Non-Equilibrium Statistical Physics of Currents in Queuing Networks
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...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer Netherlands
2012
|
| Online Access: | http://hdl.handle.net/1721.1/69099 https://orcid.org/0000-0002-7997-8962 |
| _version_ | 1826202140816703488 |
|---|---|
| author | Chernyak, Vladimir Y. Chertkov, Michael Goldberg, David A. Turitsyn, Konstantin |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Chernyak, Vladimir Y. Chertkov, Michael Goldberg, David A. Turitsyn, Konstantin |
| author_sort | Chernyak, Vladimir Y. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:02:30Z |
| format | Article |
| id | mit-1721.1/69099 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:02:30Z |
| publishDate | 2012 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/690992022-10-01T07:46:19Z Non-Equilibrium Statistical Physics of Currents in Queuing Networks Chernyak, Vladimir Y. Chertkov, Michael Goldberg, David A. Turitsyn, Konstantin Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Operations Research Center Turitsyn, Konstantin Goldberg, David A. Turitsyn, Konstantin 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. 2012-02-14T15:01:55Z 2012-02-14T15:01:55Z 2010-07 2010-01 Article http://purl.org/eprint/type/JournalArticle 0022-4715 1572-9613 http://hdl.handle.net/1721.1/69099 Chernyak, Vladimir Y. et al. “Non-Equilibrium Statistical Physics of Currents in Queuing Networks.” Journal of Statistical Physics 140.5 (2010): 819-845. https://orcid.org/0000-0002-7997-8962 en_US http://dx.doi.org/10.1007/s10955-010-0018-5 Journal of Statistical Physics Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer Netherlands Prof. Turitsyn via Angie Locknar |
| spellingShingle | Chernyak, Vladimir Y. Chertkov, Michael Goldberg, David A. Turitsyn, Konstantin Non-Equilibrium Statistical Physics of Currents in Queuing Networks |
| title | Non-Equilibrium Statistical Physics of Currents in Queuing Networks |
| title_full | Non-Equilibrium Statistical Physics of Currents in Queuing Networks |
| title_fullStr | Non-Equilibrium Statistical Physics of Currents in Queuing Networks |
| title_full_unstemmed | Non-Equilibrium Statistical Physics of Currents in Queuing Networks |
| title_short | Non-Equilibrium Statistical Physics of Currents in Queuing Networks |
| title_sort | non equilibrium statistical physics of currents in queuing networks |
| url | http://hdl.handle.net/1721.1/69099 https://orcid.org/0000-0002-7997-8962 |
| work_keys_str_mv | AT chernyakvladimiry nonequilibriumstatisticalphysicsofcurrentsinqueuingnetworks AT chertkovmichael nonequilibriumstatisticalphysicsofcurrentsinqueuingnetworks AT goldbergdavida nonequilibriumstatisticalphysicsofcurrentsinqueuingnetworks AT turitsynkonstantin nonequilibriumstatisticalphysicsofcurrentsinqueuingnetworks |