The inter-arrival times of accepted customers in an M/G/1 queue with finite capacity

This note draws attention to a practical problem of interest to physicists, namely the distribution of the inter-arrival times of those customers accepted by the M/D/1/K + 1 queue. The form of the distribution is found for all K and the generalisation to M/G/1/K + 1 is discussed. The approach follows the contour integral method described by Cohen.