4 papers
On large queue lengths in generalised Jackson networks
Anatolii A. Puhalskii
This paper proves a large deviation principle (LDP) for the stationary distribution of queue lengths in a subcritical generalised Jackson network assuming a Cramer condition on the…
On tightness and exponential tightness in generalised Jackson networks
A. Puhalskii
We give uniform proofs of tightness and exponential tightness of the sequences of stationary queue lengths in generalised Jackson networks in a number of setups which concern large…
A diffusion limit for Markov chains with log-linear interaction on a graph
Anatolii Puhalskii, Vadim Shcherbakov
In this paper we establish a diffusion limit for a multivariate continuous time Markov chain whose components are indexed by vertices of a finite graph. The components take values…
The geometry of big queues
Anatolii Puhalskii
We use Hamilton equations to find optimal paths to big queues in Jackson networks. They are shown to be given by fluid trajectories of the dual network. The fluid equations are sho…