The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/G/1/0, under the assumption of perfect information regarding the sequences {Xi, i = 1, 2, ·· ·} and {Yi, i = 1, 2, ·· ·} of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, Ti + Yi), i = 1, 2, ·· ·}, in which {Ti} denotes the sequence of arrival epochs.
