AbstractApproximate formulae for the equilibrium queue-size and queueing-time distribution in the systemGI/M/rare derived. The degree of approximation achieved depends on the particular formula used and on the values of the various parameters involved; the relative percentage errors incurred seem, however, to be well below 5 per cent for most practical purposes. It is believed that the underlying idea of "similarity" in the behaviour of queueing processes may also lead, if extended, to useful approximate formulae for more complex systems.