1. Measurement and Modelling of the Temporal Dependence in Packet loss Maya Yajnik, Sue Moon, Jim Kurose, Don Towsley Department of Computer Science University of Massachusetts Amherst

2. Temporal dependence in end-end loss Questions –what is the time correlation of loss events? –what are good models? Applications: –FEC adjustment for audio, video, data –on-line loss estimation –performance analysis –simulation

3. Overview Measurement Analysis –stationarity –data representations –temporal dependence Modelling Summary

4. Measurement Methodology Collect point-point, multicast traces of periodically generated probes period: 20ms, 40ms, 80ms, 160ms source: Univ. of Mass. Amherst Destinations:, Atlanta, Los Angeles, Seattle, St. Louis, Stockholm 128 hours of data

5. Analysis Stationarity of traces –look for change in avg., variance over trace –remove non- stationary sections RESULT: 76 hours of data

6. Data Representations binary time series –no loss: 0, no loss: 1 –eg. {00011000001} interleaved sequences of good run lengths, loss run lengths –eg.{ 000 11 00000 1 } {3,5} {2,1} good loss {{{{

7. Correlation Timescale goal: Time interval between packets, at and beyond which, loss events are independent methodology: –autocorrelation fn. 95% confidence bounds –chi square test

8. Correlation Timescales Less than 1000ms over all traces

9. Run lengths question –are they independent? methodology –autocorrelation fns., crosscorrelation fn. answer –160ms independent –20ms,40ms dependent good runs

10. question –how are they distributed? –geometrically ? methology –chi-square goodness-of-fit test good run length distribution loss run length distribution

11. Modelling question –what is a good model for characterizing loss process? models –Bernoulli –2-state –k-th order Markov chain models prob. of loss/ no loss depends only on k previous events

12. Loss Models previously used: –Bernoulli loss: independent loss, single parameter –2-state loss model: prob. of loss/no loss depends only on the previous event 2 parameters

13. Markov chain models prob. of loss/no loss depends on k previous events number of states = 2 k Bernoulli, 2-state special cases use maximum likelihood estimates of parameters

14. Models Q: what is the order of the Markov process ? –the lag beyond which the loss events are independent. –correlation timescale = (order + 1 ) x sampling interval Q: accuracy of commonly used models? –order 0  Bernoulli model accurate: 14 / 76 hr –order 1  2-state model accurate: 20 / 76 hr

15. Summary collected/ analyzed 128 hours of loss data correlation timescale : 1000ms Markov chain models of k-th order Bernoulli model accurate 14 / 76 2-state model accurate 20 / 76 sliding window better than exp. smoothing

16. Ongoing and future work richer collection of data, better analysis of stationarity more parsimonious models by state aggregation application of models to performance analysis and on-line estimation