Asymptotic results for buffer systems under heavy load

This paper considers a dam (or storage) model of the GI/G/I type with a finite capacity K. An arriving input being larger than the unfilled capacity of the dam causes an overflow where the excess amount is lost. Important performance measures for this system are the overflow probability and the long-run fraction of input that is lost. We give asymptotic expansions for these measures for large K both for the case of a load factor less than 1 and for the case of a load factor larger than 1. Also, related results are obtained for the impatient customer model of the M/G/l type.