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Research Papers

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

[+] Author and Article Information
Da Yang

School of Transportation and Logistics,
Southwest Jiaotong University,
111 Erhuanlubeiyiduan,
Chengdu 610031, China
e-mail: yangd8@gmail.com

Liling Zhu

School of Transportation and Logistics,
Southwest Jiaotong University,
111 Erhuanlubeiyiduan,
Chengdu 610031, China
e-mail: zll412@126.com

Yun Pu

School of Transportation and Logistics,
Southwest Jiaotong University,
111 Erhuanlubeiyiduan,
Chengdu 610031, China
e-mail: wdyang.111@163.com

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received April 11, 2013; final manuscript received October 23, 2013; published online February 11, 2015. Assoc. Editor: Dr. Corina Sandu.

J. Comput. Nonlinear Dynam 10(3), 031001 (May 01, 2015) (10 pages) Paper No: CND-13-1078; doi: 10.1115/1.4025896 History: Received April 11, 2013; Revised October 23, 2013; Online February 11, 2015

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

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Figures

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Fig. 1

An example of the heterogeneous traffic flow consisting of the four types of driver

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Fig. 2

Influence of the parameters in the HEOV model on the traffic flow stability

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Fig. 3

The relationship of the stationary velocity and the stability function of the heterogeneous traffic flow

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Fig. 4

The headway development plots against time and vehicle number. (a) The case of v* = 2.0, and (b) the case of v* = 2.2.

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Fig. 5

The stability functions of the four types of driver with respect to the stationary velocity

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Fig. 6

(a) The headway development against the vehicle number and time, and (b) the wave trough of the first traffic wave

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Fig. 7

The trajectories: (a) the traffic flow including 20 S-C drivers, 15 S-IC drivers, 35 IS-C drivers, and 30 IS-IC drivers, (b) the traffic flow including 1 S-C driver, 1 S-IC driver, 1 IS-C driver, and 97 IS-IC drivers

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Fig. 8

The trajectories: (a) the traffic flow including 10 S-C drivers, 20 S-IC drivers, 30 IS-C drivers, and 40 IS-IC drivers, and (b) the traffic flow including 97 S-C drivers, 1 S-IC driver, 1 IS-C driver, and 1 IS-IC driver

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Fig. 9

(a) The values of the stability function of the heterogeneous traffic flow, and (b) the neutral stability line when pS-IC = 0.5

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Fig. 10

The headway plots: (a) the unstable case when pS-C = 6%, and (b) the stable case when pS-C = 7%

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Fig. 11

The trajectories: (a) the case of the narrow parameter range Vmax∈[3.5,4] and (b) the case of the wide parameter range Vmax∈[2.1,4]

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