Pure Aloha (cont.)

P(success by given node) = P(node transmits) .

P(no other node transmits in [t0-1,t0] .

P(no other node transmits in [t0,t0 +1]

= p . (1-p)(N-1) (1-p)(N-1)

P(success by any of N nodes) = N p . (1-p)(N-1) (1-p)(N-1)

… choosing optimum p as n -> infty ...

= 1/(2e) = .18

S = throughput = “goodput”

(success rate)

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