770 research outputs found
Optimal Paths in Large Deviations of Symmetric Reflected Brownian Motion in the Octant
We study the variational problem that arises from consideration of large
deviations for semimartingale reflected Brownian motion (SRBM) in the positive
octant. Due to the difficulty of the general problem, we consider the case in
which the SRBM has rotationally symmetric parameters. In this case, we are able
to obtain conditions under which the optimal solutions to the variational
problem are paths that are gradual (moving through faces of strictly increasing
dimension) or that spiral around the boundary of the octant. Furthermore, these
results allow us to provide an example for which it can be verified that a
spiral path is optimal. For rotationally symmetric SRBM's, our results
facilitate the simplification of computational methods for determining optimal
solutions to variational problems and give insight into large deviations
behavior of these processes
Tandem queueing networks with neighbor blocking and back-offs
We introduce a novel class of tandem queueing networks which arise in modeling the congestion behavior of wireless multi-hop networks with distributed medium access control. These models provide valuable insight in how the network performance in terms of throughput depends on the back-off mechanism that governs the competition among neighboring nodes for access to the medium. The models fall at the interface between classical queueing networks and interacting particle systems, and give rise to high-dimensional stochastic processes that challenge existing methodologies. We present various open problems and conjectures, which are supported by partial results for special cases and limit regimes as well as simulation experiments
Concentration of measure and mixing for Markov chains
We consider Markovian models on graphs with local dynamics. We show that,
under suitable conditions, such Markov chains exhibit both rapid convergence to
equilibrium and strong concentration of measure in the stationary distribution.
We illustrate our results with applications to some known chains from computer
science and statistical mechanics.Comment: 28 page
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