In this section we present new analyses. We examine the probability of underflow vs. mean playout rate or average latency for three different scenarios.
First, we present the channel model used throughout this analysis. We again use the basic structure of the Markov model shown in figure 1. In the good state packets arrive in each time slot according to a Bernoulli trial with parameter . In the bad state packets arrive according to the same distribution, but now with probability these packets contain an error and must be retransmitted. Now let us call a channel instance is the mean number of packets that arrive during a frame period when the channel is in the good state. is the average duration of the good state, and is the average duration of the bad state. Note that these are related and as they appear in 1. Finally, is the probability that a packet arrives in error.
In order to proceed with the scenarios, we make the following observation concerning the relationship between packet errors and throughput. Assuming that packets in error are retransmitted using selective-repeat ARQ, the resulting throughput is simply given by in the ideal case when an infinite number of retransmission attempts are possible [3]. In reality, the number of retransmissions attempts is limited by the remaining playout time in the buffer and , the amount of time it takes for a retransmission attempt. Given a buffer size of several seconds, an on the order of several hundred milliseconds, and a sizeable , the probability that playout stops because of a failed retransmission is small. Thus we can alternately characterize a channel where . Next we define an adaption scheme. An adaption scheme is a function over the buffer state that specifies the rate at which frames are removed. Typically, playout is slowed when the number of frames in the buffer falls below the target level, . and sped up when the fullness exceeds the target level. We call the true time it should take to play out a frame . When the buffer falls below , playout time per frame is increased by a factor s >= 1. Conversely, when the buffer is over full we reduce the per-packet playout time by a factor f < 1.