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Phase Structure of Segment Dependent NCS Model 2
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| The fundamental diagram on the right came from the same two segment road L = 200 divided into L1 = 160 and L2 = 40, but now with a common U = 8. The line for a common non-acceleration rate R1 = R2 = 0.1 is superimposed on the lines for three sets of different rates R1 = 0.1, R2 = 0.4 and R1 = 0.1, R2 = 0.6 and then R1 = 0.1, R2 = 0.8. |
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As before, we find partial jamming phase at intermediate density. But unlike before, it the fundamental diagram with differnt non-acceleration rates shows a wild fluctuation of F at this phase. Very intriguingly, the fluctuation is not really arbitrary, but F fluctuate only among several discrete values which are given by
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Fw = W /( W + 1 ), W=1, 2, ..., U2
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(6.2)
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The actual value of F at a given \rho is not decided until the precise initial configuration is specified and the actual sequence of "random number" used in acceleration is precisely specified. In other word, there is no unique F for a given \rho in a strict sense. Which value among "quantized" Fw is taken by F depends on accidental elements such as the initial condition and random numbers used.
This totally unexpected results should be greeted by reader's surprise. Irrespective to their physical origin, we conclude that Nishimura model with plural segments with different non-acceleration rate has the following properties :
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* showing three phases that are free traffic, partial jamming, and jamming phases
* at the free traffic, F (\rho) is an increasing linear function * at the jamming phase, F(\rho) is a linearly decreasing function * at the partial jamming phase, F(\rho) is indefinite and fluctuates |
(6.3)
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and these are consistent the results of the observaion of real-life traffic flow.
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