Outputs (3)

Periodicity in the transient regime of exhaustive polling systems (2006)
Journal Article
MacPhee, I., Menshikov, M., Popov, S., & Volkov, S. (2006). Periodicity in the transient regime of exhaustive polling systems. Annals of Applied Probability, 16(4), 1816-1850. https://doi.org/10.1214/105051606000000376

We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the sequence of nodes... Read More about Periodicity in the transient regime of exhaustive polling systems.

Positive recurrence of processes associated to crystal growth models (2006)
Journal Article
Andjel, A., Menshikov, M., & Sisko, V. (2006). Positive recurrence of processes associated to crystal growth models. Annals of Applied Probability, 16(3), 1059-1085. https://doi.org/10.1214/105051606000000079

We show that certain Markov jump processes associated to crystal growth models are positive recurrent when the parameters satisfy a rather natural condition.

Random walk in random environment with asymptotically zero perturbation (2006)
Journal Article
Menshikov, M., & Wade, A. (2006). Random walk in random environment with asymptotically zero perturbation. Journal of the European Mathematical Society, 8(3), 491-513. https://doi.org/10.4171/jems/64

We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on $\Z^+=\{0,1,2,\ldots\}$, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results comp... Read More about Random walk in random environment with asymptotically zero perturbation.