Recall the simple model for HTTP streaming shown in Figure 9.3. Recall that B denotes the size of the client's application buffer, and Q denotes the number of bits that must be buffered before the client application begins play out. Also r denotes the video consumption rate. Assume that the server sends bits at a constant rate x whenever the client buffer is not full. 

a. Suppose that x < r. As discussed in the text, in this case play out will alternate between periods of continuous play out and periods of freezing. Determine the length of each continuous play out and freezing period as a function of Q, r, and x. 

b. Now suppose that x > r. At what time t = t_j does the client application buffer become full?

Figure 9.3

Fill rate = x Depletion rate = r Internet Video server Client application buffer B.