Fall 2006

Guidelines about homework.

- Feel free to discuss the hw problems with other students in the class. However, all aspects of the write-up itself must be your own. Copying of others' solutions is not allowed.
- I would greatly appreciate if you use a text formatter (latex, word, etc.) to create your answer set. Hand in a hard copy.
- Feel free to look up references. But be sure to cite your sources.

**Problem 1: (25 points) High-performance TCP. **Consider a standard TCP
connection with a packet size of 1500 bytes and a round-trip time of 100ms. The
average throughput of the TCP connection is 10 Gbps.

- What is the average congestion window size of this TCP connection?
- What is the average loss rate? What is the average duration (in seconds) between two losses? (Hint: you can assume that the TCP follows a saw-tooth behavior).
- We can probably see that a standard TCP does not work very well from the above calculation. Suppose you want to design a new TCP protocol which behaves like N TCP. That is, the throughput of your new TCP protocol is N time of that from a standard TCP. Your new protocol still uses the additive increase and multiplicative decrease type of mechanism. Let \alpha be your additive term and \beta be your decrement term. What relationship should \alpha and \beta satisfy?
- A new TCP protocol has been proposed which satisfies x=c/(p*R), where x is the throughput (or sending rate) of the TCP connection, p and R are the loss rate and round trip time respectively. What is the corresponding utility function of this TCP?

**Problem 2: (10 points) **Consider packet-level sampling. In particular,
you'll sample one packet in every N packets. Let P denote the number of original
packets. Let \hat{p} denote the total number of measured packets. Let \hat{P}
denote the estimated number of packets, \hat{P}=N \hat{p}.

- Prove that \hat{P} is an unbiased estimator of P.
- What is the variance of \hat{P}?

(Hint: read the paper on packet sampling we covered in class).

**Problem 3: (10 points) Basics of wireless communication and MAC.**

- Is it possible to transmit a digital signal, e.g., coded as square wave as used in wired a computer, using radio without any loss? Why?
- What are the main problems of signal propagation? Why do radio waves not always follow a straightline? Why is reflection both useful and harmful?
- What is hidden terminal problem? How does 802.11 deal with this problem?
- Describe two scenarios where two wireless links interfere with each other (in the sense that their aggregate throughput when both are active simultaneously is lower than that when they are individually active).

**Problem 4: (5 points) **According to your knowledge and the materials we
covered so far, list 3 aspects of wireless network that you found interesting
and very different from wired network.