ALOHA throughput bound
= ALOHA throughput bound
{c}
{title2=$\max_pNp(1-p)^{N-1}=(1-1/N)^{N-1}$}
For $N\geq2$ backlogged stations, the largest one-slot success probability is $(1-1/N)^{N-1}$, attained at $p=1/N$. Its limit is $e^{-1}$; the exact finite-$N$ maximum is larger, and for $N=1$ it is one.