1 KPC-Toolbox KPC-Toolbox Demonstration Demonstration Eddy Zheng Zhang, Giuliano Casale, Evgenia Smirni Eddy Zheng Zhang, Giuliano Casale, Evgenia Smirni Computer Science Department Computer Science Department College of William & College of William & Mary Mary
13
Embed
1 KPC-Toolbox Demonstration Eddy Zheng Zhang, Giuliano Casale, Evgenia Smirni Computer Science Department College of William & Mary.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Computer Science DepartmentComputer Science Department
College of William & College of William & MaryMary
2
What is KPC-Toolbox for?
KPC-Toolbox: MATLAB toolbox Workload Traces Markovian Arrival Process (MAP)
Why MAP? Very versatile High variabilityHigh variability & temporal dependence temporal dependence in Time SeriesTime Series Easily incorporated into queuing models
Friendly Interface Departure from previous Markovian fitting tools Fit the automatically (no manual tuning)
3
User Interface Requirement: Matlab installed
Input A trace of inter-event times Or a file that already stores the statistics of the trace
E.g., a file stores the moments, autocorrelations and etc
Help Information Type “help FunctionName”,
E.g., “help map_kpcfit” Website Keeps Up-To-Date Tool version
http://www.cs.wm.edu/MAPQN/kpctoolbox.html
4
A Simple Example of MAP
Two state jumps
1 20
0 bb
aa
cc
dd
D1 =
D0 =
-b-d
-a-c
Time:
a b
c
d
I1 I2
I3
Background Jumps
Jumps With Arrivals
Arrivals:
5
Challenges
How large is the MAP? MAP(n): determine n?
Which trace descriptors are important? Literature: Moments of interval times, lag-1 autocorrelation But, for long range dependentlong range dependent traces?
Need temporal dependencetemporal dependence descriptors
MAP Parameterization Construct MAP(n) with matrices D0 and D1 (2n2 – n entries)
6
Example: Important Trace Statistics
1
2
First, second, third moment and lag-1 autocorrelation accurately fit
The queuing prediction ability is not satisfactory!The queuing prediction ability is not satisfactory!
Seagate Web Server Trace Queue Prediction, 80% Utilization
Fit With MAP(2)
100 101 102 103 104 105 106 10710-4
10-3
10-2
10-1
100
Pr(
Qu
eue
Len
gth
> X
)
X [log]
Trace /M/1
MAP(2)/M/1
7
Example: Higher Order Statistics Matter
Much Better Results!Much Better Results!
Queuing Prediction, 80% Utilization
k ,....,, 21
1
2
3
4
……
… ……
… ……
…
13
14
15
16
Fit with MAP(16)
A grid of joint moments and a sequence of autocorrelations fitted, E[XiXi+kXi+k+h]
100 101 102 103 104 105 106 10710-4
10-3
10-2
10-1
100
Pr[
Qu
eue
Len
gth
> X
]
X [log]
Trace /M/1MAP(16)/M/1
Seagate Web Server Trace
8
Higher Order Correlations V.S. Moments Correlations capture sequence in the time series Correlations are very important
Summary: Matching up to the first three momentsfirst three moments is sufficient Matching higher order correlationshigher order correlations with priority
Fitting Guidelines
Ref: "KPC-Toolbox: Simple Yet Effective Trace Fitting Using Markovian Arrival Processes", G. Casale, E.Z. Zhang, E. Smirni, to appear in QEST’08