Abstract
This paper analyzes transient characteristics of Gaussian queues. More specifically, we determine the logarithmic asymptotics of ℙ(Q 0>pB,Q TB >qB), where Q t denotes the workload at time t. For any pair (p,q), three regimes can be distinguished: (A) For small values of T, one of the events {Q 0>pB} and {Q TB >qB} will essentially imply the other. (B) Then there is an intermediate range of values of T for which it is to be expected that both {Q 0>pB} and {Q TB >qB} are tight (in that none of them essentially implies the other), but that the time epochs 0 and T lie in the same busy period with overwhelming probability. (C) Finally, for large T, still both events are tight, but now they occur in different busy periods with overwhelming probability. For the short-range dependent case, explicit calculations are presented, whereas for the long-range dependent case, structural results are proven.
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