Conditional limit theorems for queues with Gaussian input, a weak convergence approach
- Dieker, A.B.
DOIAbstract
AbstractWe consider a buffered queueing system that is fed by a Gaussian source and drained at a constant rate. The fluid offered to the system in a time interval (0,t] is given by a separable continuous Gaussian process Y with stationary increments. The variance function σ2:t↦VarYt of Y is assumed to be regularly varying with index 2H, for some 0<H<1.By proving conditional limit theorems, we investigate how a high buffer level is typically achieved. The underlying large deviation analysis also enables us to establish the logarithmic asymptotics for the probability that the buffer content exceeds u as u→∞. In addition, we study how a busy period longer than T typically occurs as T→∞, and we find the logarithmic asymptotics for the probabili...
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