  We prove that the scaled maximum steady-state waiting time and the scaled
maximum steady-state queue length among $N$ $GI/GI/1$-queues in the $N$-server
fork-join queue, converge to a normally distributed random variable as
$N\to\infty$. The maximum steady-state waiting time in this queueing system
scales around $\frac{1}{\gamma}\log N$, where $\gamma$ is determined by the
cumulant generating function $\Lambda$ of the service distribution and solves
the Cram\'er-Lundberg equation with stochastic service times and deterministic
inter-arrival times. This value $\frac{1}{\gamma}\log N$ is reached at a
certain hitting time. The number of arrivals until that hitting time satisfies
the central limit theorem, with standard deviation
$\frac{\sigma_A}{\sqrt{\Lambda'(\gamma)\gamma}}$. By using distributional
Little's law, we can extend this result to the maximum queue length. Finally,
we extend these results to a fork-join queue with different classes of servers.
