5/20 I flunked calculus and now I'm struggling in my network class. In
the lecture, the professor says p is the probability that a node in
ethernet sends, N is the number of nodes, and the following is the
slotted Aloha efficiency:
N*p*(1-p)^(N-1) = ~1/e = 0.37
I completely understand how he setup the equation, but got lost
trying to derive it. He said it's junior high math and hand waived
it, but I'd like to know how you do this. Any pointer to old
calculus stuff would be appreciated, thanks.
\_ http://robotics.eecs.berkeley.edu/~wlr/12203/ethernet%201.pdf
Ok fine, the slide is a mistake and he forgot lim
\_ Also, it's (1-p)^(N-1) in the slide.
And he didn't forget lim. It's an approximation. As N
increases, S approaches 1/e. His notation's a little strange,
but taking the lim would be even stranger.
\_ As stated, this equation is simply untrue (what if N = 100?).
-- ilyas
\_ http://robotics.eecs.berkeley.edu/~wlr/12203/ethernet%201.pdf
Ok fine, the slide is a mistake and he forgot lim
\_ Also, it's (1-p)^(N-1) in the slide.
\_ ... yeah. Kind of important. -- ilyas
And he didn't forget lim. It's an approximation. As N
increases, S approaches 1/e. His notation's a little strange,
but taking the lim would be even stranger. |
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