14 research outputs found
Poisson Hypothesis for Information Networks II. Cases of Violations and Phase Transitions
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 transience property
Stationary States of the Generalized Jackson Networks
We consider Jackson Networks on general countable graphs and with arbitrary
service times. We find natural sufficient conditions for existence and
uniqueness of stationary distributions. They generalise these obtained earlier
by Kelbert, Kontsevich and Rybko.Comment: 18 pages, minor change
Poisson Hypothesis for information networks (A study in non-linear Markov processes)
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 corresponding dynamical systems, defined by the non-linear
Markov processes, have a line of fixed points which are global attractors. To
do this we derive the corresponding non-linear integral equation and we explore
its self-averaging properties. Our derivation relies on a solution of a
combinatorial problem of rode placements.Comment: 70 page
Spontaneous Resonances and the Coherent States of the Queuing Networks
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 continuous symmetry breaking at low temperatures
in statistical mechanics. The role of the inverse temperature is played by the
average load.Comment: 3 figures added, small correction
Phase transitions in the queuing networks and the violation of the Poisson hypothesis
International audienc
Absence of Breakdown of the Poisson Hypothesis I. Closed Networks at Low Load
International audienceWe 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 size. This is a "high-temperature" counterpart of our earlier result, where we have shown that at high load the relaxation time can diverge with the size of the network ("low-temperature"). In other words, the phase transitions in the networks can happen at high load, but cannot take place at low load