On a random interval graph and the maximum throughput rate in the system GI/G/1/0

摘要

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/GI1/0, under the assumption of perfect information regarding the sequences {X,, 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, T1 + Y), i = 1,2,... }, in which { I} denotes the sequence of arrival epochs.