The first mathematical model of traffic flow in the framework of Kerner s three-phase theory that mathematical simulations can show and explain traffic breakdown by an F ?
12.
Some months later, Kerner, Klenov, and Wolf developed a cellular automaton ( CA ) traffic flow model in the framework of Kerner s three-phase theory.
13.
The set 1 4 of the fundamental empirical features of traffic breakdown at a highway bottleneck has first been explained in Kerner s three-phase theory ( Figure 3 ).
14.
Thus the space gap g in car following in the framework of Kerner s three-phase theory can be any space gap within the space gap range g _ \ text { safe } \ leq g \ leq G.
15.
Once they have that key, they progressively gain access to the whole grammatical system of their language, because it is based on a single organizing binary principle ( cf . preceding paragraph, The two-phase theory or the ?double-keyboard theory ?).
16.
In Sec . 6.1 of the book has been shown that the traffic phase definitions [ " S " ] and [ " J " ] are the origin of most hypotheses of three-phase theory and related three-phase microscopic traffic flow models.
17.
In particular, new mathematical models in the framework of Kerner s three-phase theory have been introduced in the works by Jiang, Wu, Gao, et al .,, Davis, Lee, Barlovich, Schreckenberg, and Kim ( see other references to mathematical models in the framework of Kerner s three-phase traffic theory and results of their investigations in Sec . 1.7 of a review ).
18.
In accordance with this hypothesis of Kerner s three-phase theory, at a given speed in synchronized flow, the driver can make an " arbitrary choice " as to the space gap to the preceding vehicle, within the range associated with the 2D region of homogeneous synchronized flow ( Figure 4 ( b ) ) : the driver accepts different space gaps at different times and does not use some one unique gap.
19.
In Kerner s three-phase theory, a vehicle accelerates when the space gap g to the preceding vehicle is greater than a synchronization space gap G, i . e ., at g > G ( labelled by " acceleration " in Figure 5 ); the vehicle decelerates when the gap " g " is smaller than a safe space gap g _ \ text { safe }, i . e ., at g ( labelled by " deceleration " in Figure 5 ).
20.
Figure 3 : Explanations of the fundamental empirical features of traffic breakdown at a highway bottleneck with Kerner s three-phase theory : ( a, b ) Simulations of spontaneous ( a ) and induced ( b ) traffic breakdowns at a highway bottleneck . ( c ) Simulated flow-rate dependence of probability of traffic breakdown at a highway bottleneck . ( d ) Qualitative Z-characteristic for highway traffic in the speed flow-rate plane ( arrow is related to an " F " ?! " S " transition ); bottleneck states labeled by circles F and S are related to free flow and synchronized flow.
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