Hidden geometry of traffic jamming
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We introduce an approach based on algebraic topological methods that allow an accurate characterization of jamming in dynamical systems with queues. As a prototype system, we analyze the traffic of information packets with navigation and queuing at nodes on a network substrate in distinct dynamical regimes. A temporal sequence of traffic density fluctuations is mapped onto a mathematical graph in which each vertex denotes one dynamical state of the system. The coupling complexity between these states is revealed by classifying agglomerates of high-dimensional cliques that are intermingled at different topological levels and quantified by a set of geometrical and entropy measures. The free-flow, jamming, and congested traffic regimes result in graphs of different structure, while the largest geometrical complexity and minimum entropy mark the edge of the jamming region.
Source:Physical Review E, 2015, 91, 5
- Advanced analytical, numerical and analysis methods of applied fluid mechanics and complex systems (RS-174014)
- Research Agency of the Republic of Slovenia [P1-0044], European Communitys COST Action [TD1210 KNOWeSCAPE], CSIR (India) [03(1294)/13/EMR-II]