Sample-path large deviations for tandem and priority queues with Gaussian inputs.

Abstract.
This paper considers Gaussian flows multiplexed in a queueing network. A single node
being a useful but often incomplete setting, we examine more advanced models. We focus
on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service
rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large
deviations theorem can be applied to calculate the asymptotics of the overflow probability
of the second queue. More specifically, we derive a lower bound on the exponential decay
rate of this overflow probability and present an explicit condition for the lower bound to
match the exact decay rate. Examples show that this condition holds for a broad range
of frequently-used Gaussian inputs. The last part of the paper concentrates on a model
for a single node, equipped with a priority scheduling policy. We show that the analysis
of the tandem queue directly carries over to this priority queueing system.
Key words: sample-path large deviations; Gaussian traffic ;Schilder's theorem ;Tandem queue; Priority queue; Communication networks; Differentiated services
Short title: Tandem and priority queues
Subject classifications: primary 60K25; secondary 60F10, 60G15