藉由將個體差異性引入一維微觀尺度的交通模型,我們同時定性與定量上分析個體差異性如何影響交通系統。我們發現在高密度的情況下存在適當個體差異性可以有效降低交通系統的不穩定度,並減緩塞車的現象。此外,我們藉由研究高密度車流如何在交通系統中傳播發現一個系統的發生塞車與否只和個體差異如何被選取有關,與個體差異如何在空間中分佈並無太大關連。最後,此理論所推導出的結果可以被拓展至其他具有同性質的交通模型上。

The individual difference, particularly in drivers’ distance perception, is introduced in the microscopic one-dimensional optimal velocity model to investigate its effect on the onset of the jamming instability seen in traffic systems. We show analytically and numerically that the individual difference helps to inhibit the traffic jam at high vehicle densities while it promotes jamming transition at low vehicle densities. In addition, the jamming mechanism is further investigated by tracking how the spatial disturbance travels through traffics. We find that the jamming instability is uniquely determined by the overall distribution of drivers' distance perception rather than the spatial ordering of vehicles. Finally, a generalized form of the optimal velocity function is considered to show the universality of the effect of the individual difference.

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Bando's Model . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Effect of Individual Difference . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Individual Difference . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 Linear Stability Analysis . . . . . . . . . . . . . . . . . . . . 9
3.1.2 Propagation of Disturbances . . . . . . . . . . . . . . . . . . 16
3.1.3 Irrelevance of Spatial Ordering of Vehicles . . . . . . . . . . 20
3.2 Universality of The Effect of Individual Difference . . . . . . . . . . 22
4 Phenomenon and Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 Hysteresis-like Phase Diagram . . . . . . . . . . . . . . . . . . . . . 25
4.2 Scattering Fundamental Diagram . . . . . . . . . . . . . . . . . . . 29
5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . 33
A. Calculation of Second Perturbation . . . . . . . . . . . . . . . . . . . 33
B. Calculation of Propagation Distribution . . . . . . . . . . . . . . . . . 33

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