Invariant rate functions for discrete-time queues (Q1413674)

The paper considers a discrete-time queueing model. The queue has arrival process \(\{A_n, n\in\mathbb{Z}\}\), where \(A_n\) denotes the amount of work arriving in the \(n\)th time slot. Let \(S_n\) be the maximum amount of work that can be completed in the \(n\)th time slot. The processes \(\{A_n\}\) and \(\{S_n\}\) are assumed to be stationary and ergodic sequences of positive real random variables. Assuming the service process satisfies a sample path large deviation principle, the authors identify a class of arrival processes that have sample path large deviation behaviour that is preserved by the queue. Also, they establish a large deviation analogue of quasi-reversibility for this class of arrival processes.