Mathematics of Traffic

[ed84c]

Just watching on the way home today, I was wondering there must be some underlying mathematics to traffic patterns, Probability of Jams etc?

[tinyboy21]

...Are you serious...

 

just asking

[ed84c]

yes, chaos theory managed to explain weather paterns.

 

Note: I am sad

[tinyboy21]

yes' date=' chaos theory managed to explain weather paterns.

 

Note: I am sad[/quote']

 

 

I belittle you.

 

*I curl into the fetal position*

[ed84c]

wtf are you talking about?

[tinyboy21]

I am asking you what area you are thinking of calculating the traffic.

[matt grime]

Chaos theory doesn't explain weather patterns. Models of weather patterns are chaotic systems. Transpiration, convection, and so on explain weather patterns. Just as the fact that too much traffic in too small a road system explains congestion. Mathematics has been used to model congestion, and has been used to create ways to control flows and so on, but it isn't causal. You may wish to learn about queue theory, markov chains and so on to understand the techniques involved.

[tinyboy21]

Chaos theory doesn't explain weather patterns. Models of weather patterns are chaotic systems. Transpiration, convection, and so on explain weather patterns. Just as the fact that too much traffic in too small a road system explains congestion. Mathematics has been used to model congestion, and has been used to create ways to control flows and so on, but it isn't causal. You may wish to learn about queue theory, markov chains and so on to understand the techniques involved.

 

 

What he said.

[ed84c]

when i said 'explains how weather paterns work'

 

I didnt mean 'explains the weather'

 

but

 

'explains why weather paterns exist/ why they are'

[5614]

well the more cars the more likely

 

the more side turnings the more likely

 

the more traffics light a lot more likely

 

temporary traffic lights / road works a lot a lot more likely.

[nur_agus_ipftiuii]

I think someone will found it many years later from now.

[ed84c]

Wtf

[5614]

he means:

 

"I think someone will find it many years later from now."

 

where it = a mathematical formula/theory for traffic

 

come on, he's not english... dont tell me you couldnt have worked that out for yourself?

[The Rebel]

Just watching on the way home today, I was wondering there must be some underlying mathematics to traffic patterns, Probability of Jams etc?

 

I have to admit I have wondered about the possibility of modelling traffic, although I'm not sure if this is the line you're going down. For example would it be possible to think of roads like electronic circuits where each one would have a different average speed, average rate of flow. If three roads were connected in different ways, e.g. traffic lights, give way, roundabouts, would it be possible to map a prediction for tha behaviour of the thirs road from the two others. How would verifying components (junctions, etc.) change the flow.

 

Perhaps there is a traffic modelling program already out there?

[ed84c]

i was thinking more along the lines of obscure beefy equations, lots of number crunching. Ever seen the film pi?

[Paul Trow]

Take a look at http://www.math.toronto.edu/mathnet/carcompet/carcompet.html

[matt grime]

I don't have time to check that link, but, ed84c, like I said mathematics has been used to model these things. Check out Markov chains and queue processes.

 

And chaos still doesn't explain why weather patterns are the way they are. Chaotic systems display topological trnasitivity and sensitive dependence on initial conditions and are a purely mathematical definition. It doesn't explain why the patterns come as they do it explains why we can't predict them accurately, it explains properties about the model of the weather. Coffee table mathematics books have a lot to answe for.

[ed84c]

uhrghuh.

 

You misinterpreted me AGAIN

 

basically what i meant by explaining 'how they are' is that they are Chaotic and un predictable.

[ed84c]

Note: the mathematics in this part is quite challenging and requires a knowledge of calculus.

 

hmmm, I know a little about Derivatives, but not enough i dont think.

 

Im 15.

[matt grime]

uhrghuh.

 

You misinterpreted me AGAIN

 

basically what i meant by explaining 'how they are' is that they are Chaotic and un predictable.

 

 

Then saying "why they are" was a bad choice of words.

[ed84c]

my apologies for the confusion.

 

It is to be fair quite a difficult thing to put into words.

[matt grime]

Have you looked up the probability stuff? Seriously, this is a large area of research over the last 30 years.

[badchad]

I'm no mathematician, but in addition to models, I'm sure city planners, etc. sample traffic patterns. Obviously there will be a much heavier flow of traffic during rush hour VS. the middle of the day. All they have to do is count the number of cars passing a particular spot. Then they time or adjust the traffic lights accordingly.

 

I see this on my way to work. The "timing" of the lights changes depending on the time of day.