We consider an infinite sequence of customers of types
𝓒={1,2,...,I} and an infinite sequence of
servers of types 𝓢={1,2,...,J}, where a server
of type j can serve a subset of customer types C(j) and where a
customer of type~$i$ can be served by a subset of server types S(i). We
assume that the types of customers and servers in the infinite sequences
are random, independent, and identically distributed, and that customers
and servers are matched according to their order in the sequence, on a
first-come--first-served (FCFS) basis. We investigate this process of
infinite bipartite matching. In particular, we are interested in the rate
ri,j that customers of type i are assigned
to servers of type j.
We present a countable state Markov chain to describe this process, and
for some previously unsolved instances, we prove ergodicity and existence
of limiting rates, and calculate ri,j.
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