  In recent years a number of models involving different compatibilities
between jobs and servers in queueing systems, or between agents and resources
in matching systems, have been studied, and, under Markov assumptions and
appropriate stability conditions, the stationary distributions have been shown
to have product forms. We survey these results and show how, under an
appropriate detailed description of the state, many are corollaries of similar
results for the Order Independent Queue. We also discuss how to use the product
form results to determine distributions for steady-state response times.
