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Non-Equilibrium Statistical Physics of Currents in Queuing Networks
- Source :
- Prof. Turitsyn via Angie Locknar
- Publication Year :
- 2010
- Publisher :
- arXiv, 2010.
-
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.<br />Comment: 26 pages, 5 figures
- Subjects :
- FOS: Computer and information sciences
Phase transition
Computer Science - Information Theory
Markov process
FOS: Physical sciences
Scale (descriptive set theory)
Type (model theory)
Expected value
01 natural sciences
010104 statistics & probability
symbols.namesake
0103 physical sciences
FOS: Mathematics
Statistical physics
0101 mathematics
010306 general physics
Mathematical Physics
Condensed Matter - Statistical Mechanics
Physics
Queueing theory
Statistical Mechanics (cond-mat.stat-mech)
Information Theory (cs.IT)
Condensation
Probability (math.PR)
Statistical and Nonlinear Physics
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Condensed Matter - Disordered Systems and Neural Networks
symbols
Node (circuits)
Mathematics - Probability
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Prof. Turitsyn via Angie Locknar
- Accession number :
- edsair.doi.dedup.....5b1e549bfd83b5337ec9c1144cee9ce6
- Full Text :
- https://doi.org/10.48550/arxiv.1001.5454