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COMP 5320/6320 Assignment 1

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COMP 5320/6320
Design and Analysis of Computer Networks
Homework Assignment 1
1. Calculate the total time required to transfer a 1000-KB file in the following cases, assuming an RTT of
50 ms, a packet size of 1 KB data, and an initial 2×RTT of “handshaking” before data is sent. We define
the total time of transferring the file as the time elapsed from the starting of initial handshaking to the instant
when the last bit arrives at the receiver.
(a) The bandwidth is 1.5 Mbps, and data packets can be sent continuously.
(b) The bandwidth is 1.5 Mbps, but after we finish sending each data packet we must wait one RTT before
sending the next.
(c) The bandwidth is “infinite,” meaning that we take transmit time to be zero, and up to 20 packets can be
sent per RTT.
(d) The bandwidth is infinite, and during the first RTT we can send one packet (21-1
), during the second
RTT we can send two packets (22-1
), during the third we can send four (23-1
), and so on.
2. In the figure below, all frames are generated at node A and sent to node C through node B. Determine
the minimum transmission rate required between nodes B and C so that the buffers of node B are not flooded,
based on the following conditions:
• The data rate between A and B is 100 kilobits/s.
• The propagation delay is 5 µs/km for both lines.
• There are full-duplex lines between the nodes.
• All data frames are 1000 bits long; ACK frames are separate frames of negligible length.
• Between A and B, a sliding-window flow control with a window size of 3 is used.
• Between B and C, stop-and-wait flow control is used.
• There are no errors.
3. For each of the following sets of codewords, please give the appropriate (n,k,d) designation where n is
number of bits in each codeword, k is the number of message bits transmitted by each code word and d is
the minimum Hamming distance between codewords. What is the coding rate (k/n), error detection
capability, and error correction capability for each coding scheme?
A. {111, 100, 001, 010}
B. {00000, 01111, 10100, 11011}
4. In an error-correction code, an important constraint that the coding scheme must satisfy isthat the number
of added check bits should be sufficient to identify unique error patterns (note that no error is also a valid
error pattern). Now suppose that we decide to use a (n, 20, 3) error correction code to transmit 20-bit
messages. What’s the minimum value of n that will allow the code to correct single bit errors? Show the
reason and the calculation for full credits.
5. Consider the Markov chain with three states, S={1, 2, 3}, that has the following transition matrix
(a) Draw the state transition diagram for this chain.
(b) If we know P(X1=1)=P(X1=2)=1/4, find P(X1=3, X2=2, X3=1).
6. Consider the Markov chain in the following figure. There are two recurrent classes, R1={1, 2} and
R2={5,6,7}. Assuming initial state X0=3. Find the probability that the chain gets absorbed in R1.

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