Discrete Models of Traffic Flow (1-2)

Quantitative Description of Traffic Flow 2

Traffic Jam

Every driver is familair with traffic jam, it does not seem necessary to elaborate on its definitions. In order to treat the traffic jam in quantitative term, however, it it necessary to sort things out a little bit.

At traffic jam, you find many cars around you, and in contrast, when the road is empty around you, the traffic is smooth. Suppose, for example, that you drive Yasukuni avenue in central Tokyo in New Year vacation. It takes just 5 minutes from Hitokuchi zaka to reach Jinpo cho which would have been a 30 minutes drive in regular day traffic of conjestion. The number of cars certainly has close relation to the appearence of traffic jam. Obviously, when the numnber of cars is twice on a road with twice the lenth, the situation is unchanged. It is the number of cars per unit length of road, or the density of cars, that is relevant here. The density is the most basic quantity of the traffic.

Let us now move from Tokyo to Kochi, and drive on the 4 km of Three Way Signal - Tosa Yamada Value segment of National Road 195. The road is mostly empty apart from one part, where there is a slow moving block made of 15 cars headed by a rambling mini-van. You feel no less frustrated in this block of jam compared to Tokyo traffic, when you see a distant car running smoothly far in front of your block. Even when the density of the traffic as a whole is low, there can be a traffic jam of this type, which is caracterized by the low value of the velocity of the block of cars.

Average Velocity as Measure of Traffic Jam

In the above example, there are 16 cars in total, among which 15 are in the jamming block. Consider another case of 8 cars in a jamming block and other 8 cars smoothly moving in sparse distance. If you are still in that block, you feel the same frustration (or worse), but if you summ up the satisfaction of all drivers, this latter one is a traffic jam of less malignant sort. We learn that it is the average velocity, which is calculated as an addition of the velocities of all cars devide by the number of cars, that should be taken as a measure of traffic jam.

So our tentative concusion is that, from the stand point of drivers, the degree of traffic jam should be measured by the average velocity of a traffic flow. If the average velocity reaches the speed limit of a road, the traffic is free flow and thers is no conjestion. As the average velocity becomes lower, the traffic congestion is worse, and it becomes an absolute jam at zero average velocity.