# ELEC 3120 Computer Communication Networks Homework 1

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P1. (14 pts.) Consider two hosts, A and B, connected by a single link of rate R. 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. (2pts)
b. Determine the transmission time of the packet, dtrans, in terms of L and R. (2pts)
c. Ignoring processing and queuing delays, obtain an expression for the end-to-end delay. (2pts)
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?
(2pts)
e. Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit of the packet? (2pts)
f. Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit of the packet? (2pts)
g. Suppose s = 2.5×108
, L = 60 bits, and R = 65 kbps. Find the distance m so that dprop equals dtrans. (2pts)

P2. (12 pts.) Suppose users share a 4.5 Mbps link. Also suppose each user requires 250 kbps when transmitting, but
each user transmits only 15 percent of the time. (See the discussion of packet switching versus circuit switching.)
a. When circuit switching is used, how many users can be supported? (2pts)
b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is
transmitting. (2pts)
c. Suppose there are 200 users. Find the probability that at any given time, exactly n users are transmitting
simultaneously. (Hint: Use the binomial distribution.) (4pts)
d. Find the probability that there are 25 or more users transmitting simultaneously. (4pts)

ELEC 3120 Computer Communication Networks
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P3. (10 pts.) (a) Suppose 10 packets arrive simultaneously to a link at which no packets are currently being transmitted
or queued. Each packet is of length 50bits, and the link has transmission rate 5Mbps. What is the average queuing
delay for the 10 packets? (5pts) (b) Now suppose that 10 such packets arrive to the link every 10−4
seconds. What
is the average queuing delay of a packet? (5pts)
P4. (10 pts.) Consider the scenario illustrated as following. Assume Rs is 20 Mbps, Rc is 10 Mbps, and the server is
continuously sending traffic to the client.
a. Assuming the router between the server and the client can buffer at most four messages. After how many
messages sent by the server will packet loss starts occurring at the router? (4pts)
b. Generalizing that the router can buffer m messages. After how many messages sent by the server will packet
loss starts occurring at the router? (6pts)
P5. (14 pts.) Consider users A and B who share a link with rate of 𝑅𝑆=1000bps to send their data. Both users generate
two consecutive packets of L=1000 bits length and these packets arrive at the switch through two dedicated links