Can anyone explain traffic jams, from a mathematical perspective?

Question

Here's what I don't understand: if 1 car gan go 60 mph on a freeway with relative ease, why can't 1000 cars going in the same direction ALSO go 60 mph with relative ease? Why is it that, as more vehicles get added into the mix, the slower everyone seems to go? Is it simply the random mix of idiocy, people changing lanes, larger vehicles vs smaller, exiting & entering vehicles? And is it unavoidable human nature to gawk at a traffic accident, thereby slowing down the people behind you?
It seems like every day I hear traffic reports of accidents at the same locations & just wondering WHY??? And, with that knowledge, what can be done to decrease the probability of repeated accidents?

Sorry -- lots of questions -- but I've wondered abou these things for years.

I know cars aren't psychic. But on a road with no control devices such as stop signs or traffic lights, shouldn't it be theoretically possible for a "block" or group of vehicles to travel at the same velocity as one vehicle? Somewhat like a stock car race -- a few dozen cars are travelling rapidly and they are bunched fairly close together. So, it's POSSIBLE for a group of cars to travel fast together (i.e., speed, in and of itself, is not the obstacle). Is the problem the entrance/exit to and from the freeway?

Answer 1

There's a portion of Operations Research called 'queuing theory.' If you are interested I'd suggest searching for some material, which explores different patterns of delivery vs. flow.

Answer 2

you just have to think logically.when one car speed at 60 mph alone on a freeway,there is no car in front of that car and there is no traffic light.but when there are 1000 cars on the same road,the cars in front of yours may not be able to move as the traffic light is red.which cause the cars behind to slow down.which cause that car that goes 60 mph to slow down too.it is like you go to a bookshop,you buy a book and queue up for payment and there are lots of people in front of you.why can't you just push them in front?of course you can't,you have to wait till they make their payment first.if you want to decrease the probability of repeated accidents,you may consider putting a sign telling drivers do not drive faster than 50 mph.that's what many country like singapore is doing.decrease the driving speed which drivers may not listen.

Answer 3

Mathematical? I guess you could say input raffic > output traffic.

However, when you say that a car goes to 60mph with ease, not every car is giong to do that at the exact time. Funnily enouhg, cars aren't psychic. There's a delay as people realise that the person in front of them is moving, and that it is indeed safe for them to drive forward. People also don't want to be too clse while drivign 60mph, and cars get pretty close when stoppe din a traffic jam.

Answer 4

I always thought that the "go fast, slow down" cycles on a freeway could be described with a differential equation, although I never worked on it.

The oscillating traffic seems to be described by the standard "spring problem" that is covered in differential equations coursework.
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