  Fork-join network is a class of queueing networks with applications in
manufactory, healthcare and computation systems. In this paper, we develop a
simulation algorithm that (1) generates i.i.d. samples of the job sojourn time,
jointly with the number of waiting tasks, exactly following the steady-state
distribution, and (2) unbiased estimators of the derivatives of the job sojourn
time with respect to the service rates of the servers in the network. The
algorithm is designed based on the Coupling from the Past (CFTP) and
Infinitesimal Perturbation Analysis (IPA) techniques. Two numerical examples
are reported, including the special 2-station case where analytic results on
the steady-state distribution is known and a 10-station network with a
bottleneck.
