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math-ph2004
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…
math-ph2003★ 5 cited
Poisson Hypothesis for information networks (A study in non-linear Markov processes)
Alexander Rybko, Senya Shlosman
In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the correspond…