THE DELAY TO PEDESTRIANS CROSSING A ROAD
THE DELAY TO PEDESTRIANS CROSSING A ROAD
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DOI：
10.1093/biomet/38.3-4.383
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发表时间：
1951-12
期刊：
影响因子：
2.7
通讯作者：
J. Tanner
中科院分区：
文献类型：
--
作者：
J. Tanner
独立的。换句话说，我们假设车辆“随机”到达。在实践中，随机假设通常是不正确的，但是Adams（1936）已经表明，在相当广泛的条件下，这种近似是相当好的。行人以每单位时间n的速率到达X点，同样是随机的，与车辆的通过无关。每个行人在看到下一个间隔I内没有车辆会通过X时就开始过马路，此时假定每个行人之间的时间不变。在实践中，行人通常是三三两两到达的，这些“到达组”的到达是完全随机的，这个理论将适用于这种情况下的行人群。然而，该理论如何适用于个人而非抵达群体的一些指示给出。每个行人被耽搁的时间为T，每个行人被耽搁的时间不同。设P(T)为延迟大于T的概率，设f(T)存在时为T的频率函数，则dP(T) f(T)= dT。对于上述假设情况，我们将推导出函数P(T)以及在一定时间过路或等待的行人群体的大小分布。一些结果可以推广到存在两种交通流的情况下，当临界间隙I不恒定时，当我们给定不同规模的到达群体的比例时。这个理论被用来估计如果在人行横道竖立“预先警告标志”会给行人和车辆造成的延误。这是为了给道路使用者更多的指导，让他们知道谁有通行权。结果并不都是新的；Adams（1936）引用了行人平均延迟时间的最简单公式。Garwood（1940）考虑了一个与交通灯有关的问题，这个问题在数学上几乎与此相同，后来将结果应用于一个和两个交通流的行人延误。自这篇论文发表以来，Raff（1951）通过考虑车辆的“阻塞”推导出了平均延迟，如？本论文的第2部分。他还注意到？的式(7)2 - 1所示。
independent. We assume, in other words, that vehicles arrive 'at random'. The assumption of randomness is not usually true in practice, but Adams (1936) has shown that the approximation is quite good under a fairly wide range of conditions. Pedestrians arrive at X at a rate n per unit time, also at random, and independently of the passage of vehicles. Each pedestrian starts to cross the road as soon as it can be seen that no vehicle will pass X during the next interval I, a time assumed for the moment not to vary from one pedestrian to another. In practice, pedestrians often arrive in twos and threes, these 'arrival groups' arriving sufficiently at random, and the theory will apply in this case to groups of pedestrians. However, some indication of how the theory can be applied to individuals rather than arrival groups is given. Each pedestrian will be delayed for a time T, varying from one pedestrian to another. Let P(T) be the probability of a delay greater than T, and let f(T), when it exists, be the frequency function of T, so dP(T) f(T)= dT We shall derive for the above hypothetical situation the function P(T) and the distributions of the sizes of groups of pedestrians crossing or waiting at certain times. Some of the results are extended to the cases when there are two streams of traffic, when the critical gap I is not constant, and when we are given the proportion of arrival-groups of different sizes. The theory has been applied to estimate the delays which would occur to pedestrians and vehicles if 'advance warning signs' were erected at pedestrian crossings. These are intended to give more guidance to road users as to who has the right of way. The results are not all new; the simplest formula for the mean delay to pedestrians was quoted by Adams (1936). Garwood (1940) considered a problem connected with traffic lights which was mathematically almost the same as this, and later applied the results to pedestrian delays for one and two traffic streams. Since this paper was submitted for publication, Raff (1951) has derived the mean delay by a consideration of 'blocks' of vehicles, as in ? 2 3 of the present paper. He also notes equation (7) of ? 2-2 1.