Iannini M L L, Dickman Ronald
Departamento de Física and National Institute of Science and Technology for Complex Systems, ICEx, Universidade Federal de Minas Gerais, C. P. 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil.
Phys Rev E. 2017 Feb;95(2-1):022106. doi: 10.1103/PhysRevE.95.022106. Epub 2017 Feb 6.
We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not decelerate if their speed is smaller than the headway (number of empty sites to the car ahead). (In the original NS model, such a reduction in speed occurs with probability p, independent of the headway, as long as the current speed is greater than zero.) In the modified model the free-flow state (with all vehicles traveling at the maximum speed, v_{max}) is absorbing for densities ρ smaller than a critical value ρ_{c}=1/(v_{max}+2). The phase diagram in the ρ-p plane is reentrant: for densities in the range ρ_{c,<}<ρ<ρ_{c}, both small and large values of p favor free flow, while for intermediate values, a nonzero fraction of vehicles have speeds <v_{max}. In addition to representing a more realistic description of driving behavior, this change leads to a better understanding of the phase transition in the original model. Our results suggest an unexpected connection between traffic models and stochastic sandpiles.
我们考虑一种修正的纳格尔 - 施雷肯贝格（NS）模型，在该模型中，如果驾驶员的速度小于车头间距（前方车辆前方的空位数），则他们不会减速。（在原始的NS模型中，只要当前速度大于零，这种速度降低就会以概率p发生，与车头间距无关。）在修正模型中，自由流状态（所有车辆以最大速度(v_{max})行驶）对于小于临界值(\rho_{c}=1/(v_{max}+2))的密度(\rho)是吸收态。(\rho - p)平面中的相图是折返的：对于(\rho_{c,<}<\rho<\rho_{c})范围内的密度，p的小值和大值都有利于自由流，而对于中间值，有非零比例的车辆速度(<v_{max})。除了代表对驾驶行为更现实的描述外，这种变化还能更好地理解原始模型中的相变。我们的结果表明交通模型和随机沙堆之间存在意想不到的联系。
