Exact asymptotics for nonlinear large deviations of a queue in a network
We
are interested in estimating the probability of rare events in queueing
networks described as a Markov chain. Unless the stationary
distribution can be explicitly computed, such results are usually
difficult to obtain even by simulation. In particular the rare event
where one queue of interest gets large can occur in a variety ways.
Here
we develop an new approach to deriving exact asymptotics that allows us
to analyze situations where the fluid limit of excursions to the rare
event is nonlinear. These so called cascade paths arise when customers
first overload another queue and then cascade over into the queue of
interest which in turn overloads.