Name
Abstract | ||
|---|---|---|
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely
specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition rates between
nodes. For such systems, we ask the question “What is the most likely way for large currents to accumulate over time in a
network ?”, where time is large compared to the system correlation time scale. We identify two interesting regimes. In the
first regime, in which the accumulation of currents over time exceeds the expected value by a small to moderate amount (moderate
large deviation), we find that the large-deviation distribution of currents is universal (independent of the interaction details),
and there is no long-time and averaged over time accumulation of particles (condensation) at any nodes. In the second regime,
in which the accumulation of currents over time exceeds the expected value by a large amount (severe large deviation), we
find that the large-deviation current distribution is sensitive to interaction details, and there is a long-time accumulation
of particles (condensation) at some nodes. The transition between the two regimes can be described as a dynamical second order
phase transition. We illustrate these ideas using the simple, yet non-trivial, example of a single node with feedback. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10955-010-0018-5 | Journal of Statistical Physics |
Keywords | Field | DocType |
Statistics of non-equilibrium currents,Open queueing networks,Condensation phenomenon,Birth-death processes | Statistical physics,Markov process,Phase transition,Current distribution,Mathematical analysis,Condensation,Expected value,Queueing theory,Moderate amount,Mathematics,Fold (higher-order function) | Journal |
Volume | Issue | ISSN |
140 | 5 | 0022-4715 |
Citations | PageRank | References |
1 | 0.38 | 13 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vladimir Y. Chernyak | 1 | 173 | 14.84 |
| Michael Chertkov | 2 | 465 | 59.33 |
| David A. Goldberg | 3 | 21 | 2.32 |
| Konstantin Turitsyn | 4 | 1 | 1.40 |