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Questions:
You are required to answer the following questions from the attached document
“HomeAssign_1_Questions.pdf”:Question Question
P.2 P.20
P.3 P.23
P.4 P.25
P.6 P.31
P.8 P.33
P.10
P2. Equation 1.1 gives a formula for the end-to-end delay of sending one packet
of length L over N links of transmission rate R. Generalize this formula for
sending P such packets back-to-back over the N links.
P3. Consider an application that transmits data at a steady rate (for example, the
sender generates an N-bit unit of data every k time units, where k is small and
fixed). Also, when such an application starts, it will continue running for a
relatively long period of time. Answer the following questions, briefly justifying your answer:
a. Would a packet-switched network or a circuit-switched network be more
appropriate for this application? Why?
b. Suppose that a packet-switched 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 than the
capacities of each and every link. Is some form of congestion control
needed? Why?
P4. Consider the circuit-switched network in Figure 1.13. Recall that there are 4
circuits on each link. Label the four switches A, B, C and D, going in the
clockwise direction.
a. What is the maximum number of simultaneous connections that can be in
progress at any one time in this network?
b. Suppose that all connections are between switches A and C. What is the
maximum number of simultaneous connections that can be in progress?
c. Suppose we want to make four connections between switches A and C,
and another four connections between switches B and D. Can we route
these calls through the four links to accommodate all eight connections?
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, dprop, in terms of m and s.
b. Determine the transmission time of the packet, dtrans, in terms of L
and R.
c. Ignoring processing and queuing delays, obtain an expression for the endto-end delay.
d. Suppose Host A begins to transmit the packet at time t = 0. At time t = dtrans,
where is the last bit of the packet?
e. Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit of
the packet?
f. Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit of
the packet?
g. Suppose s = 2.5 · 108, L = 120 bits, and R = 56 kbps. Find the distance m
so that dprop equals dtrans.
P8. Suppose users share a 3 Mbps link. Also suppose each user requires
150 kbps when transmitting, but each user transmits only 10 percent of the
time.
a. When circuit switching is used, how many users can be supported?
b. For the remainder of this problem, suppose packet switching is used. Find
the probability that a given user is transmitting.
c. Suppose there are 120 users. Find the probability that at any given time,
exactly n users are transmitting simultaneously. (Hint: Use the binomial
distribution.)
d. Find the probability that there are 21 or more users transmitting
simultaneously.
P10. Consider a packet of length L which begins at end system A and travels over
three links to a destination end system. These three links are connected by
two packet switches. Let di
, si
, and Ri denote the length, propagation speed,
and the transmission rate of link i, for i = 1, 2, 3. The packet switch delays
each packet by d
proc. Assuming no queuing delays, in terms of di
, si
, Ri
,
(i = 1,2,3), and L, what is the total end-to-end delay for the packet? Suppose
now the packet is 1,500 bytes, the propagation speed on all three links is 2.5 ·
108 m/s, the transmission rates of all three links are 2 Mbps, the packet switch
processing delay is 3 msec, the length of the first link is 5,000 km, the length
of the second link is 4,000 km, and the length of the last link is 1,000 km. For
these values, what is the end-to-end delay?
P20. Consider the throughput example corresponding to Figure 1.20(b). Now
suppose that there are M client-server pairs rather than 10. Denote Rs
, Rc
, and
R for the rates of the server links, client links, and network link. Assume all
other links have abundant capacity and that there is no other traffic in the
network besides the traffic generated by the M client-server pairs. Derive a
general expression for throughput in terms of Rs
, Rc
, R, and M.
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 Rs 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 inter-arrival 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., Rc < Rs
). 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
queuing before the second link? Explain.
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 ! 108 meters/sec.
a. Calculate the bandwidth-delay product, R ! dprop.
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 bandwidth-delay 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.
P31. In modern packet-switched networks, including the Internet, the source host
segments long, application-layer 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. Figure 1.27 illustrates the end-to-end
transport of a message with and without message segmentation. Consider a
message that is 8 · 106 bits long that is to be sent from source to destination in
Figure 1.27. 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
store-and-forward 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 800 packets, with each
packet being 10,000 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. In addition to reducing delay, what are reasons to use message segmentation?
e. Discuss the drawbacks of message segmentation.
P33. Consider sending a large file of F bits from Host A to Host B. There are three
links (and two switches) between A and B, and the links are uncongested (that
is, no queuing delays). Host A segments the file into segments of S bits each and
adds 80 bits of header to each segment, forming packets of L = 80 + S bits. Each
link has a transmission rate of R bps. Find the value of S that minimizes the
delay of moving the file from Host A to Host B. Disregard propagation delay.
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