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Burst Error Source Model

  In Steinbach [1], packet interrarrival times are deterministic. The channel model is Markov as in the previous case (see figure 1), but now when the model is in the good state, a packet arrives every tex2html_wrap_inline913 seconds. In the bad state packets arrive in error. Thus, unlike Yuang, Steinbach's analysis considers missing packets and retransmissions. By making simplifying assumptions, Steinbach provides accurate expressions for the probability of underflow given average burst lengths, and the expected amount of latency for a given adaptive playout scheme and channel parameters. One simplifying assumption is that burst error states occur far enough apart in time so that the buffer can return to its target level between burst errors. The other assumption is that there is excess bandwidth available to allow retransmissions and regularly scheduled packets to arrive concurrently.

First, Steinbach finds the average value of the maximum sustainable burst error length, as a function of playout time for a given target buffer size and adaption scheme.


The probability of underflow given a burst is then,


where is tex2html_wrap_inline915 is distributed geometrically with parameter tex2html_wrap_inline855 (see figure 1). Similarly, the average excess delay during a burst error is given as a function of s, the slowdown factor, tex2html_wrap_inline921 the speedup factor allowable with the given excess bandwidth, the burst error length, tex2html_wrap_inline915 , the length of the good channel period tex2html_wrap_inline925 , and the packet and frame durations tex2html_wrap_inline927 and tex2html_wrap_inline913 :


The expected amount of delay during a streaming session is found by taking the expected value with respect to the distributions on tex2html_wrap_inline915 , (Geom( tex2html_wrap_inline855 )), and tex2html_wrap_inline925 (Geom( tex2html_wrap_inline853 )) of equation 9.

Mark Kalman
Tue Mar 13 05:01:37 PST 2001