  In this paper, we introduce a slight variation of the Dominated Coupling From
the Past algorithm (DCFTP) of Kendall, for bounded Markov chains. It is based
on the control of a (typically non-monotonic) stochastic recursion by a
(typically monotonic) one. We show that this algorithm is particularly suitable
for stochastic matching models with bounded patience, a class of models for
which the steady state distribution of the system is in general unknown in
closed form. We first show that the Markov chain of this model can be easily
controlled by an infinite-server queue. We then investigate the particular case
where patience times are deterministic, and this control argument may fail. in
that case we resort to an ad-hoc technique that can also be seen as a control
(this time, by the arrival sequence). We then compare this algorithm to the
classical CFTP one, and show how our perfect simulation results can be used to
estimate, and compare, the loss probabilities of various systems in
equilibrium.
