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