Estimation and Removal of Clock Skew from Network Delay Measurements Sue B. Moon, Paul Skelly ,Don T

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Estimation and Removal of Clock Skew from Network
Delay MeasurementsSue B. Moon, Paul Skelly ,Don
TowsleyProceedings of IEEE INFOCOM 1999, New
York, NY, March1999.
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Outline

• Motivation
• Clock Terminology
• Desirable properties of skew estimation
  algorithms
• Algorithms
• Comparison
• Conclusion

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Outline

• Motivation
• Clock Terminology
• Desirable properties of skew estimation
  algorithms
• Algorithms
• Comparison
• Conclusion

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OTT -2 seconds !!
142044
141844
Computer B
Computer A
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Motivation

• Network transit times are used to infer
  fundamental network properties delay,
  bottleneck link speed, available bandwidth,
  queuing.
• For delay measurements ,a sender needs to add
  timestamps to packets for a receiver to gather
  delay information
• Echo based techniques versus receiver based
  techniques

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• Since the clocks at both end systems are involved
  in measuring delay, the synchronization of the
  two clocks becomes an issue in the accuracy of
  the delay measurement.
• When two clocks run at different frequencies
  (i.e. have a clock skew) inaccuracies are
  introduced in the measurement. We focus on
  filtering out the effects of clock skew,
  specifically in one-way delay measurements

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• The measured delay is not the actual delay but
  includes the clock offset between the two clocks
  plus the end-to-end delay
• End-to-end delay consists of transmission and
  propagation delays plus variable queuing delay

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• Why does the delay show an increasing trend
  (100ms over the duration of 70 minutes) at the
  receiver?
• Increasing congestion and queuing delay?However,
  minimum observed delay increases over time.
• Speed difference between the sender and receiver
  clocks?
• The linear increase in delay attests to a
  constant speed difference between the sender and
  receiver clocks
• If the clocks have a non-zero skew, not only is
  the end-to-end delay measurement off by an amount
  equal to the offset, but it also gradually
  increases or decreases over time depending on
  whether the sender clock runs slower or faster
  than the receiver clock.

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• It is difficult to tell how much of the 31.15
  seconds is due to the time difference between
  clocks and the fixed transmission and propagation
  delay, without the availability of more
  information.
• Due to this lack of information in one-way delay
  measurements we focus on the variable portion in
  one-way delay measurements

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Outline

• Motivation
• Clock Terminology
• Desirable properties of skew estimation
  algorithms
• Algorithms
• Comparison
• Conclusion

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Clock Terminology

• Ct(t) t
• Resolution The smallest unit by which time is
  updated (a tick)
• Offset The difference between the time
  reported by a clock and the true time
• The offset of Ca is (Ca(t)-t).
• The offset of the clock Ca relative to
  Cb at time t 0 is Ca(t)-Cb(t)
• Frequency The rate at which the clock
  progresses. The frequency at time t of Ca is
  Ca(t)
• Skew The difference in the frequencies of a
  clock and the true clock. The
  skew of Ca relative to Cb at time t
  (Ca(t) Cb(t))
• Drift The drift of clock Ca is C(t). The drift
  of Ca relative to Cb at time t 0 is (Ca(t)
  Cb(t))
• Accuracy How close the absolute value of
  offset (at a particular moment) is to zero

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Clock Terminology (Contd.)

• Two clocks are said to be synchronized at a
  particular moment if both the relative offset and
  skew are zero.
• When it is clear that we refer to two clocks,
  neither of which is the true clock in our
  discussion, we simply refer to relative offset
  and relative skew as offset and skew,
  respectively.
• We assume that the sender and receiver clocks
  have constant frequencies, and their skew and
  clock ratio are constant over time (drift 0)

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Reasons for modeling a clock as a piecewise
continuous function

• We have modeled a clock as a piecewise continuous
  function in order to take into account the
  restrictions of real clocks.
• A clock in a computer is a step function with
  increments at every unit of its time resolution.
• We consider the time reports by a real clock with
  a fixed minimum resolution as samples of a
  continuous function at specific moments
• The abrupt time adjustment possible through a
  time resetting system call. Some systems that do
  not run NTP have a very coarse-grain (in the
  order of hours) synchronization mechanism in the
  cron table.
• The time adjustment in such a case can be several
  orders of magnitude larger than the usual
  increment of the clock resolution, and the time
  can even be set backward.

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• If there is a clock skew, the clock offset
  increases/decreases over time depending on the
  sign of the skew
• The change in offset can be used to estimate the
  clock skew
• It is more convenient to use timestamps relative
  to a specific point in time, such as the
  departure or arrival of the first packet, than
  absolute timestamps

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• Let a and ß be the estimates for a and d1.
• Then the delay after skew removal is

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Outline

• Motivation
• Clock Terminology
• Desirable properties of skew estimation
  algorithms
• Algorithms
• Comparison
• Conclusion

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Desirable properties of skew estimation algorithms

• The time and space complexity of algorithm should
  be linear in N.
• We will compare the time complexity of skew
  estimation algorithms as a function of the number
  of delay measurements.

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Desirable properties of skew estimation
algorithms (Contd.)

• Since the purpose of the skew estimation is to
  remove the skew from delay measurements, it is
  desirable that the delays be non-negative after
  the skew is removed

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Desirable properties of skew estimation
algorithms (Contd.)

• The skew estimation algorithm should be robust in
  the sense that it is not affected by the
  magnitude of the actual skew.
• That is, the difference between the estimate and
  the actual skew should be independent of the
  actual skew.

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Outline

• Motivation
• Clock Terminology
• Desirable properties of skew estimation
  algorithms
• Algorithms
• Comparison
• Conclusion

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LINEAR PROGRAMMING ALGORITHM

• To fit a line that lies under all the data
  points, but as closely to them as possible.
• Feasible region the line should lie under all
  the data points
• Objective Function To minimize the sum of the
  distances between the line and all the data
  points on the y-axis.

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• There are infinitely many pairs of D and that
  satisfy the condition above, if the feasible
  region defined above is not trivial.
• Our objective function to minimize the distance
  between the line
• and all the delay measurements is stated as

Objective Function
Constraint
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Other Algorithms
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PAXSONS ALGORITHM

• Step 1. Partition di s into segments, and pick
  the minimum delay measurement from each segment.
  The selected measurements are called the
  de-noised one-way transit times (OTTs).
• Step 2. Pick the median of the slopes of all
  possible pairs of the de-noised OTTs. If the
  median slope is negative, assume that the OTTs
  have a decreasing trend (here we assume a
  decreasing trend is detected).
• Step 3. Select the cumulative minima test from
  the denoised OTTs and test if the number of
  cumulative minima is large enough to show that
  the decreasing trend found in Step 2 is
  probabilistically not likely, if there is no
  trend
• Step 4. If it passes the cumulative minima test,
  pick the median from the slopes of all possible
  pairs of the cumulative minima output it as the
  estimate of a-1. Otherwise, the algorithm
  concludes that there is no skew, and outputs a
  0.

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PIECEWISE MINIMUM ALGORITHM

• Partitions the delay measurements into segments
• Pick a minimum from each segment
• Connect them to obtain a concatenation of line
  segments.
• The minima are the same as the de-noised OTTs
  in Paxsons algorithm. The resulting
  concatenation of line segments is the estimate of
  the skew, and is very unlikely to be a straight
  line.
• When the skew is as obvious as in our figure the
  resulting concatenation of line segments is close
  to a straight line, and can be used as a rough
  estimate.

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LINEAR REGRESSION ALGORITHM

• Linear regression is a standard technique for
  fitting a line to a set of data points.
• It is optimal in the mean square sense if the
  network delays are normally distributed, but is
  not robust in the presence of outliers.
• It is not a good choice for a skew estimation,
  even when applied to the de-noised OTTs above.
• It can be used only as a reference algorithm that
  requires no knowledge of the underlying behavior
  of delay measurements.

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Outline

• Motivation
• Clock Terminology
• Desirable properties of skew estimation
  algorithms
• Algorithms
• Comparison
• Conclusion

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Computational Complexity

• Time complexity of a two variable linear
  programming problem is proven to be O(N). The
  algorithm, exploits the fact that tis are sorted
• The other three algorithms have the complexity of
  O(N).

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Non-negative delay after the skew removal

• In order to guarantee that the delay remains
  positive after the after the skew is removed, a
  skew estimation algorithms must estimate d1
  correctly.
• The linear programming algorithm ,however, is the
  only one that estimates d1..
• Paxsons original algorithm for skew estimation
  is for two-way measurements after the clock
  offset has been removed.
• The linear regression algorithm provides an
  estimate of ß. However, this is just the
  y-intercept of the regression line which bears no
  relevance to the correct estimation of d1
• The piecewise minimum algorithm outputs a
  concatenation of line segments, and the slopes of
  those line segments are skew estimates. The
  algorithm does not have any provision to
  guarantee that all the data points lie above the
  concatenation of line segments.

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Robustness

• Linear Programming algorithm satisfies robustness
  .i.e. the estimated skew doesn't depend on the
  magnitude of clock skew.
• Linear Regression Algorithm satisfies this
  property.
• Piecewise minimum is effected by the magnitude of
  skew since it depends on the calculation of
  minima.
• Simulations of Paxson's algorithm also show that
  it doesnt satisfy this property.

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Simulation on Paxsons algorithm
Purpose To show the variability of the
difference in the actual and the estimated skew
over a range of clock skews.
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Measurements
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Trace I Measurements
Linear Programming Algorithm

• Linear Programming Algorithm works well with
  Trace I readings ?

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Trace I Measurements (continued)
Paxsons Algorithm

• Works well too ?

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Trace II Measurements
Linear Programming Algorithm

• Takes into account the excessive congestion due
  to multicasting ?

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Trace II Measurements (continued)
Paxsons Algorithm

• Paxsons algorithm works well with the high loss
  rate too ?

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Trace II Measurements (continued)
Linear Regression Algorithm

• Delay has a decreasing trend which is not true.
• Doesnt work well in the presence of outliers ?

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Trace II Measurements (continued)
Piecewise Minimum Algorithm

• Effect of the congestion in the network delay is
  removed ?

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Simulation

• Purpose of simulation is to examine the average
  performance of skew estimation algorithms.
• Assume exponential distribution of end-to-end
  delay with varying mean.

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Simulation (continued)
Linear Programming Algorithm
Paxsons Algorithm

• Linear Programming algorithm has less variance as
  compared to
• Paxsons algorithm.

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Conclusion

• The linear regression and piecewise minimum
  algorithms demonstrated a poor performance over
  traces of Internet delay measurements.
• As compared to Paxsons, Linear Programming
  Algorithm is unbiased and has less variance.

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References

• Estimation and removal of clock skew from Network
  Delay Measurements- Sue B. Moon, Paul Skelly ,Don
  Towsley
• On Calibrating Measurements of Packet Transit
  Time Vern Paxson