Effect of individual differences on the jamming transition in traffic flow

Yi-Chieh Lai and Kuo-An Wu

Phys. Rev. E 104, 014311 – Published 23 July 2021

Abstract

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.

Received 8 February 2021
Revised 17 June 2021
Accepted 12 July 2021

DOI:https://doi.org/10.1103/PhysRevE.104.014311

Physics Subject Headings (PhySH)

Collective behavior Complex systems Jamming Traffic

Collective dynamics Living matter & active matter Self-propelled particles

Statistical Physics & ThermodynamicsNonlinear DynamicsGeneral PhysicsInterdisciplinary Physics

Authors & Affiliations

Yi-Chieh Lai and Kuo-An Wu ^*

Department of Physics, National Tsing Hua University, 30013 Hsinchu, Taiwan

^*kuoan@phys.nthu.edu.tw

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Issue

Vol. 104, Iss. 1 — July 2021

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Images

Figure 1
Phase diagram of the traffic system. Note that $τ_{0}$ is the threshold value of the relaxation time when the individual difference is absent (i.e., $σ = 0$ ). The black line plots the neutral stability boundary of Eq. (24). Solid green squares and solid blue triangles represent the jammed and unjammed state, respectively, predicted from Eq. (24). Red circles are the simulation results of Eq. (9), which is consistent with the prediction obtained by solving the eigenvalue problem (not shown) of the coupled Eqs. (16). One hundred realizations of Gaussian random fields are carried out for each simulation data point. The phase diagram is obtained for $N / L = 1$ , $h = 2$ , and $N = 512$ .
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Figure 2
A log-log plot of simulation results of the deviation of $1 / τ$ from $1 / τ_{0}$ as a function of $σ / {\tilde{w}}_{0}$ for various global vehicle densities ranging from $N / L = 0.2$ to $N / L = 1$ . The simulation results are well fitted by a power-law relation with an exponent of 2. The simulation results are obtained with parameters $h = 2$ and $N = 512$ .
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Figure 3
Plot of the coefficient $β$ as a function of $γ$ for different values of $h$ . $β$ is always negative at high vehicle densities, which inhibits the jamming transition, while $β$ becomes positive at low vehicle densities, which promotes the jamming transition. The value of $h$ characterizes the rate change of the velocity function as the headway changes, which uniquely determines the critical vehicle density at which $β = 0$ .
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Figure 4
The amplitude of the slowest decaying eigenvector over time for simulations of 16 vehicles, $N / L = 1$ , $σ / {\tilde{w}}_{0} = 0.176$ , and $τ = 1.096$ in the unjammed region. Six different spatial configurations are generated by reshuffling the ordering of vehicles. Different symbols represent different configurations. Note that the amplitude oscillates with time, and only the peak values are shown.
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Figure 5
Phase diagram of the traffic system shown in Eq. (32). The black line plots the neutral stability boundary of Eq. (34) for $Cov (w, g) = 0$ , and solid green squares and solid blue triangles represent the jammed and unjammed states, respectively. Numerical simulations of Eq. (32) for $Cov (w, g) = 0$ are shown in red circles. Orange diamonds and dotted line represent the result of simulations and analytical results, respectively, for the scenario where $w_{n} = g_{n}$ . One hundred realizations of Gaussian random fields are carried out for each simulation data point. The phase diagram is obtained for $R = 1$ , $λ = 1$ , $N / L = 1$ , $h = 2$ , and $N = 256$ .
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