Outline

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

2. Outline • Motivation • Clock Terminology • Desirable properties of skew estimation algorithms • Algorithms • Comparison • Conclusion University of Maryland

3. Outline • Motivation • Clock Terminology • Desirable properties of skew estimation algorithms • Algorithms • Comparison • Conclusion University of Maryland

4. OTT = -2 seconds !! 14:20:44 14:18:44 Computer B Computer A University of Maryland

5. 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 University of Maryland

6. 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 University of Maryland

7. 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 University of Maryland

8. 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. University of Maryland

9. Outline • Motivation • Clock Terminology • Desirable properties of skew estimation algorithms • Algorithms • Comparison • Conclusion University of Maryland

10. 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 C’a(t) Skew: The difference in the frequencies of a clock and the “true” clock. The skew of Ca relative to Cb at time t (C’a(t) – C’b(t)) Drift: The drift of clock Ca is C”(t). The drift of Ca relative to Cb at time t ≥ 0 is (C”a(t) – C”b(t)) Accuracy : How close the absolute value of offset (at a particular moment) is to zero University of Maryland

11. Clock Terminology (Contd.) • Two clocks are said to be synchronizedat 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 clockshave constant frequencies, and their skew and clock ratio areconstant over time (drift = 0) University of Maryland

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14. Let α and β be the estimates for α and d1. • Then the delay after skew removal is University of Maryland

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16. Outline • Motivation • Clock Terminology • Desirable properties of skew estimation algorithms • Algorithms • Comparison • Conclusion University of Maryland

17. 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. University of Maryland

18. 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 University of Maryland

19. 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. University of Maryland

20. Outline • Motivation • Clock Terminology • Desirable properties of skew estimation algorithms • Algorithms • Comparison • Conclusion University of Maryland

21. 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. University of Maryland

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23. 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: University of Maryland

24. Other Algorithms University of Maryland

25. PAXSON’S 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 α-1. Otherwise, the algorithm concludes that there is no skew, and outputs α = 0. University of Maryland

26. 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 Paxson’s 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. University of Maryland

27. 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. University of Maryland

28. Outline • Motivation • Clock Terminology • Desirable properties of skew estimation algorithms • Algorithms • Comparison • Conclusion University of Maryland

29. Computational Complexity • Time complexity of a two variable linear programming problem is proven to be O(N). The algorithm, exploits the fact that ti’s are sorted • The other three algorithms have the complexity of O(N). University of Maryland

30. 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.. • Paxson’s 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 β. 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. University of Maryland

31. 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 doesn’t satisfy this property. University of Maryland

32. Simulation on Paxson’s algorithm Purpose :To show the variability of the difference in the actual and the estimated skew over a range of clock skews. University of Maryland

33. Measurements University of Maryland

34. Trace I Measurements Linear Programming Algorithm • Linear Programming Algorithm works well with Trace I readings  University of Maryland

35. Trace I Measurements (continued) Paxson’s Algorithm • Works well too  University of Maryland

36. Trace II Measurements Linear Programming Algorithm • Takes into account the excessive congestion due to multicasting  University of Maryland

37. Trace II Measurements (continued) Paxsons Algorithm • Paxsons algorithm works well with the high loss rate too  University of Maryland

38. Trace II Measurements (continued) Linear Regression Algorithm • Delay has a decreasing trend which is not true. • Doesn’t work well in the presence of outliers  University of Maryland

39. Trace II Measurements (continued) Piecewise Minimum Algorithm • Effect of the congestion in the network delay is removed  University of Maryland

40. 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. University of Maryland

41. Simulation (continued) Linear Programming Algorithm Paxson’s Algorithm • Linear Programming algorithm has less variance as compared to Paxson’s algorithm. University of Maryland

42. Conclusion • The linear regression and piecewise minimum algorithms demonstrated a poor performance over traces of Internet delay measurements. • As compared to Paxson’s, Linear Programming Algorithm is unbiased and has less variance. University of Maryland

43. 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 University of Maryland