Synthesizing Representative I/O Workloads for TPC-H J. Zhang*, A. Sivasubramaniam*, H. Franke, N....
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Transcript of Synthesizing Representative I/O Workloads for TPC-H J. Zhang*, A. Sivasubramaniam*, H. Franke, N....
Synthesizing Representative I/O Workloads for TPC-H
J. Zhang*, A. Sivasubramaniam*, H. Franke, N. Gautam*, Y. Zhang, S.
Nagar
* Pennsylvania State UniversityIBM T.J. Watson
Rutgers University
Outline
• Motivation• Related Work• Methodology
– Arrival Time– Access Pattern– Request Sizes
• Accuracy of synthetic traces• Concluding Remarks
Motivation
• I/O subsystems are critical for commercial services and in production environments.
• Real applications are essential for system design and evaluation.
• TPC-H is a decision-support workload for business enterprises.
Disadvantages of Traces
• Not easily obtainable• Can be very large• Difficult to get statistical confidence• Very difficult to change workload behavior• Does not isolate the influence of one
parameter
• On the other hand, a deeper understanding of the workload can:• Help generate a synthetic workload• Help in system design itself.
What do we need to synthesize?
• Inter-arrival times (temporal behavior) of disk block requests.
• Access pattern (spatial behavior) of blocks being referenced
• Size (volume) of each I/O request.
Related work
• Scientific Application I/O behavior– Time-series models for arrivals– Sequentiality/Markov models for
access pattern• Commercial/production
workloads– Self-similar arrival patterns – Sequentiality in TPC-H/TPC-D
• No prior complete synthesis of all three attributes for TPC-H
Our TPC-H Workload
• Trace Collection Platform– IBM Netfinity 8-way SMP with 2.5GB
memory and 15 disks– Linux 2.4.17– DB2 UDB EE V7.2
• TPC-H Configuration– Power Run of 22 queries– Partitioning tables across the disks– 30 GB dataset
Validation
Identify characteristi
cs
Disksim 2.0
Original I/O traces
Generate
synthetic traces
Response time
CD
F
RMS: root-mean-square error of differences between two CDF curves
nRMS: RMS/m, m is average response time for the original trace
Metrics
Overall Methodology
• Arrival pattern characteristics– Investigate correlations
• Time series• Self-similar• iid distributions
• Access pattern characteristics– Sequentiality/pseudo
sequentiality/randomness– Size characteristics
• Investigating correlations between time, space and volume to get final synthesis
Arrival pattern
• Statistical analysis– Auto-correlation
function (ACF) plots
• Shows the correlation between current inter-arrival time and one that is x-steps away
– Correlations seem very weak (<0.15 for 12 queries, and <0.30 for the rest)•Errors with Time series models
(AR/MA/ARIMA/ARFIMA) are high• No suggestions for self-similar either
– Perhaps iid (independent and identically distributed) is not a bad assumption.
• Fitting distributions– Tried hyper-exponential/normal/pareto– Used Maximum Likelihood Estimator
(normal/pareto) and Expectation Maximization (hyper-exponential) to estimate distribution parameters
– Use K-S test to measure goodness-of-fit– Maximum distance between fitted
distribution and original CDF was ensured to be less than 0.1
Comparing CDF of fitted distribution and data
Access Pattern (Location + Size)
• Most studies use sequentiality to describe TPC-H
• However, this is not always the case.
Cat1: Q10
Q4, Q14
Cat2: Q12,
Q1,Q3,Q5,Q7,
Q8,Q15,Q18,
Q19,Q21
Cat3: Q20
Q9, Q17
Arrival Time
Locati
on Locati
on L
ocati
on
Arrival Time
Arrival Time
Category 1: Intermingling sequential streams
• Consider the following:– Run: A strictly sequential set of I/O
requests– Stream: A pseudo-sequential set of
I/O requests that could be interrupted by another stream.
– i.e. a stream could have several runs that are interrupted by runs of other streams.
Run and Stream
1-4 5-8 11-149-10 15-18
An example run of 5 requests
1-4 7-8 11-149-12
A stream (pseudo-sequential) of 4 requests
An example trace:1-4 7-8 11-149-12
100-104 105-108 109-112
Stream AStream B
1-4 7-8 11-14100-104 105-108 109-112 Trace 9-12
Secondary Attributes• Run Length: # of requests in a run• Run Start location: start sector of run• Stream Length: # of requests in a stream• Inter-stream Jump Distance: spatial separation
between start of run and previous request• Intra-stream Jump Distance: spatial separation
between successive requests within a stream• Number of active streams (at any instant)• Interference Distance: number of requests
between 2 successive requests in a stream
• Derive empirical distributions for these from the trace
Location Synthesis - Q10(Time and size from trace)
LocIID: locations are i.i.d.
LocRUN: incorporate run length distribution and run start location distribution.
LocSTREAM: combine all stream and run statistics.
Request Size
• Requests are one of
– 64, 128, 192, 256, 320, 384, 448, 512 blocks
• But attributes (location, size, time) are not independent !!!
Correlations between size and location
64 128 192 256 320 384 448 512
.716
.009
.010
.009
.009
.011
.011
.225
.577
.012
.013
.012
.013
.015
.016
.342
.916
.004
.004
.004
.004
.005
.005
.057
Size
All req.Run start
Within run
Fraction of requests
Correlations between size and time
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29I nter- arrival time interval
Siz
e fr
eque
ncy
512
128- 448
64
Correlations between location and time
Final Synthesis Methodology (Category 1)
Location: use LocSTREAM to generate start locations. Two kinds of requests: a run start request or a request within a run
Time: use Pr(inter-arrival time | run start requests) and Pr(inter-arrival time | within a run requests) to generate times.
Size: 1)For run start request, use Pr(size | inter-arrival
times of run start requests) to generate sizes.2)For within a run requests, use Pr(size | within a
run requests) to generate sizes.
• Can be easily adapted for Category 2 (strictly sequential) and Category 3 (random) queries.
• Validation: Compare the response time characteristics of synthesized and real trace.
Storage Requirements
Q1 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
3.46
3.64
2.76
3.43
3.46
3.47
3.66
.004
2.79
0.10
0.09
0.20
0.07
0.01
0.04
0.05
0.15
0.16
Storage Fraction(x0.00
1)nRMS
Q12 Q14 Q15 Q17 Q18 Q19 Q20 Q21
3.73 6.49 3.46 2.03 3.54 3.44 4.57 2.95
0.06 0.19 0.01 0.05 0.06 0.03 0.10 0.07
Storage Fraction(x0.00
1)nRMS
Contributions• A synthesis methodology to capture
– Inter-mingling streams of requests– Exploiting correlations between
request attributes• An application of this methodology
to TPC-H• Along the way (for TPC-H),
– iid can capture arrival time characteristics
– Strict sequentiality is not always the case
Backup slides
Validating arrival time synthesis
LocSTREAM
1. Use Pr(stream length) to generate stream lengths.
2. Use Pr(run length | stream length) to generate run lengths for each stream length.
3. Generate start location for each run:a) Use Pr(inter-stream jump dist.) to generate the start
location of the first run in the stream.b) Use Pr(intra-stream jump distance | this stream) to
generate other runs’ start location in this stream.
4. Use Pr(interference distance) to interleave all streams.