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
KPC-Toolbox Demonstration. Eddy Zheng Zhang, Giuliano Casale, Evgenia Smirni Computer Science Department College of William & Mary. What is KPC-Toolbox for?. KPC-Toolbox: MATLAB toolbox Workload Traces Markovian Arrival Process (MAP) Why MAP? Very versatile - PowerPoint PPT Presentation
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Computer Science DepartmentComputer Science DepartmentCollege of William & College of William & MaryMary
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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)
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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
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A Simple Example of MAP Two state jumps
1 2 00 bbaa
ccdd
D1 =
D0 =-b-d
-a-c
Time:
a bc
d
I1 I2
I3
Background Jumps Jumps With Arrivals
Arrivals:
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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)
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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(Q
ueue
Len
gth
> X)
X [log]
Trace /M/1 MAP(2)/M/1
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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[Q
ueue
Len
gth
> X]
X [log]
Trace /M/1MAP(16)/M/1
Seagate Web Server Trace
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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