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Exact asymptotics for a queue with fractional Brownian input and applications in ATM networks. (English) Zbl 1001.60042
A single channel FIFO fluid queue with an infinite buffer space and fractional Brownian input is studied. A pair of lower and upper bounds is obtained for the tail distribution of the transient queue length resulting in a logarithmic characterization of the tail distribution. The exact asymptotics for the transient queue-length tail distribution is also obtained.

MSC:
60G18 Self-similar stochastic processes
60G70 Extreme value theory; extremal stochastic processes
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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