Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues

A fluid queue with ON periods arriving according to a Poisson process and having a long-tailed distribution has long range dependence. As a result, its performance deteriorates. The extent of this performance deterioration depends on a quantity determined by the average values of the system parameters. In the case when the the performance deterioration is the most extreme, we quantify it by studying the time until the amount of work in the system causes an overflow of a large buffer. This turns out to be strongly related to the tail behavior of the increase in the buffer content during a busy period of the M/G/infinity queue feeding the buffer. A large deviation approach provides a powerful method of studying such tail behavior.