Adaptive Monitoring of Bursty Data Streams

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Adaptive Monitoring of Bursty Data Streams

• Brian Babcock, Shivnath Babu, Mayur Datar, and
  Rajeev Motwani

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Monitoring Data Streams

• Lots of data arrives as continuous data streams
• Network traffic, web clickstreams, financial data
  feeds, sensor data, etc.
• We could load it into a database and query it
• But processing streaming data has advantages
• Timeliness
• Detect interesting events in real time
• Take appropriate action immediately
• Performance
• Avoid use of (slow) secondary storage
• Can process higher volumes of data more cheaply

3
Network Traffic Monitoring

• Security (e.g. intrusion detection)
• Network performance troubleshooting
• Traffic management (e.g. routing policy)

Internet
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Data Streams are Bursty

• Data stream arrival rates are often
• Fast
• Irregular
• Examples
• Network traffic (IP, telephony, etc.)
• E-mail messages
• Web page access patterns
• Peak rate much higher than average rate
• 1-2 orders of magnitude
• Impractical to provision system for peak rate

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Bursts Create Backlogs

• Arrival rate temporarily exceeds throughput
• Queues of unprocessed elements build up
• Two options when memory fills up
• Page to disk
• Slows system, lowers throughput
• Admission control (i.e. drop packets)
• Data is lost, answer quality suffers
• Neither option is very appealing ?

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Two Approaches to Bursts

• Minimize memory usage
• Reduce memory used to buffer data backlog ?
  avoid running out of memory
• Schedule query operators so as to release memory
  quickly during bursts
• Sometimes this is not enough
• Shed load intelligently to minimize inaccuracy
• Use approximate query answering techniques
• Some queries are harder than others to
  approximate
• Give hard queries more data and easy queries less

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Outline

• Operator Scheduling

• Problem Formalization
• Intuition Behind the Solution
• Chain Scheduling Algorithm
• Near-Optimality of Chain Scheduling
• Experimental Results

• Load Shedding

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Problem Formalization

• Inputs
• Data flow path(s) consisting of sequences of
  operators
• For each operator we know
• Execution time (per block)
• Selectivity

Time t4
Time t2
Selectivity s4
Selectivity s2
Time t1
Time t3
Selectivity s1
Selectivity s3
Stream
Stream
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Progress charts
(0,1)
Opt1
Block Size
(1,0.5)
Opt2
(4,0.25)
Opt3
(0,0)
(6,0)
Time
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Problem Formalization

• Inputs
• Data flow path(s) consisting of sequences of
  operators
• For each operator we know
• Execution time (per block)
• Selectivity
• At each time step
• Blocks of tuples may arrive at initial input
  queue(s)
• Scheduler selects one block of tuples
• Selected block moves one step on its progress
  chart
• Objective
• Minimize peak memory usage(sum of queue sizes)

Time t4
Time t2
Selectivity s4
Selectivity s2
Time t1
Time t3
Selectivity s1
Selectivity s3
Stream
Stream
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Main Solution Idea

• Fast, selective operators release memory quickly
• Therefore, to minimize memory
• Give preference to fast, selective operators
• Postpone slow, unselective operators
• Greedy algorithm
• Operator priority selectivity per unit time
  (si/ti)
• Always schedule the highest-priority available
  operator
• Greedy doesnt quite work
• A good operator that follows a bad operator
  rarely runs
• The bad operator doesnt get scheduled
• Therefore there is no input available for the
  good operator

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Bad Example for Greedy
Tuples build up here
Opt1
Opt2
Opt3
Block Size
Time
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Chain Scheduling Algorithm
Opt1
Block Size
Opt2
Lower envelope
Opt3
Time
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Chain Scheduling Algorithm

• Calculate lower envelope
• Priority slope of lower envelope segment
• Always schedule highest-priority available
  operator
• Break ties using operator order in pipeline
• Favor later operators

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FIFO Example
(0,1)
Opt1
(1,0.5)
Block Size
Opt2
(4,0.25)
Opt3
(0,0)
(6,0)
Time
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Chain Example
(0,1)
Opt1
(1,0.5)
Block Size
Opt2
(4,0.25)
Lower envelope
Opt3
(0,0)
(6,0)
Time
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Memory Usage
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Chain is Near-Optimal
Theorem Given a system with k queries, all
operator selectivities 1, Let C(t) of
blocks of memory used by Chain at time t. At
every time t, any algorithm must use C(t) - k
memory.

• Memory usage within small constant of optimal
  algorithm that knows the future
• Proof sketch
• Greedy scheduling is optimal for convex progress
  charts
• Best operators are immediately available
• Lower envelope is convex
• Lower envelope closely approximates actual
  progress chart
• Details on next slide

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Lemma Lower Envelope is Close to Actual
Progress Chart

• At most one block in the middle of each lower
  envelope segment
• Due to tie-breaking rule
• (Lower envelope 1) gives upper bound on actual
  memory usage
• Additive error of 1 block per query

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Performance Comparison
spike in memory due to burst
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Outline

• Operator Scheduling
• Load Shedding
• Motivation for Load Shedding
• Problem Formalization
• Load Shedding Algorithm
• Experimental Results

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Why Load Shedding?

• Data rate during the burst can be too fast for
  the system to keep up
• Chain Scheduling helps to minimize memory usage,
  but CPU may be the bottleneck
• Timely, approximate answers are often more useful
  than delayed, exact answers
• Solution When there is too much data to handle,
  process as much as possible and drop the rest
• Goal Minimize inaccuracy in answers while
  keeping up with the data

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Related Approaches

• Our focus sliding window aggregation queries
• Goal is minimizing inaccuracy in answers
• Previous work considered related questions
• Maximize output rate from sliding window
  joinsKang, Naughton, and Viglas - ICDE 03
• Maximize quality of service function for
  selection queriesTatbul, Cetintemel, Zdonik,
  Cherniak, Stonebraker-VLDB 03

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Problem Setting
Q1
Q2
Q3
S
S
S
?
?
?
?
R
S1
S2
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Inputs to the Problem
Q1
Q2
Q3
S
S
S
?
?
?
?
R
S1
S2
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Load Shedding via Random Drops
(time, selectivity)
(t3, s3)
Load rt1 rs1t2 rs1s2t3
(t2, s2)
Sampling Rate p
(t1, s1)
Need Load 1
Stream Rate r
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Problem Statement

• Relative error is metric of choice Estimate -
  Actual
• Actual
• Goal Minimize the maximum relative error across
  queries, subject to Load 1
• Want low error with high probability

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Quantifying Effects of Load Shedding
Scale answer by 1/(p1p2)
S3
Sampling Rate p2
?2
Sampling Rate p1
?1

• Product of sampling rates determines answer
  quality

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Relating Load Shedding and Error

• Equation derived from Hoeffding bound
• Constant Ci depends on
• Variance of aggregated attribute
• Sliding window size

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Choosing Target Sampling Rates
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Calculate Ratio of Sampling Rates

• Minimize maximum relative error ? Equal relative
  error across queries
• Express all sampling rates in terms of common
  variable ?

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Placing Load Shedders
Target .8?
Target.6?
S
S
?
?
Sampling Rate .75 .6? /.8?
?
Sampling Rate .8?
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Experimental Results
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Experimental Results
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Conclusion

• Fluctuating data stream arrival rates create
  challenges
• Temporary system overload during bursts
• Chain scheduling helps minimize memory usage
• Main idea give priority to fast, selective
  operators
• Careful load shedding preserves answer quality
• Relate target sampling rates for all queries
• Place random drop operators based on target
  sampling rates
• Adjust sampling rates to achieve desired load

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Thanks for Listening!

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