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Exact overflow asymptotics for queues with many Gaussian inputs. (English) Zbl 1041.60036
Summary: We consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

MSC:
60G15 Gaussian processes
60G70 Extreme value theory; extremal stochastic processes
60K25 Queueing theory (aspects of probability theory)
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