  Using a result of Blanchet and Wallwater (2015: Exact sampling of stationary
and time-reversed queues. ACM TOMACS, 25, 26) for exactly simulating the
maximum of a negative drift random walk queue endowed with independent and
identically distributed (iid) increments, we extend it to a multi-dimensional
setting and then we give a new algorithm for simulating exactly the stationary
distribution of a first-in-first-out (FIFO) multi-server queue in which the
arrival process is a general renewal process and the service times are iid; the
FIFO GI/GI/c queue with 2 \le c < 1. Our method utilizes dominated coupling
from the past (DCFP) as well as the Random Assignment (RA) discipline, and
complements the earlier work in which Poisson arrivals were assumed, such as
the recent work of Connor and Kendall (2015: Perfect simulation of M/G/c
queues. Advances in Applied Probability, 47, 4). We also consider the models in
continuous-time and show that with mild further assumptions, the exact
simulation of those stationary distributions can also be achieved. We also
give, using our FIFO algorithm, a new exact simulation algorithm for the
stationary distribution of the infinite server case, the GI/GI/\infty model.
Finally, we even show how to handle Fork-Join queues, in which each arriving
customer brings c jobs, one for each server.
