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CS558, Homework 4

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• 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