1. Consider a TCP connection between two points that are 200 km apart. Assume the transmission speed is 10 Mbps (10 220 bps) and the propagation speed is 200 108 meters/s. Assume 16-bit sequence number. The TCP initially sends a segment of 1024 bytes and each time it receives an ACK it doubles the number of segments it sends until the full capacity is reached. (a) Calculate the initial RTT, assuming there is no other delay besides the transmission delay and propagation delay. (b) How long does it take to reach its full capacity? (c) What is the maximum throughput? (d) At full capacity, how long does it take for the sequence number to wrap around? 2. Prove that isomorphic graphs have the same degree sequence. But the converse is not true. 3. We have covered three approaches in building a layer-3 network topology, i. Using network management tools such as traceroute to extract network connectivity. ii. Using degree-based models to generate a topology. iii. Using engineering-based models to generate a topology. Briefly discuss (in your own words), which one gives you a more realistic topology in terms of: (a) Time to build the topology. (b) Core node degree. (c) Edge node degree. (d) The role of randomness in building the topology. (e) Throughput performance. (f) Utilization performance. Illustrate by example if appropriate. 4. Arrayed-Waveguide Grating (AWG) is a passive optical device that routes each wavelength of an input to a different output to provide non-blocking connectivity. In an AWG, the wavelength w of input port i is routed to output port [(i + w

# recent advances in networking

1. Consider a TCP connection between two points that are 200 km apart. Assume the transmission speed is 10 Mbps (10 220 bps) and the propagation speed is 200 108 meters/s. Assume 16-bit sequence number. The TCP initially sends a segment of 1024 bytes and each time it receives an ACK it doubles the number of segments it sends until the full capacity is reached. (a) Calculate the initial RTT, assuming there is no other delay besides the transmission delay and propagation delay. (b) How long does it take to reach its full capacity? (c) What is the maximum throughput? (d) At full capacity, how long does it take for the sequence number to wrap around? 2. Prove that isomorphic graphs have the same degree sequence. But the converse is not true. 3. We have covered three approaches in building a layer-3 network topology, i. Using network management tools such as traceroute to extract network connectivity. ii. Using degree-based models to generate a topology. iii. Using engineering-based models to generate a topology. Briefly discuss (in your own words), which one gives you a more realistic topology in terms of: (a) Time to build the topology. (b) Core node degree. (c) Edge node degree. (d) The role of randomness in building the topology. (e) Throughput performance. (f) Utilization performance. Illustrate by example if appropriate. 4. Arrayed-Waveguide Grating (AWG) is a passive optical device that routes each wavelength of an input to a different output to provide non-blocking connectivity. In an AWG, the wavelength w of input port i is routed to output port [(i + w