Suppose a wide road is somehow constricted at one place, allowing only one car at a time. Unless the traffic is very sparse, the vehicles will gather before the constriction and a given car will have to wait till it gets a chance to pass through. At a time which car will exit? Perhaps it is the one, with a driver who can jostle and aggressively put its nose into the constriction. We assume that the quantitative measure of aggressiveness depends on the nature of the individual and increases monotonically with waiting time. Our precise hypothesis is that the aggressiveness of a given driver who has been stranded for time $\tau$, is the product of two quantities $N$, and ${\tau }^{\sigma }$, where $N$ is fixed for a given individual but varies randomly from person to person (in the range 0 to 1), while $\sigma$ is the same for all individuals. We show that this hypothesis leads to the conclusion that the probability of waiting for a time $\tau$ is proportional to ${\tau }^{\sigma +1}$. Although the applicability of our hypothesis to real situations is difficult to verify at microscopic level, we note that empirical studies confirm such algebraic decay with an exponent $\sigma =1.5$ and 2.5 in two cities of India and 0.5 for a traffic intersection in Germany. We shall present some justifications for our hypothesis along with some variants and limitations of our model.

假设一条宽阔的道路以某种方式被限制在一个地方，一次只允许一辆车。除非交通非常稀疏，否则车辆将在狭窄处聚集，并且给定的汽车将不得不等待直到有机会通过。一次哪辆车会退出？也许是这样，驾驶员可以争吵并积极地将鼻子伸进狭窄部位。我们假设侵略性的定量度量取决于个人的性质，并且随着等待时间的增加而单调增加。我们确切的假设是，被困在时间上的给定驾驶员的进取心$\tau$是两个数量的乘积 $ñ$， 和 ${\tau }^{\sigma }$， 在哪里 $ñ$ 对于给定的个人是固定的，但因人而异（在0到1的范围内），而 $\sigma$对所有个人都是一样的。我们证明了这一假设得出的结论是，等待时间的概率$\tau$ 与...成正比 ${\tau }^{\sigma +\mathrm{1个}}$。尽管我们的假设在现实情况下的适用性很难在微观水平上验证，但我们注意到，经验研究证实了这种代数衰减具有指数性$\sigma =\mathrm{1个}。5$在印度的两个城市中为2.5，在德国的交通交叉口中为0.5。我们将为我们的假设提出一些论证，以及我们模型的一些变体和局限性。