Networks and Delay

Kurose & Ross, Chapter 1, Problem P6
This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagation speed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B.
a. Express the propagation delay, $d_{prop}$, in terms of m and s.
b. Determine the transmission time of the packet, $d_{trans}$, in terms of L and R.
c. Ignoring processing and queuing delays, obtain an expression for the endtoend delay.
d. 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?
e. Suppose $d_{prop}$ is greater than $d_{trans}$. At time $t = d_{trans}$, where is the first bit of the packet?
f. Suppose $d_{prop}$ is less than $d_{trans}$. At time $t = d_{trans}$, where is the first bit of the packet?
g. Suppose $s = 2.5 \times 10^8$, $L = 120$ bits, and $R = 56$ kbps. Find the distance m so that $d_{prop}$ equals $d_{trans}$.

Kurose & Ross, Chapter 1, Problem P23
Consider Figure 1.19(a):
Assume that we know the bottleneck link along the path from the server to the client is the first link with rate $R_s$ bits/sec. Suppose we send a pair of packets back to back from the server to the client, and there is no other traffic on this path. Assume each packet of size L bits, and both links have the same propagation delay $d_{prop}$.
a. What is the packet interarrival time at the destination? That is, how much time elapses from when the last bit of the first packet arrives until the last bit of the second packet arrives?
b. Now assume that the second link is the bottleneck link (i.e. $R_c < R_s$). Is it possible that the second packet queues at the input queue of the second link? Explain. Now suppose that the server sends the second packet T seconds after sending the first packet. How large must T be to ensure no queueing before the second link? Explain.

Kurose & Ross, Chapter 1, Problem P25
Suppose two hosts, A and B, are separated by 20,000 kilometers and are connected by a direct link of $R = 2$ Mbps. Suppose the propagation speed over the link is $2.5 \times 10^8$ meters/sec.
a. Calculate the bandwidthdelay product, $R \times d_{prop}$.
b. Consider sending a file of 800,000 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?
c. Provide an interpretation of the bandwidthdelay product.
d. What is the width (in meters) of a bit in the link? Is it longer than a football field?
e. 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.

Kurose & Ross, Chapter 1, Problem P26
Referring to the problem above, suppose we can modify R. For what value of R is the width of a bit as long as the length of the link?

Kurose & Ross, Chapter 1, Problem P27
Consider the same problem above, but now with a link of $R = 1$ Gbps.
a. Calculate the bandwidthdelay product, $R \times d_{prop}$.
b. Consider sending a file of 800,000 bits from Host A to Host B. Suppose the file is sent continuously as one big message. What is the maximum number of bits that will be in the link at any given time?
c. What is the width (in meters) of a bit in the link?

Kurose & Ross, Chapter 1, Problem P31
In modern packetswitched networks, the source host segments long, applicationlayer messages (for example, an image or a music file) into smaller packets and sends the packets into the network. The receiver then reassembles the packets back into the original message. We refer to this process as message segmentation. The figure below illustrates the endtoend transport of a message with and without message segmentation.
Consider a message that is $8 \times 10^6$ bits long that is to be sent from source to destination in the figure. Suppose each link in the figure is 2 Mbps. Ignore propagation, queuing, and processing delays.
a. Consider sending the message from source to destination without message segmentation. How long does it take to move the message from the source host to the first packet switch? Keeping in mind that each switch uses storeandforward packet switching, what is the total time to move the message from source host to destination host?
b. Now suppose that the message is segmented into 4,000 packets, with each packet being 2,000 bits long. How long does it take to move the first packet from source host to the first switch? When the first packet is being sent from the first switch to the second switch, the second packet is being sent from the source host to the first switch. At what time will the second packet be fully received at the first switch?
c. How long does it take to move the file from source host to destination host when message segmentation is used? Compare this result with your answer in part (a) and comment.
d. Discuss the drawbacks of message segmentation.

Use the following network and the convention that 1 kB = $10^3$ bytes and 1 MB = $10^6$ bytes.
a. Node A transmits a stream of 1 kB packets to node C. Assuming no other traffic in the network, explain why there will never be any queueing delay at node B.
b. Draw a diagram that represents the stream of packets over time, using the example covered in class.
c. How long would it take to transfer a 1 MB file, divided into 1 kB packets, from A to C? Which type of delay dominates?
d. If both links are upgraded to a rate of 1 Gbps, how long would it take to transfer a 1 MB file from A to C? Which type of delay dominates now?

Use the following network and the convention that 1 kB = $10^3$ bytes and 1 MB = $10^6$ bytes.
a. Node A transmits 1000 packets, each of size 1 kB, to node C. Explain why there will be queueing delay at node B.
b. Draw a diagram that represents the stream of packets over time, using the example covered in class.
c. Derive a formula for the queueing delay for packet k What is the largest number of packets the queue will ever hold?
d. How long would it take to transfer a 1 MB file, divided into 1 kB packets, from A to C? Does the queueing delay affect transfer time?