Alternative Models 3
Model of Nishimura, Cheon and Seba
Pushing the motivational argument aside, for a moment, we present one of our model first. Going back to the stage of introducing the model by Nagel and Schreckenberg, we consider a traffic model specified by the following three set rules
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* A car increases its velocity by one unitunless it exceeds the give speed limit U.
* A car decreases its velocity by one unit at random ocasion with a given probability R.
* If a car with current velocity is projected to cause collision with the preceeding car, it decreases its velocity down to the point of avoiding the collision.
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(5.1)
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We see that these rules are all exactly identical to the ones for Nagel-Schreckenberg. The only difference is in the ordering of the second and third rules which are now reversed. Looking the the first two rules, it is almost identical to having one step acceleration with probability (1-R), apart from the case where the car is already in the speed limit at the first step. Assuming that the difference in the treatment of this exceptional case makes no big difference to the overall results, we replace the above rule by a simplified rules of traffic flow evolution:
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* A car increases its velocity by one unit with probability (1-R) within the speed limit U.
* A car decreases its velocity by one unit at random ocasion with a given probability R.
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(5.2)
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Just as before, additing the rule to change the positions X[i] after the determination of the velocitis V[i], we obtain now three rules as the updating scheme ( X[i] \to X'[i] , V[i] \to V'[i] )
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1) V[i] \to V'[i] = min( U, V[i]+1) with probability (1-R)
2) if ( X[i]+V[i] >= X[i+1] ) then V[i] \to V'[i] = X[i+1]-X[i]-1
3) X[i] \to X'[i] = X[i]+V'[i]
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(5.3)
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This model is proposed by Nishimura, Cheon and Seba, which we hereafter refer to as Nishimura model for briefness' sake. It is a seemingly very slight variant of the standard model, on we stress however that it is rather a simplification, not the ellaboration of the standard model.
There is no difference between the standard model and Nishimura model for R = 0. Also, when the car density is low, the breaking by the recognition of the preceeding car is not triggered so often, and then there will be no difference between the two models again.
The difference is mainly felt when a car is at the inside of a jamming block: In standard model, there will be ocasional decerelation. In Nishimura model, however, that is suppressed because of the construction of the rule. If you examin the drivers' behavior in real-life traffic, you find that while in the jam, the drivers are less succeptible to sudden speed down. This is so both to avoid the accidents in the trffic, and so because to avoid the breaking in of the other cars. So we might even think that Nishimura model capture the drivers' behavior in a better fashion
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