  The problem of appropriately matching items subject to compatibility
constraints arises in a number of important applications. While most of the
literature on matching theory focuses on a static setting with a fixed number
of items, several recent works incorporated time by considering a stochastic
model in which items of different classes arrive according to independent
Poisson processes and assignment constraints are described by an undirected
non-bipartite graph on the classes. In this paper, we prove that the Markov
process associated with this model has the same transition diagram as in a
product-form queueing model called an order-independent loss queue. This allows
us to adapt existing results on order-independent (loss) queues to stochastic
matching models and, in particular, to derive closed-form expressions for
several performance metrics, like the waiting probability or the mean matching
time, that can be implemented using dynamic programming. Both these formulas
and the numerical results that they allow us to derive are used to gain insight
into the impact of parameters on performance. In particular, we characterize
performance in a so-called heavy-traffic regime in which the number of items of
a subset of the classes goes to infinity while items of other classes become
scarce.
