Section 18.8. Exercises


18.8. Exercises

1.

We want to transmit a speaker's voice through a digital radio broadcast system that uses 8-bit code PCM (explained in Chapter 17) placed on the Internet.

  1. How many bits are produced in each second?

  2. Estimate the size of an encapsulated RTP/IP datagram (the basic transmission unit of data in the Internet) that carries a half second of PCM-encoded audio using UDP.

2.

Two voice sources come to one server for live transmission together, using RTP packets. Each source bandwidth has been compressed to 31 Kb/s.

  1. Show an overview of the encapsulated RTP/IP datagram, and estimate the size of each packet, utilizing an RTP packet using UDP.

  2. How many packets are produced each 5 minutes?

3.

We have five packets to transmit in real time. The estimated average jitter until the time of the first packet is 0.02 ms. Table 18.1 shows the timestamps of RTP data packets indicated by the source, t i , and the arrival times of RTP packets at the receiver a i . Assume that the normalizing coefficient k is 0.2.

  1. Estimate the average jitter until every packet has arrived.

  2. What would be possible reason(s) that t i increases at a different rate from i ?

Table 18.1. Exercise 3 example of source timestamps and receiver arrival times for five packets

i

a i

t i

1

43

69

1

45

74

1

47

73

1

49

91

1

51

99


4.

SCTP is applied to transmit a color video clip between two points of an IP network requiring 4 minutes of network use. Each image of this video clip consists of 1,024 x 1,280 pixel blocks, and the video consists of 30 images per second. The video clip is not compressed but is passed through the quantization process, and each pixel can be a value among a sample space of 77 numbers . One-tenth of each row of a frame (image) is formatted by one packet.

  1. Find the size of each SCTP chunk , including its header.

  2. Find the total size of each SCTP packet, including its header.

  3. Find the total size of bits transmitted, based only on payload packets.

  4. Determine the required bandwidth between these two nodes.

5.

Suppose that a live transmission of a compressed color video movie between two points of an IP network requires 2 hours of network use. We want to apply SCTP for this transmission. Each image of this video consists of 1,024 x 1,280 pixel blocks, and the video consists of 30 images per second. One option is to encapsulate each block of pixels in a chunk, allowing each row of a frame (image) to be formatted by one packet. Assume that each pixel block is compressed on average to 10 phrases and each phrase requires on average 5 bits.

  1. Find the size of each SCTP chunk, including its header.

  2. Find the total size of each SCTP packet, including its header.

  3. Find the total size of bits transmitted, based only on payload packets.

  4. Determine the required bandwidth between these two nodes.

6.

Assume that a real-time bursty source is modeled using a Brownian motion process X( t ). Let Z( t ) = X( t ) + 2 t .

  1. Find the probability distribution function (PDF) of Z( t ).

  2. Find the joint PDF of Z( t ) and X( t + 1).

7.

In Figure 18.15, a remote medical emergency unit is streaming the 70-cycle/ minute heartbeat of a patient to a hospital, using SCTP. Each heart cycle has six peaks: P, Q, R, S, T, and U. Suppose that all information about each peak is formatted into one chunk of the SCTP data packet. Because of their importance and complexity, each of the Q, R, and S pulses requires four samples; P, T, or U require only one sample each.

  1. Determine the required bandwidth between the unit and the hospital.

  2. If multiple samples are included in a packet, find the maximum number of heartbeat cycles that can be formatted into a packet.

  3. Evaluate the approach presented in part (b), and compare it with the original one.

Figure 18.15. Exercise 7 example of remote medical emergency unit streaming a patient's heartbeat of to a hospital. The heartbeat signal is converted to stream of packets.


8.

For self-similar traffic, we have seen the relationship between the expected values in Equation (18.4), using the Hurst parameter, H

  1. Derive a relationship between the variances of the two sides of Equation (18.3).

  2. Compare situations in which the Hurst parameter, H , takes values 0.5, 0.8, or 1 in Equation (18.3).

9.

To better understand the behavior of bursty traffic, such as a video streaming source, assume that the traffic is described by a Pareto distribution with k = 1. Plot PDFs of the following two cases of ± , and compare them with that of an exponential distribution. Comment on the heavy-tailed phenomenon .

  1. ± = 0.8

  2. ± = 3.8

10.

Computer simulation project . We want to simulate self-similar traffic. First, develop a random number generator. Then, develop source code that defines the following components , and integrate the these two programs to simulate the self-similar traffic:

  1. Source ID

  2. Priority of the packets

  3. Elapsed time (in byte transmission times)

  4. Packet size (bytes)

  5. Number of packets remaining in current burst



Computer and Communication Networks
Computer and Communication Networks (paperback)
ISBN: 0131389106
EAN: 2147483647
Year: 2007
Pages: 211
Authors: Nader F. Mir

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