Sai Venkata Ramana A, Jabari Saif Eddin
New York University Abu Dhabi, Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates.
New York University Tandon School of Engineering, Brooklyn, New York, USA.
Phys Rev E. 2022 Jul;106(1-1):014113. doi: 10.1103/PhysRevE.106.014113.
Kinetics of dilute heterogeneous traffic on a two-lane road is formulated in the framework of Ben-Naim-Krapivsky model and stationary state properties are analytically derived in the asymptotic limit. The heterogeneity is introduced into the model as a quenched disorder in desired speeds of vehicles. The two-lane model assumes that each vehicle or platoon in a lane moves ballistically until it approaches a slow-moving vehicle or platoon and then joins it. Vehicles in a platoon are assumed to escape the platoon at a constant rate by changing lanes after which they continue to move at their desired speeds. Each lane is assumed to have a different escape rate. As the stationary state is approached, the platoon densities 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^{}∼R^{-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^{}≪1, is proportional to R^{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.
在Ben-Naim-Krapivsky模型的框架下，建立了双车道道路上稀疏散异交通流的动力学模型，并在渐近极限下解析推导了稳态特性。将异质性作为车辆期望速度的淬火无序引入模型。双车道模型假设，车道中的每辆车或车队以弹道方式移动，直到接近慢速行驶的车辆或车队，然后加入其中。车队中的车辆假定以恒定速率通过变道逃离车队，之后它们继续以期望速度行驶。假定每条车道有不同的逃离速率。当接近稳态时，两条车道中的车队密度变得相等，而在逃离速率较低的车道中，车辆密度和通量更高。如果车道逃离速率的调和平均值与道路上的平均初始通量相当，那么大多数车辆享受自由流。在自由流状态下，平均车队规模接近1。如果调和平均值低于平均初始通量，那么期望速度低于特征速度v的车辆仍享受自由流，而期望速度大于v的车辆则经历拥堵，并在较慢车辆后面形成车队。特征速度取决于两条车道（用1和 -1表示）的逃逸时间均值[R=(R₁ + R₋₁)/2]，即v*∼R⁻¹/μ⁺²，其中μ是小速度极限下期望速度的淬火无序分布的指数。当v*≪1时，车道中的平均车队规模与R^(μ + 1/μ + 2)成正比，再加上一个与车道有关的修正项。还研究了双车道交通流中车队规模分布的动力学方程。结果表明，只有当平均逃逸速率与车队规模无关时，才会出现车队长度与道路长度一样大的稳态。
