论文标题
两条车道交通中的固定状态：动力学理论的见解
Stationary states in two lane traffic: insights from kinetic theory
论文作者
论文摘要
Ben-Naim Krapivsky模型的框架中制定了两条车道道路上稀释的异质交通的动力学，并且在渐近极限中分析得出固定状态性能。异质性以所需速度的车辆速度引入。该模型假设车道中的每个车辆/排在弹道上移动，直到它接近移动的车辆/排，然后加入。假定排中的车辆通过更换车道以恒定的速度逃脱排。假定每个车道具有不同的逃生率。随着固定状态的接近，两个车道的排密度相等，而车道的车辆密度和通量在车道上较高，较低的逃逸速率。如果车道的逃逸率的谐波平均值与道路上的平均初始通量相当，则大多数车辆都可以自由流动。平均排大小接近自由流程中的统一。如果谐波平均值低于平均初始通量，那么所需速度的车辆低于特征速度$ v^*$仍然可以享受自由流动，而这些速度大于$ v^*$体验的速度的车辆在较慢的车辆后面形成了Platoons。特征速度取决于两个车道（1和-1代表）的逃逸时间$（r_1+r _ { - 1}）/2）$，为$ v^* \ sim r^{ - \ sim r^{ - \ frac {1} {1} {μ+2}}} $，其中$μ$ limim限制了quine desept fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen fepen desceend nibe desceent in desceend fepen fepen。当$ v^* \ ll 1 $时，车道中的平均排大小与$ r^{\ frac {μ+1} {μ+2}} $和车道依赖性校正成正比。还研究了排两个车道交通的排尺寸分布的方程式。结果表明，只有在平均逃逸率独立于排尺寸的情况下，只有在平均逃逸率独立的情况下才会发生排行管的固定状态。
Kinetics of dilute heterogeneous traffic on a two lane road is formulated in the framework of the Ben-Naim Krapivsky model and stationary state properties are analytically derived in the asymptotic limit. The heterogeneity is introduced as a quenched disorder in desired speeds of vehicles. The model assumes that each vehicle/platoon in a lane moves ballistically until it approaches a slow moving vehicle/platoon and then joins it. Vehicles in a platoon are assumed to escape the platoon at a constant rate by changing lanes. Each lane is assumed to have a different escape rate. As the stationary state is approached, the platoon density in the two lanes become equal, whereas the vehicle densities and fluxes are higher in the lane with lower escape rate. A majority of the vehicles enjoy a free-flow if the harmonic mean of the escape rates of the lanes is comparable to average initial flux on the road. The average platoon size is close to unity in the free-flow regime. If the harmonic mean is lower than the average initial flux, then vehicles with desired speeds lower than a characteristic speed $v^*$ still enjoy free-flow while those vehicles with desired speeds that are greater than $v^*$ experience congestion and form platoons behind the slower vehicles. The characteristic speed depends on the mean of escape times $(R=(R_1+R_{-1})/2)$ of the two lanes (represented by 1 and -1) as $v^* \sim R^{-\frac{1}{μ+2}}$, where $μ$ is the exponent of the quenched disorder distribution for desired speed in the small speed limit. The average platoon size in a lane, when $v^* \ll 1$, is proportional to $R^{\frac{μ+1}{μ+2}}$ plus a lane dependent correction. Equations for the kinetics of platoon size distribution for two-lane traffic are also studied. It is shown that a stationary state with platoons as large as road length can occur only if the mean escape rate is independent of platoon size.
