IBM T.J. Watson Research Center
Self-Tuning Memory Management of
A Database System
Yixin Diao
diao@us.ibm.com
Sigmetrics 2008 Tutorial: Introduction to Control Theory
and Its Application to Computing Systems
IBM T.J. Watson Research Center
DB2 Self-Tuning Memory Management
DB2 UDB Server
Memory pools
DB2
Clients
Disks
 Technical problems
– Large systems with varying
workloads and many
configuration parameters
– Autonomic computing: systems
self-management
Agents
Memory pools
 Challenges from systems
aspects
– Heterogeneous memory pools
– Dissimilar usage
characteristics
 Challenges from control
aspects
– Adaptation and self-design
– Reliability and robustness
2
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Load Balancing for Database Memory
Measured Output 1
Resource
Allocation 1
Load Balancing
Resource
Consumer 1
• Fairness  optimal ?
• Common measured output ?
Load
Balancer
Resource
Allocation N
Resource
Consumer N
Saved System Time (xi )
BenefitPerPage (yi )
Measured Output N
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
00
Resource
savedTime
OLTP
simPages

xi  pi 1  e  qiui
yi 
1000
2000
3000
4000
dxi
 pi qi e  qiui
dui
5000
Entry size (Page)
3

SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
Memory Pool Size (ui )
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Constrained Optimization and Regulatory Control
Saved System
Disk Time
Time
( xi(x
)i )
Regulatory Control
n
J   xi
Overall
O
I
d1(k)
d1(k)
i 1
Mem pool 1 (x1)
+
-
u1(k)
e1(k)
+
+
Load
Balancer
BenefitPerPage (y1)
-
eN(k)
+
uN(k)
+
Resource
y1(k)
+
+
w1(k)
1N,1
N
Resource
Consumer N
+
+
yN(k)
w (k)
wN(k)
Mem pool 2 (x2)
Mem
size 1 (u1)
MemoryPool1
Optimal memory allocation
Constrained Optimization
J  f u1 , u 2 ,  , u N 
N
g u1 , u 2 ,  , u N    ui  U  0
i 1
hu1 , u2 ,  , u N   ui  bi  0
dN(k)
f
1

ui N
Mem size 2 (u2)
4
O
dNI (k)
f
0

j 1 u j
N
Karush-Kuhn-Tucker conditions
L  f u1 , u2 , , u N   g u1 , u2 , , u N 
  hu1 , u2 , , u N 
L f

   i  0
ui ui
 i  0 if ui  bi ;  i  0 if ui  bi
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Dynamic State Feedback Controller
 State space model
y k 1  Ayk   Buk   d I k 
 Control error
1

ek    1N , N  I  y k   d O k 
N

 Integral control error
eI k 1  eI k   ek 
 Feedback control law
uk   KPek   KI eI k 
5
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Incorporating Const of Control into Controller Design
Memory Pool A
Remove
these
pages
Benefit
Pool Size
h11-12b
h11-12b
0.12
1600
1400
Ts=12449
0.1
1200
before
write dirty pages to disk
Disk
Benefit
Entry size (MB)
0.08
1000
800
0.06
600
0.04
400
0.02
200
0
0
50
100
0
150
0
50
Interval
hc11-17
after
0.06
Ts=15703
1400
0.05
1200
0.04
1000
Benefit
Entry size (MB)
150
hc11-17
1600
Memory Pool B
100
Interval
800
0.03
600
0.02
400
0.01
200
0
before
0
20
40
60
80
100
Interval
120
140
0
160
0
20
40
60
hc11-21
OS
140
160
180
0.05
0.045
1400
Ts=24827
0.04
1200
0.035
1000
0.03
Benefit
Entry size (MB)
120
hc11-21
1600
allocate extra memory
80
100
Interval
800
0.025
0.02
600
0.015
Major cost: write dirty, move memory, victimize hot
400
0.01
200
0
0.005
0
10
20
30
40
50
60
Interval
70
80
90
100
0
0
20
40
60
Interval
80
100
120
Linear quadratic regulation (LQR)
J =  [eT(k) eTI(k)] Q [eT(k) eTI(k)]T
+ uT(k) R u(k)
Define Q and R regarding to performance
6
• Cost of transient load imbalances
• Cost of changing resource allocations
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Adaptive Controller Design
Local linear model
Decentralized integral control
Response Time Benefit
Interval
Tuner
DB2 Clients
Step Tuner
Model
Builder
Entry Size
Accurate
Y
MIMO
Control Algorithm
N
Memory
Statistics
Collector
Greedy
(Constraint)
Fixed
Step
4-Bit
(Oscillation)
Entry
Size
DB2 Memory Pool
Response Time Benefit
7
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
squid.torolab.ibm.com
Machine:
IBM7028-6C4
CPU:
4x 1453MHz
Memory:
16GB
Disk:
25x 9.1G
Experimental Assessment

OLTP workload: multiple (20) buffer pools
0.05
2
0.04
Response time
benefits
0.03
4
300
Memory sizes
1.5
200
50
100
150
200
0
0
Throughput
100
0.5
0.01
0
0
Increase TP from
~100 to ~250
1
0.02

x 10
50
100
150
0
0
200
50
100
150
200
DSS workload: various query lengths
800
0
20
40
hc09-09
Interval
60
80
6000
5000
0
20
40
Interval
hc12-10
60
80
4000
> 2x improvement
3000
0.02
0.02
0.015
0.015
2000
0.01
1000
0.01
0.005
0
20
40
Interval
60
80
0
hc11-05
1500
Reduce 63%
1000
500
0
Some indexes dropped
0
20
40
60
80
100
Interval
120
140
160
avg = 2285
180
avg= 959
0 1 2 3 4 5 6 7 8 910111213141516171819202122232425262728293031323334
Order of execution
0.005
0
avg= 6206
7000
0.025
Benefit
Benefit
Execution time for Query 21 (10 stream avg)
200
0
0.025
8
400
DSS workload: index drop
Entry size (MB)
200
STMM tuning
Ts = 10680s
600
Time in seconds
400
Entry size (MB)
Entry size (MB)
ConfigAdvisor
settings
Ts = 26342s
600
0

hc12-10
hc09-09
800
0
20
40
Interval
60
80
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Comparing Control and Optimization Techniques
Control-based approach
Local linear model
Optimization-based approach
Gradient method
Decentralized integral control
Projected gradient (quasi-Newton)
Constraint enforcement (projection method)
Step length (modified Armijo rule)
Strictly applies constrained optimization
Less dependence on the model
Similarity in a simplified scenario
9
Differences in design considerations

“Pure” average vs. convex sum

Pole location vs. Armijo rule

Steady-state gain vs. Hessian matrix
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Simulation Study: Comparison with Optimization Approach
Control-based approach
4
2
Optimization-based approach
PI
x 10
u
1.5
Memory
size
WL change
1
0.5
0
0
20
40
60
80
100
120
140
160
180
200
350
Without noise
(single run)
300
J
Total
saved
time
250
200
150
0
20
40
60
80
100
k
120
140
160
180
200
Control intervals
4
2
PI
x 10
u
1.5
1
0.5
0
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
80
100
k
120
140
160
180
200
350
J
300
Effect of noise
(multiple runs)
250
200
150
More robust and better uncertainty management
10
Faster convergence, but more sensitive to noise
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation
IBM T.J. Watson Research Center
Summary
 DB2 self-tuning memory management
– Interconnection, heterogeneity, adaptation and
robustness, cost of control
 Constrained optimization with a linear feedback
controller
 Experimental assessment for OLTP and DSS
workloads
11
SIGMETRICS 2008: Introduction to Control Theory. Abdelzaher, Diao, Hellerstein, Lu, and Zhu.
© 2008 IBM Corporation