristic code.
CPLEX does not scale well.
Heuristics can cope with higher problem sizes.
Conclusions
Lower alpha values achieve better results. Alpha of 0 is the best when using random node selection.
Random node selection obtains the best results.
More iterations achieve better benefits.
Conclusions
J. L. Berral García, R. Gavaldà Mestre, J. Torres Viñals, and others, “An integer linear programming representation for data-center power-aware management,” 2011.
http://upcommons.upc.edu/handle/2117/11061
Reference
ILP model and Heuristic
Authors: Josep Subirats
Arinto Murdopo
Ioanna Tsalouchidou