I hadn't really thought this through properly --- just noticed that the video compares two systems comprising masses and springs, which is formally identical to a circuit with inductance coils and capacitors. However the paradox involves the height of the mass [which unexpectedly increases after one supporting string is cut]. It's unclear to what property of AC (or indeed of traffic flow) this might correspond! So some direct bijection between traffic flow and (say) current would be required to make the analogy work. Traffic engineers must surely have already investigated the matter; I have yet to conduct a search. WFL On 5/24/15, James Propp <jamespropp@gmail.com> wrote:
It'd be interesting to see an AC circuit analogue of Braess' paradox, because of the contrast with DC circuits: Rayleigh's monotonicity law says that paradoxes like this can't occur in purely resistive networks.
Jim Propp
On Saturday, May 23, 2015, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I think I've now got the hang of this: more intuitively, the traffic network can instead be modelled by an AC electrical circuit.
The fluid dynamical aspects of flow along a single road might perhaps be incorporated by combining both models into a hydraulic analogue computer.
Next time you're stuck in a traffic jam, try figuring out whether it's a UTM. Or would be, when/if ever it got moving again ...
WFL
On 5/22/15, Fred Lunnon <fred.lunnon@gmail.com <javascript:;>> wrote:
The "standing wave" phenomenon in heavy traffic mentioned in the article is straightforward application of fluid dynamics, which I had ample opportunity to analyse during a particularly excruciating expedition along the London orbital motoway years ago.
I had to view the video in full-screen mode before I could follow it; now I understand the mechanical paradox, which still surprises me. But I don't see how the mechanical model maps to a traffic situation.
WFL
On 5/21/15, Mike Stay <metaweta@gmail.com <javascript:;>> wrote:
This short link also works and has no tracking data.
http://theconversation.com/the-maths-of-congestion-springs-strings-and-traff...
On Thu, May 21, 2015 at 3:19 PM, Fred Lunnon <fred.lunnon@gmail.com
<javascript:;>>
wrote:
See embedded video. New to me, though I had previously heard rumours ...
http://theconversation.com/the-maths-of-congestion-springs-strings-and-traff...
[no line breaks in above link!]
WFL
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