# CS558, Homework 4

• Question 1

• Show that the solution of:

 ``` 1 - p b 3 E[W] ------- + E[W] = --- E[W] ( --- E[W] - 1 ) + ------ p 4 2 2 ```

is:

 ``` -------------------------- / 2+b / 8(1-p) 2+b 2 E[W] = ----- + \ / -------- + ( ----- ) 3b \/ 3bp 3b This is formula (13) in Padhye's paper ```

You can use your Mathematical skills or use Maple. If you use your Math. skills, write out the derivation. If you use Maple, enter the Maple commands used in a file and turn the file in as "hw4a" using:

/home/cs558000/turnin MapleCommandsFileName1 hw4a

You need to learn Maple on your own - try Google or "? command" (from inside Maple).

Hint: use the "solve" command

• Question 2

• Show that the Exact TCP Throught solution given in:

can be approximated by:

 ``` ------- 1 / 3 B(p) = ----- \ / ----- RTT \/ 2bp ```

Again, you can use your Mathematical skills or use Maple. If you use your Math. skills, write out the derivation. If you use Maple, enter the Maple commands used in a file and turn the file in as "hw4b" using:

/home/cs558000/turnin MapleCommandsFileName2 hw4b

Hint: if you use Maple, try the "series" command