ECE 363
Communication Networks

Assignment Submission

Assignments

1. Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the distance between them is d meters, and the propagation speed along the link is v meters/sec. Host A is to send a packet of size L bits to Host B.
   (a) Express the propagation delay, t_prop, in terms of d and v.
   (b) Determine the transmission time of the packet, t_trans, in terms of L and R.
   (c) Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.
   (d) Suppose Host A begins to transmit the packet at time t = 0. At time t = t_trans, where is the last bit of the packet?
   (e) Suppose t_prop is greater than t_trans. At time t = t_trans, where is the first bit of the packet?
   (f) Suppose t_prop is less than t_trans. At time t = t_trans, where is the first bit of the packet?
   (g) Suppose v = 2 × 10⁸ meters/sec, L = 1 Mbit, and R = 100 Mbps. Find the distance d such that t_prop = t_trans.
2. Consider the queueing delay in a router buffer. Suppose all packets have length L bits and the transmission rate is R bps.
   (a) Suppose that N packets simultaneously arrive at the buffer every LN/R seconds. Find the average queueing delay of a packet. (Hint: The queueing delay for the first packet is zero, for the second packet is L/R, for the third packet is 2L/R, … The Nth packet has already been transmitted when the next batch of packets arrives.)
   (b) Suppose that N packets arrive at the buffer every LN/R seconds, and the inter-arrival time of two adjacent packets is L/(2R), i.e. if the first packet arrives at time t₀, then the 2nd packet arrives at t₀ + L/(2R), the 3rd packet arrives at t₀ + 2L/(2R), …, and the Nth packet arrives at t₀ +(N-1)L/(2R). Find the average queueing delay of a packet.
3. Suppose there is an R = 10 Mbps microwave link between a geostationary satellite and its base station on Earth. The distance between the satellite and base station is 36,000 km. Every minute the satellite takes a digital image and sends it to the base station.
   (a) What is the propagation delay of the link?
   The bandwidth-delay product is the volume of bits on a link when it is used to send a message
   R × t_prop
   What is the bandwidth-delay product for this satellite link?
   (c) Let L be the size of the image in bits. What is the minimum value of L for the microwave link to be in continuous use?
4. Consider a 1 Gbps link and N users accessing this link using statistical multiplexing. Each user accesses the link 5% of the time with a data rate of 200 Mbps.
   (a) What is the maximum number of users such that the probability of the demand exceeding the link capacity is .1%?
   (b) What is the statistical multiplexing gain?
   (c) What is the average rate of transmission with 10 users? Is this below the link capacity? Can congestion still occur in this case?
5. Consider a system with a link bandwidth of 3.1 kHz.
   (a) If 16-QAM modulation is employed, what is the maximum achievable data rate assuming a noiseless channel? [Hint: Nyquist rate]
   (b) If the link signal-to-noise ratio (SNR) is 30 dB, what is the maximum achievable data rate? [Hint: channel capacity]
   
6. In a store-and-forward packet switching system, the processing delay in a switch is t_proc = .020 msec. Is this likely to be a major factor in the response of a client-server system where the client is in Vancouver and the server is in Toronto? Assume they are connected by fiber optics.
7. Ten signals, each requiring 4000 Hz, are multiplexed onto a single channel using FDM. What is the minimum bandwidth required for the muliplexed channel? Assume 10% guard bands are required including at the beginning and end of the channel.

1. The following data occurs for which the byte-stuffing algorithm should be used: A B ESC C ESC FLAG FLAG D. What is the output after stuffing?
2. You receive the following data: 0110 0111 1100 1111 0111 1101. You know that the protocol uses bit stuffing. Show the data after destuffing.
3. When bit stuffing is used, is it possible for the loss, insertion, or modification of a single bit to cause an error not detected by the checksum? If not, why not? If so, how? Does the checksum length play a role here?
4. The eight bit message 1010 1111 is to be encoded using a Hamming code. What is the coeword after encoding? Number the bits from left to right.
5. The twelve bit string 0111 0101 1101 is received after a Hamming codeword is transmitted over a noisy channel. Determine the message associated with this bit string. Assume that not more than 1 bit is in error.
6. The bit string 11100110 is to be transmitted using a CRC trailer. The generator polynomial is G(x) = x⁴ + x³ + 1. Determine the transmitted bit string. Suppose that the third bit from the left is inverted during transmission. Show that this error is detected at the receiver. Give an example of bit errors in the transmitted bit string that will not be detected by the receiver.
7. A channel has a rate of R = 4 kbps and a propagation delay of t_prop = 20 msec. For what range of frame sizes does the stop-and-wait protocol give an efficiency of at least 50%?

Aaron Gulliver
2026-1-29