CS 655: Computer Networks Fall 2024

Homework 1

To be completed individually or in group size of two. Please review the academic conduct rules mentioned in the syllabus.

Answer all questions. Submit on Gradescope.

1. Hosts A and B are each connected to a router R via 100Mbps links as shown.

   The propagation delay on each link is 20 μs. R is a store-and-forward device; it begins relaying a received packet 35 μs after it has finished receiving it. Calculate the total time required to transmit 1250 bytes from A to B

   1. As a single packet.

   2. As two 5000-bit packets sent one right after the other.

2. Suppose that a certain communications protocol involves a per-packet overhead of 50 bytes for headers. We send 1 million bytes of data using this protocol; however, one data byte is corrupted and the entire packet containing it is thus lost. There are 3 options for packet size (header + payload): 1000, 10000 and 20000 bytes. Which of these sizes is optimal (i.e., minimum overhead)? (Hints: lost packet needs to be retransmitted)

3. Traffic intensity plays an important role in estimating the extent of queuing delay.

   1. True or false: When traffic intensity ≤ 1, there will be no queuing delay. Please also explain why.

   2. For a given router R with a single outgoing link and infinite buffer, suppose packet length is 1250 bytes and transmission rate of R’s outgoing link is 10Mbps.

      Calculate the average queuing delay for following packet arriving rates

      1. One packet arrives every 1ms

      2. 10 packets arrive simultaneously every 10ms

      3. 100 packets arrive simultaneously every 100ms

4. There are 3 links between hosts A and B with the transmission rates being 100Mbps, 20Mbps and 50Mbps. We define throughput as the measurement of all data transferring (whether that be useful or not), goodput measures useful data only. (For simplicity, only consider retransmissions as overhead)

   1. Suppose both routers R1 and R2 have infinite buffers. What are the throughputs and goodputs when A sends at rate 5Mbps, 10Mbps, 20Mbps, 50Mbps and 100Mbps?

   2. Suppose R1’s buffer is infinite while R2’s buffer can only hold one packet. What’s the answer for a) now?

   3. Suppose both R1 and R2’s buffer is finite, what will happen if A keeps sending at rate 50Mbps? What’s the throughput? What will happen to goodput?

5. The Unix utility ping can be used to find the RTT to various Internet hosts. Read the man page for ping, and use it to find the RTT to www.google.com. Measure the RTT values at different times of day and compare the results. What do you think accounts for the differences?

6. The Unix utility traceroute, or its Windows equivalent tracert, can be used to find the sequence of routers through which a message is routed. Use this to find the path from your site to www.google.com. How well does the number of hops correlate with the measured RTTs (is the RTT measured for router i always less than that for router i + 1)? Have you observed any packet loss?