Mathematics of Traffic

a_unique_person

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a_unique_person
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When I was working on a very large computer project once, and it was way over budget and late, (not all due to me, I can assure you, in case you were wondering), I asked my manager if it was worth computerising all this stuff, if a simple manual, or semi automated system mightn't be better.

He told me he wondered too, sometimes, but the fact was that things like the phone system were a good analogy. A manual system with operators connecting you just wouldn't work. It would just about take more operators than there were people to run the whole thing.

The traffic where I live just keeps getting worse, with travel times getting longer, and the average speed at peak hour dropping regularly, to about 25k/h, IIRC.

I was wondering if this is an analogous situation. A car trip is like a phone call, except that we do it physically. The road system is like the phone system, except that it can't be computerised.

They build new freeways every so often, they widen roads, jiggle with traffic light timings, but, it seems to me, it is a game that they can't win. People just get more cars, the suburbs keep expanding, people get jobs miles away from where they live that they have to drive to.

Proponents of freeways say we just need more of them, but I think they are heading up a dead end lane. Every freeway carries more traffic, and keeps loading up till it is overloaded.

The main freeway system is fine for the tollway operators, they just have to charge for each journey, and the cost is the same, no matter how long it takes. However, any slight traffic accident throws the whole thing into chaos, both ways. The traffic going in the direction the accident happened in has blocked of lanes, or the whole road, and traffic going the other way slows down to have a look.

Any opinions out there on if this traffic problem can ever be solved?
 
My biological metaphor for traffic has become blood flow, in which cars are like platelets with an intrinsic 'stickiness'. If traffic flows too much then clots are created- steady flow suddenly blocks. There is then a freeing of the clot at the far end, while new platelets accrete upstream.

I don't know how far this metaphor can be taken or whether it is already a well-explored model.

Edited to add: Tow-trucks are phagocytic cells. Is there an analogy for the regulating effect of police cars?

Traffic cones are atherosclerotic plaques?
 
This precise exercise was one of the logic design exercises I had to work on when I was an undergraduate in the 1970's. We used Simula (a precursor OO language) on a Control Data Cyber (at UNSW, if anyone remembers it) to simulate simple traffic operations, and then build up a more complex situation from the components we created.

Road traffic is actually a complex queueing situation, and all but the most simple and rigid scenarios can become chaotic in rapid order. But the trick is not how to prevent a traffic snarl occuring - they occur even in the most well-regulated scenarios. The trick is how well the system will unsnarl one when it occurs. In effect, you need to know how strongly the system gravitates towards "attractors" that represent stable solutions, and how to make such attractors even more likely.

I could go on about this, but no doubt some young-and-lovely smarty-pants will take the opportunity to kick my flabby butt on this subject! So suffice to say: Yes, it has indeed been studied in detail for some time. But I'd suggest any results have rarely been taken heed of by town and traffic planners.
 
I've got nothing to add except to say if I had my time again I'd love to be a traffic engineer. I think it would be fascinating.
 
a_unique_person said:
I was just wondering if this issue has been modelled mathematically, and if the problem of switch boards connecting enough phone calls applies to traffic.
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I don't think they are altogether similar. Road traffic involves open-ended I/O of traffic, both externally and internally (cars join a traffic system from "out in the country", and also "from garages near the city"). Phone calls are end-to-end via a closed limited capacity linking network.
 
Iconoclast said:
I've got nothing to add except to say if I had my time again I'd love to be a traffic engineer. I think it would be fascinating.
Click to expand...

As Iconoclast indicates, it's a branch of Civil Engineering. As such, there are many resources for information on it. I don't have any links for you, as I only took a couple of courses in the basics, years ago.
 
Zep said:
I don't think they are altogether similar. Road traffic involves open-ended I/O of traffic, both externally and internally (cars join a traffic system from "out in the country", and also "from garages near the city"). Phone calls are end-to-end via a closed limited capacity linking network.
Click to expand...

Do the various approaches tend to model cars as particles with rules attached (like my blood cell picture) or as flows in a continuum?
 
A few years ago some germans made a SimCity-like game called Mobility. It's supposed to be focussed on the traffic simulation. Don't know if they still develop it. Used to be freeware.

link
 
You need to turn to economics to understand these issues.

Very, very briefly.

zero cost at point of consumption = over consumption (i.e. congestion)

external costs => marginal cost > average cost = over consumption (congestion.)


That is why you get the phenomenon of "you build it and they will fill it" with respect to increasing road capacity.

It is also why the solution is in pricing. Chargning at point of consumption for road use (notice how freeways in France are congestion free?) and congestion charging (congestion in London has drop more than 20% since its introduction).
 
Badly Shaved Monkey said:
Do the various approaches tend to model cars as particles with rules attached (like my blood cell picture) or as flows in a continuum?
Click to expand...
The simulations I did were as particles-plus-rules (sped, size, etc), going from one queue to another (usually intersections) where they were processed according to rules (traffic lights, stop signs, turn left or right, etc). Build a series of queues as complex as you like, set the rules for stuff, feed cars in at various points, log the results. Simple, really.

The difference between blood cells and traffic would be that blood cells move in a generally closed system (retains its queue contents - always moving), whereas most traffic is an open system (queue contents can eventually all disappear - no traffic at all).

[edit due to pushing the button too early]
 
Drooper said:
You need to turn to economics to understand these issues.

Very, very briefly.

zero cost at point of consumption = over consumption (i.e. congestion)

external costs => marginal cost > average cost = over consumption (congestion.)


That is why you get the phenomenon of "you build it and they will fill it" with respect to increasing road capacity.

It is also why the solution is in pricing. Chargning at point of consumption for road use (notice how freeways in France are congestion free?) and congestion charging (congestion in London has drop more than 20% since its introduction).
Click to expand...
In effect, you are increasing the attractiveness of particular solutions to the problem by modifying one of the variables - in this case, increasing the unit cost for vehicles using the roads (in addition to rego, petrol, depreciation, insurance, etc), to make car travel less attractive on a commercial basis.

There may be other solutions that allow traffic to work even better, but the cost involved could make them futile, or they are overly simplistic (e.g. only one vehicle at a time on the roads => no traffic jams whatsoever then, but it's also totally cost-ineffective, not to mention stupid).
 
Badger said:
As Iconoclast indicates, it's a branch of Civil Engineering. As such, there are many resources for information on it. I don't have any links for you, as I only took a couple of courses in the basics, years ago.
Click to expand...
I should stress that it's not the "civil" aspects of traffic engineering that interest me, it's the things like flow simulation that AUP is talking about that I'd love to do.
 
Originally posted by Drooper
congestion charging (congestion in London has drop more than 20% since its introduction).
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That might be good for the people who pay and drive, but what about the people who are prevented from driving by the price? They'd rather put up with the congestion and not have to pay. Is there some sense in which congestion charging is better overall?
 
a_unique_person said:

Any opinions out there on if this traffic problem can ever be solved?
Click to expand...

The analogy is similar to packet routing in a network. Make the noise filters and data packets smarter and much, much, more traffic can be handled.

In other words, smarter road design, traffic light synchorization according to traffic levels, and probably most significantly, smart cars meaning remove the driver control on freeways at least, so cars can move at the same speed with tailgate separation and know when slowdowns or speedups ahead are coming up.

All it takes is money. Eventually the bottlenecks will make it cost effective.
 
Drooper said:
zero cost at point of consumption = over consumption (i.e. congestion)
Click to expand...
Obviously, that's not a universal rule. There are plenty of times and places where there is no congestion, so clearly there's more to congestion than just undercharging.

That is why you get the phenomenon of "you build it and they will fill it" with respect to increasing road capacity.
Click to expand...
I'm not convinced of the validity of this argument. Yes, new freeways seem to get filled, but would that growth not have happened without the freeway? People see new freeways and then more traffic, and think that the former caused the second, but isn't the reverse a reasonable assumption as well? Don't civil engineers, knowing that there will be more traffic, build more freeways? Furthermore, even if all new freeways will eventually fill up, does that really mean that the freeways served no purpose? Does the fact that a good is fully consumed somehow make that good useless?

Actually, in a way, carpool lanes are an attempt at an economic solution.

But I think that the real cause of congestion is having home, school, and work being separated, and reducing the demand for road use would yield better results than trying to optimize servicing that demand. That, and more, and better, mass transit.
 
An article appeared on SlashDot today about an engineer who's been doing some traffic light simulations, he has some idead about how to reduce congestion using a rule that a large enough group of approaching cars should be able to 'force' the traffic lights to green:

http://www.primidi.com/2004/12/05.html
 
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