21 citations · 32 across the 7 of their papers we have counts for
7 papers
Recombination processes and non-linear Markov chains
Sergey Pirogov, Aleksandre Rybko, Anastasia Kalinina +1
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity of recombining segments, s…
Stationary States of the Generalized Jackson Networks
Alexander Rybko, Senya Shlosman
We consider Jackson Networks on general countable graphs and with arbitrary service times. We find natural sufficient conditions for existence and uniqueness of stationary distribu…
Absence of Breakdown of the Poisson Hypothesis I. Closed Networks at Low Load
Alexander Rybko, Senya Shlosman, Alexander Vladimirov
We prove that the general mean-field type networks at low load behave in accordance with the Poisson Hypothesis. That means that the network equilibrates in time independent of its…
Spontaneous Resonances and the Coherent States of the Queuing Networks
Alexander Rybko, Senya Shlosman, Alexander Vladimirov
We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the…
Poisson Hypothesis for Information Networks II. Cases of Violations and Phase Transitions
Alexander Rybko, Senya Shlosman
We present examples of queuing networks that never come to equilibrium. That is achieved by constructing Non-linear Markov Processes, which are non-ergodic, and possess eternal tra…
Poisson Hypothesis for Information Networks (A study in non-linear Markov processes) I. Domain of Validity
A. Rybko, S. Shlosman
In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queueing networks. We prove it in some simple limiting cases. We sho…