15 research outputs found
On many-server queues in heavy traffic
We establish a heavy-traffic limit theorem on convergence in distribution for
the number of customers in a many-server queue when the number of servers tends
to infinity. No critical loading condition is assumed. Generally, the limit
process does not have trajectories in the Skorohod space. We give conditions
for the convergence to hold in the topology of compact convergence. Some new
results for an infinite server are also provided.Comment: Published in at http://dx.doi.org/10.1214/09-AAP604 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Moderate Deviations for Queues in Critical Loading
We establish logarithmic asymptotics of moderate deviations for the processes of queue length and waiting times in single server queues and open queueing networks in critical loading. Our results complement earlier heavy-traffic approximation results
Large deviation limits of invariant measures
This paper is concerned with the general theme of relating the Large
Deviation Principle (LDP) for the invariant measures of stochastic processes to
the associated sample path LDP. It is shown that if the sample path deviation
function possesses certain structure, then the LDP for the invariant measures
is implied by the sample path LDP, no other properties of the stochastic
processes in question being material. As an application, we obtain an LDP for
the stationary distributions of jump diffusions. Methods of large deviation
convergence and idempotent probability play an integral part