Cellular automata approach to three-phase traffic theory

The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a three-phase traffic theory proposed by Kerner. This is achieved by a synchronization distance, within which a vehicle always tries to adjust its speed to the one of the vehicle in front. In the CA models presented, the modelling of the free and safe speeds, the slow-to-start rules as well as some contributions to noise are based on the ideas of the Nagel-Schreckenberg type modelling. It is shown that the proposed CA models can be very transparent and still reproduce the two main types of congested patterns (the general pattern and the synchronized flow pattern) as well as their dependence on the flows near an on-ramp, in qualitative agreement with the recently developed continuum version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002. J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different than in previously considered CA traffic models. The probability of the breakdown phenomenon (i.e., of the phase transition from free flow to synchronized flow) as function of the flow rate to the on-ramp and of the flow rate on the road upstream of the on-ramp is investigated. The capacity drops at the on-ramp which occur due to the formation of different congested patterns are calculated.Comment: 55 pages, 24 figure

Physics of Autonomous Driving based on Three-Phase Traffic Theory

We have revealed physical features of autonomous driving in the framework of the three-phase traffic theory for which there is no fixed time headway to the preceding vehicle. A comparison with the classical model approach to autonomous driving for which an autonomous driving vehicle tries to reach a fixed (desired or "optimal") time headway to the preceding vehicle has been made. It turns out that autonomous driving in the framework of the three-phase traffic theory exhibits the following advantages in comparison with the classical model of autonomous driving: (i) The absence of string instability. (ii) Considerably smaller speed disturbances at road bottlenecks. (iii) Autonomous driving vehicles based on the three-phase theory decrease the probability of traffic breakdown at the bottleneck in mixed traffic flow consisting of human driving and autonomous driving vehicles; on the contrary, even a single autonomous driving vehicle based on the classical approach can provoke traffic breakdown at the bottleneck in mixed traffic flow.Comment: 5 pages, 4 figure

Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition

We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter region where the uniform solution is stable against a localized perturbation. We also found an oscillatory solution in the linearly unstable region and its period is not commensurate with the periodicity of the car index space. The oscillatory solution has some features in common with the synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp

The cubic chessboard

We present a survey of recent results, scattered in a series of papers that appeared during past five years, whose common denominator is the use of cubic relations in various algebraic structures. Cubic (or ternary) relations can represent different symmetries with respect to the permutation group S_3, or its cyclic subgroup Z_3. Also ordinary or ternary algebras can be divided in different classes with respect to their symmetry properties. We pay special attention to the non-associative ternary algebra of 3-forms (or ``cubic matrices''), and Z_3-graded matrix algebras. We also discuss the Z_3-graded generalization of Grassmann algebras and their realization in generalized exterior differential forms. A new type of gauge theory based on this differential calculus is presented. Finally, a ternary generalization of Clifford algebras is introduced, and an analog of Dirac's equation is discussed, which can be diagonalized only after taking the cube of the Z_3-graded generalization of Dirac's operator. A possibility of using these ideas for the description of quark fields is suggested and discussed in the last Section.Comment: 23 pages, dedicated to A. Trautman on the occasion of his 64th birthda

Mechanical restriction versus human overreaction triggering congested traffic states

A new cellular automaton (CA) traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to construct the condition of collision-free movement. The strict collision-free criterion imposed by the mechanical restrictions is softened in certain traffic situations, reflecting human overreaction. It is shown that the present model reliably reproduces most empirical findings including synchronized flow, the so-called {\it pinch effect}, and the time-headway distribution of free flow. The findings suggest that many free flow phenomena can be attributed to the platoon formation of vehicles ({\it platoon effect})Comment: 5 pages, 3 figures, to appear in PR

Microscopic features of moving traffic jams

Empirical and numerical microscopic features of moving traffic jams are presented. Based on a single vehicle data analysis, it is found that within wide moving jams, i.e., between the upstream and downstream jam fronts there is a complex microscopic spatiotemporal structure. This jam structure consists of alternations of regions in which traffic flow is interrupted and flow states of low speeds associated with "moving blanks" within the jam. Empirical features of the moving blanks are found. Based on microscopic models in the context of three-phase traffic theory, physical reasons for moving blanks emergence within wide moving jams are disclosed. Structure of moving jam fronts is studied based in microscopic traffic simulations. Non-linear effects associated with moving jam propagation are numerically investigated and compared with empirical results.Comment: 19 pages, 12 figure