Exercises

Chapter 1

Homework (7 exercises) [ Here [doc] ]

[Due Date: 04/04/1432]

Problem P3

Consider an application which transmits data at a steady rate (e.g., the sender generates a bit unit of data every time units, where is small and fixed). Also, when such an application starts, it will stay on for relatively long period of time. Answer the following questions, briefly justifying your answer:

1. Would a packet-switched network or a circuit-switched network be more appropriate for this application? Why?
2. Suppose that a packet-switching network is used and the only traffic in this network comes from such applications as described above. Furthermore, assume that the sum of the application data rates is less that the capacities of each and every link. Is some form of congestion control needed? Why?

Problem P5

This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, Hosts A and B, connected by a single link of rate bps. Suppose that the two hosts are separted by meters, and suppose the propagation speed along the link is meters/sec. Host A is to send a packet of size bits to Host B.

1. Express the propagation delay,
   d_prop
   in terms of
   m
   and
   s
   .
2. Determine the transmission time of the packet,
   d_trans
   in terms of
   L
   and
   R
   .
3. Ignoring processing and queing delays, obtain an expression for the end-to-end delay.
4. Suppose Host A begins to transmit the packet at time
   t=0
   . At time
   t=d_trans
   , where is the last bit of the packet?
5. Suppose
   d_prop
   is greater than
   d_trans
   . At time
   t=d_trans
   , where is the first bit of the packet?
6. Suppose
   d_prop
   is less than
   d_trans
   . At time
   t=d_trans
   , where is the first bit of the packet?
7. Suppose
   s
   =2.5*10⁸,
   L
   =100bits and
   R
   =28 kbps. Find the distance
   m
   so that
   d_prop
   equals
   d_trans
   .

Problem P7

Suppose users share a 1Mbps link. Also suppose each user requires 100 Kbps when transmitting, but each user transmits only 10 percent of the time.

1. When circuit switching is used, how many users can be supported?
2. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting.
3. Suppose there are 40 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution.)
4. Find the probability that there are 11 or more users transmitting simultaneously.

Problem P9

Consider a packet of length which begins at end system A, travels over one link to a packet switch, and travels from the packet switch over a second link to a destination end system. Let , , and denote the length, propagation speed, and the transmission rate of link , for =1,2. The packet switch delays each packet by d_proc.

1. Assuming no queuing delays, in terms of
   d_i
   ,
   s_i
   ,
   R_i
   , (
   i
   =1,2), and
   L
   , what is the total end-to-end delay for the packet?
2. Suppose now the packet length is 1000 bytes, the propagation speed on both links is 2.5 10⁸ m/s, the transmission rates of both links is 1Mbps, the packet switch processing delay is 2 msec, the length of the first link is 6000 km, and the length of the last link is 3000 km. For these values, what is the end-to-end delay?

Problem P13

Consider the queueing delay in a router buffer (preceding an outbound link). Suppose all packets are bits, the transmission rate is bps and that packets arrive to the buffer every seconds. Find the average queueing delay of a packet. (Hint: The queuing delay for the first packet is zero; for the second packet ; for the third packet . The packet has already been transmitted when the second batch of packets arrives.)

Problem P18

Suppose two hosts, A and B, are separated by 10,000 kilometers and are connected by a direct link of = 2 Mbps. Suppose the propagation speed over the link is 2.5.10⁸ meters/sec.

1. Calculate the bandwidth-delay product,
   R.d_prop
   .
2. Consider sending a file of 400,000 bits from Host A to Host B. Suppose the file is sent continuously as one large message. What is the maximum number of bits that will be in the link at any given time?
3. Provide an interpretation of the bandwidth-delay product.
4. What is the width (in meters) of a bit in the link?
5. Derive a general expression for the width of a bit in terms of the propagation speed
   s
   , the transmission rate
   R
   , and the length of the link
   m
   .

Problem 28

An image is 1024 x 768 pixels with 3 bytes/pixel. Assume the image is uncompressed. How long does it take to transmit it over a 56-kbps modem channel? Over a 1-Mbps cable modem? Over a 10-Mbps Ethernet? Over a 100-Mbps Ethernet?

Chapter 3

Homework (7 exercises) [ Here [doc] ]

[Due Date: 28/04/1432]

Exercise 1

Suppose that a Data-Link connection is established between two Data-Link Layer entities A and B using HDLC Protocol. We suppose that A wants to send to B in a single frame the three following bytes:

• Byte 1: 01100101
• Byte 2: 01101111
• Byte 3: 10111111

We suppose that B has nothing to send to A.

1. What is the type of the frame used to transfer these bytes?
2. What is the total number of bits sent from A to B including all control fields?
3. Give the binary content of the Control field of the previous frame (sent from A to B) if A requires an immediate acknowledgement.
4. Cite in the correct order the three tasks performed by the node B when it receives the previous frame sent by A.
5. Give the binary content of the control field of the frame sent by node B to node A to acknowledge the frame received from node A.
6. What are the mechanisms used by the HDLC protocol to handle both losses and duplicates?

Chapter 4

Homework (3 exercises) [ Here [doc] ]

[Due Date: 16/05/1432]

Chapter 5

Homework (6 exercises) [ Here [doc] ]

[Due Date: 04/06/1432]