Measurement and modelling of the temporal dependence in packet loss

Understanding and modelling packet loss in the Internet is especially relevant for the design and analysis of delay-sensitive multimedia applications. We present analysis of 128 hours of end-to-end unicast and multicast packet loss measurement. From these we selected 76 hours of stationary traces for further analysis. We consider the dependence as seen in the autocorrelation function of the original loss data as well as the dependence between good run lengths and loss run lengths. The correlation timescale is found to be 1000 ms or less. We evaluate the accuracy of three models of increasing complexity: the Bernoulli model, the 2-state Markov chain model and the k-th order Markov chain model. Out of the 38 trace segments considered, the Bernoulli model was found to be accurate for 7 segments, and the 2-state model was found to be accurate for 10 segments. A Markov chain model of order 2 or greater was found to be necessary to accurately model the rest of the segments. For the case of adaptive applications which track loss, we address two issues of on-line loss estimation: the required memory size and whether to use exponential smoothing or a sliding window average to estimate average loss rate. We find that a large memory size is necessary and that the sliding window average provides a more accurate estimate for the same effective memory size.