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the buffer size is infinite but the server sends bits at variable rate x(t). Specifi- cally, suppose x(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. 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 playout 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 func- tion of Q, B, T, and H, determine the time t = t when the client applica- tion buffer first becomes full. 2T 37 4T Bit rate x(t)

the buffer size is infinite but the server sends bits at variable rate x(t). Specifi- cally, suppose x(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. 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 playout 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 func- tion of Q, B, T, and H, determine the time t = t when the client applica- tion buffer first becomes full. 2T 37 4T Bit rate x(t)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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B Fill rate = x Depletion rate = r Internet Video server Client application buffer Figure 7.3 • Analysis of client-side buffering for video streaming Let's assume that the server sends bits at a constant rate x whenever the client buffer is not full. (This is a gross simplification, since TCP's send rate varies due to congestion control; we’ll examine more realistic time-dependent rates x(t) in the problems at the end of this chapter.) Suppose at time t = 0, the application buffer is empty and video begins arriving to the client application buffer. We now ask at what time t = t, does playout begin? And while we are at it, at what time t = tfdoes the client application buffer become full? First, let's determine tp, the time when Q bits have entered the application buffer and playout begins Recall that bits arrive to the client application buffer at
Transcribed Image Text:B Fill rate = x Depletion rate = r Internet Video server Client application buffer Figure 7.3 • Analysis of client-side buffering for video streaming Let's assume that the server sends bits at a constant rate x whenever the client buffer is not full. (This is a gross simplification, since TCP's send rate varies due to congestion control; we’ll examine more realistic time-dependent rates x(t) in the problems at the end of this chapter.) Suppose at time t = 0, the application buffer is empty and video begins arriving to the client application buffer. We now ask at what time t = t, does playout begin? And while we are at it, at what time t = tfdoes the client application buffer become full? First, let's determine tp, the time when Q bits have entered the application buffer and playout begins Recall that bits arrive to the client application buffer at
P3. Recall the simple model for HTTP streaming shown in Figure 7.3. Suppose the buffer size is infinite but the server sends bits at variable rate x(t). Specifi- cally, suppose x(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. 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 playout 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 func- tion of Q, B, T, and H, determine the time t = tf when the client applica- tion buffer first becomes full. H- 2T 3T 4T Time Bit rate x(t)
Transcribed Image Text:P3. Recall the simple model for HTTP streaming shown in Figure 7.3. Suppose the buffer size is infinite but the server sends bits at variable rate x(t). Specifi- cally, suppose x(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. 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 playout 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 func- tion of Q, B, T, and H, determine the time t = tf when the client applica- tion buffer first becomes full. H- 2T 3T 4T Time Bit rate x(t)
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