Introduction to Data Communications - Excercise 5

Tuesdays (23.10) group is moved to wednesday (24.10) 10.00-12.00 @ T/B 247

1. Twenty-four voice signals are to be multiplexed and transmitted over twisted pair. Each voice signal requires 4 kHz. What is the bandwidth required for FDM? Assuming a bandwidth efficiency of 1 bps/Hz, what is the bandwidth required for TDM using PCM, where the required data rate is 64 kbps?
2. Find the number of the following devices that could be accommodated by a 1.544 Mbps TDM line if 1 percent of the line capacity is reserved for synchronization purposes.
   1. 110-bps teleprinter terminals
   2. 300-bps computer terminals
   3. 1200-bps computer terminals
   4. 9600-bps computer output ports
   5. 64-kbps PCM voice-frequency lines
3. Assume that the velocity of propagation on a TDM bus is 0.8c, its length is 10 m, the data rate is 500 Mbps and c is 3x10^8 m/sec. How many bits should be transmitted in a time slot to achieve a bus utilization of 99 percent?
4. Explain the flaw in the following reasoning: Packet switching requires control and address bits to be added to each packet. This introduces considerable overhead in packet switching. In circuit switching, a transparent circuit is established. No extra bits are needed.
   1. Therefore, there is no overhead in circuit switching.
   2. Because there is no overhead in circuit switching, line utilization must be more efficient than in packet switching.
5. Define the following parameters for a switching network:
   N = number of hops between two given end systems.
   L = message length in bits.
   B = data rate, in bits per second (bps), on all links
   P = fixed packet size, in bits
   H = overhead (header) bits per packet
   S = call setup time (circuit switching or virtual circuit) in seconds
   D = propagation delay per hop in seconds
   
   1. For N = 4, L = 3200, B = 9600, P = 1024, H = 16, S = 0.2, D = 0.001, compute the end-to-end delay for circuit switching, virtual circuit packet switching, and datagram packet switching. Assume that there are no acknowledgements. Ignore processing delay at the nodes.
   2. Derive general expressions for the three techniques of part (a), taken two at a time (three expressions in all), showing the conditions under which the delays are equal.
6. Consider a packet-switching network of N nodes, connected by the following topologies:
   1. Star: One central node with no attached station; all other nodes attach to the central node.
   2. Loop: Each node connects to two other nodes to form a closed loop.
   3. Fully Connected: Each node us directly connected to all other nodes.
   For each case, give the average number of hops between stations. Draw a schematic drawing of each topology.
7. Evaluate how Dijkstra's routing algorithm works ( http://cs.joensuu.fi/pages/parkkinen/datacom/kuvat/dijkstra1.gif). Run an example of algorithm by using the network on page 15 of Chapter "Packet Switching" in the lecture notes.