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- Title
Simple stochastic model with safe speed using Exchange approach to recognizing synchronized flow as speed-synchronized phase.
- Authors
Fukuichi, Masayuki
- Abstract
In order to unravel the physical and mathematical mystery of synchronized-flow mechanism and to reveal the fundamental mechanism and origin of synchronized flow produced by nonlinear stochastic processes, we have produced simple stochastic traffic flow models (the gradual-NaSch, Phoenix and mPhoenix models) with nonlinear safe speeds. In the mNaSch model and our gradual-NaSch model, the i th vehicle's speed is the same as or different from the j th vehicle's speed because they are discrete values. In the mNaSch and gradual-NaSch models, the same discrete values of the i th and j th states make it easy to identify synchronized flow with speed-synchronized phase of the i th and j th states. On the other hand, when we deal with synchronized flow in continuous traffic flow models, we face a problem. Continuous values cause the difficulty in identification of synchronization. In order to definitely clarify whether or not synchronized flow occurs in continuous models, we have established a novel idea of Exchange approach to recognizing synchronized flow as speed-synchronized phase. Our idea is generated from the analogical image that the whole system of synchronized metronomes does not change even if the i th and j th synchronized metronomes are exchanged. The Exchange approach (exchanging the i th vehicle's state for any j th vehicle's state in the whole system of traffic flow), which causes distortion such as a collision if non-synchronized vehicle's states are exchanged and makes it possible to definitely clarify whether or not synchronized flow occurs in continuous models, is applied to our simple stochastic continuous model (the mPhoenix model). On the basis of the Exchange approach, we can recognize that the mPhoenix model surely reproduces synchronized flow. In addition, we have proposed mathematical approach to deriving nonlinear safe speeds which guarantee collision free driving and reproduce synchronized flow.
- Subjects
STOCHASTIC models; TRAFFIC flow; SPEED; STOCHASTIC processes; PHASE transitions
- Publication
International Journal of Modern Physics C: Computational Physics & Physical Computation, 2024, Vol 35, Issue 6, p1
- ISSN
0129-1831
- Publication type
Article
- DOI
10.1142/S0129183124500761