Recall the simple model for HTTP streaming shown in Figure 9.3. Suppose the buffer size is infinite but the server sends bits at variable rate x(t). Specifically, suppose (t) has the following saw-tooth shape. The rate is initially zero at time t = 0 and linearly climbs to H at time t = T. It then repeats this pattern again and again, as shown in the figure below.

a. What is the server’s average send rate?

b. Suppose that Q = 0, so that the client starts playback as soon as it receives a video frame. What will happen?

c. Now suppose Q > 0 and HT/2 ≥ Q. Determine as a function of Q, H, and T the time at which playback first begins.

d. Suppose H > 2r and Q = HT/2. Prove there will be no freezing after the initial play out delay.

e. Suppose H > 2r. Find the smallest value of Q such that there will be no freezing after the initial playback delay.

f. Now suppose that the buffer size B is finite. Suppose H > 2r. As a function of Q. B, T, and H, determine the time t = t_j when the client application buffer first becomes full.

Figure 9.3

27 3 4T Time Bit rate x(t) Fill rate = x Depletion rate =r Internet Video server Client application buffer