  We consider a stochastic bipartite matching model consisting of multi-class
customers and multi-class servers. Compatibility constraints between the
customer and server classes are described by a bipartite graph. Each time slot,
exactly one customer and one server arrive. The incoming customer (resp.
server) is matched with the earliest arrived server (resp. customer) with a
class that is compatible with its own class, if there is any, in which case the
matched customer-server couple immediately leaves the system; otherwise, the
incoming customer (resp. server) waits in the system until it is matched.
Contrary to classical queueing models, both customers and servers may have to
wait, so that their roles are interchangeable. While (the process underlying)
this model was already known to have a product-form stationary distribution,
this paper derives a new compact and manageable expression for the
normalization constant of this distribution, as well as for the waiting
probability and mean waiting time of customers and servers. We also provide a
numerical example and make some important observations.
