Talk:Braess's paradox

Financial Example
The slowing of the speed of money due to hoarding by those with much more than they spend, is less than optimal, and may be comparatively detrimental, when compared with the value of the residue when a portion of the hoarded value is pumped into circulation through those who are more likely to spend it immediately (increase consumption), and to increase productivity (employment).  Can this financial Braess' paradox be proven as an apparent choice against best interest? By analogy, the traffic flow slows when the 'short-cut' is introduced because the immediate (selfish routing) response of some drivers reduces their travel time (until it is used by a majority), at which time it is easy for them to see that their travel time has actually increased, and many return to their previous route (ignoring the short-cut)(stop hoarding). The traffic analogy seems to break-down because it is easy for drivers to compare their daily travel time by route, as it changes with the migration of other drivers to the new route, and then back, as the new route fails. It is not so easy for "the 1%", or mega-corporations(stakeholders), to compare the alternative to hoarding because 'speeding up money flow' is a slowly responding marginal benefit. --Wikidity (talk) 04:39, 23 June 2015 (UTC)

Possessive Apostrophe
Isn't it Braess'? Not Braess's... Apostrophe-'S' is used when the owner of the object doesn't not end with 'S', just an apostrophe is used for owners ending with an 'S'. For instance, George Lucas' Star Wars, not George Lucas's Star Wars. —Preceding unsigned comment added by 24.219.164.86 (talk) 15:44, 27 September 2010 (UTC)

Why is adding a crossroad considered "adding capacity?" The phrase "added capacity" to me sounds like adding a third route of equal capacity to the first two, which would indeed solve the problem. The phrasing "adding choice to the system" or something similar would be more accurate. --Monguin61 21:13, 10 December 2005 (UTC)

I like your comment - a road is NOT necessarily capacity. we added a link to a network and traffic slowed when the arriving cars (packets), could not exit as fast! — Preceding unsigned comment added by 71.219.216.193 (talk) 18:30, 4 January 2014 (UTC)

This is actually pretty good but "For a better explanation, please see this link:" sounds, well, too humble. Either it's been explained adequately in which case there's no need for apology, or it hasn't, in which case, skip the apology and expand the article.radek 06:58, 12 March 2006 (UTC)

Add: How far from optimal is traffic at equilibrium
I think the following information should be added:

- If latency function are linear then adding an edge can never make total travel time at equilibrium worse than by a factor of 4/3

- At worst traffic in equilibrium is twice as bad as socially optimal

--Grondax (talk) 15:33 11 Novermber 2008 (EST)


 * It looks like someone added the thing about traffic at equilibrium, but the proof given only implies that traffic at the energy minimizing equilibrium is at most twice as bad. Is it true in general (or is the energy-minimizing equilibrium the only one in general)? If so, please add that if you have a proof or citation. Also, please add the thing about adding an edge never making an equilibrium more than 1/3 worse if you have a citation or proof. --skeptical scientist (talk) 04:50, 14 November 2015 (UTC)

The example is flawed.
This example is flawed..

Suppose I'm a 'rational' traveler, and the third route gets added. I know that everyone is taking the new route, thinking it will be faster, so I take Start->B->End instead. Start->B takes 45 minutes. B->End takes 0 minutes, because everyone else is trying the new 'faster' route. I get home in 45 minutes. Everyone else eventually realizes that this new route isn't any faster, and everyone ignores it, and eventually I suppose it gets closed to reduce maintenance costs.

And this example is flawed, and I dare say the entire theory, because people will COMMUNICATE with one another. —Preceding unsigned comment added by 71.193.207.197 (talk) 00:41, 3 May 2008 (UTC)


 * I agree the example is flawed, but I don't think its necessary for people to communicate with each other to find the optimal solution. If x people take Start->A->End, y people take Start->A->B->End, and z people take Start->B->End, then (x, y, z) = (1301, 896, 1803) yields an optimal solution of 63 minutes on average and 71 minutes in the worst route (the z route). Given enough time and sensitivity, isn't it likely that uninformed drivers would naturally arrive at this equilibrium? --Beefyt (talk) 17:52, 4 September 2008 (UTC)


 * Only if the z drivers were unaware that they could get from Start to B in 21.97 minutes by taking the route via A instead of going directly to B, which takes 45 minutes. Similarly the direct route from A to End takes 45 minutes but going first to B makes it 26.99 minutes. Once they realize this the drivers will start switching their routes in favour of the shorter ones, which will in turn become longer due to the increased traffic. We eventually end up in the situation described in the article. In other words, your equilibrium is unstable, given the assumption that drivers can choose their route freely and that they are minimizing their own time spent on the way. I can't see any error in the example. 81.83.2.11 (talk) 21:42, 30 November 2008 (UTC)


 * I don't think that the example is flawed. The original message here has flawed reasoning: if everyone is taking the new route (Start-A-B-End) then the proposed route (Start-B-End) will take 45 minutes for Start->B plus 4000/100=40 minutes for B->End, as everyone taking the new route must also travel on the B->End segment. So the travel time will be 85 minutes for this route, not 45 minutes. The rational traveller will take the new route with everyone else. Perhaps the explanation in the article isn't/wasn't clear on this point. This is clearly not the optimal solution in terms of average travel time, but is the result of each driver individually choosing the fastest route. 121.98.212.178 (talk) 06:50, 25 June 2009 (UTC)

The example is not flawed. In fact, Rapoport et al. tested Braess paradox in their paper Choice of routes in congested trafﬁc networks: Experimental tests of the Braess Paradox, Games and Economic Behavior 65 (2009) (2009). In their experiment, they tested the hypothesis that (a) equilibrium behavior predicted by game theory will emerge and (b) communication has an effect on the equilibrium. In the case of (a): yes, equilibrium behavior emerges exactly as Braess's paradox predicts. In the case of (b): the only effect communication has on equilibrium behavior is that people converge faster on equilibrium when they can communicate freely.--76.118.178.197 (talk) 20:51, 1 August 2011 (UTC)

The example is flawed because it requires roads with infinite throughput. --Yecril (talk) 09:21, 10 March 2014 (UTC)
 * Exactly, that's the right answer! The RedBurn (ϕ) 14:53, 11 October 2017 (UTC)
 * No, the conditions are stated for 4000 travellers leaving START. The rates of travel on each section apply where number of travellers T is up to and including 4000. Each section may have greater capacity, at which the rates of travel (45 mins and T/100 mins and 0 mins) may stay the same, but that's not the problem here. The problem here is to deal with the 4000 known to be leaving START. Akld guy (talk) 19:32, 11 October 2017 (UTC)

Article title
Shouldn't that be "Braess' paradox"? Paradoctor (talk) 08:35, 6 March 2010 (UTC)

whole article poorly veiled propaganda
this whole article is poorly veiled propaganda by the current communist administration to justify government ownership of roads. After all, who but the government could remove a link to benefit "everyone"? By generating this absurd fake propaganda, it hopes to ply public sympathy toward state involvement and ownership. Naturally the actual proposed "facts" are totally rubbish: it is obvious that you could never decrease traffic congestion in an area by removing already congested roads.

The article is an obvious hoax from the first sentence: "Braess's paradox, credited to the mathematician Dietrich Braess" redlinks.

I've added a deletion tag. 82.113.121.167 (talk) 01:27, 31 March 2010 (UTC)
 * And I've declined the speedy as it is not spam. There are plenty of google books hits for this suggest AFD. Dloh  cierekim  01:34, 31 March 2010 (UTC)
 * "to justify government ownership of roads" LOL! 63.166.115.40 (talk) 18:44, 13 July 2010 (UTC)


 * Google scholar hits. Google book hits Google web hits.
 * These include--
 * Scientific American
 * Herr Doktor Professor Braess's web page. at Ruhr University Bochum.
 * Software Testing Paradoxes by James McCaffrey at Microsoft Developer Network Dloh  cierekim  02:05, 31 March 2010 (UTC)
 * It seems to me some dogmatic libertarian view ha chrashed here :-). But I'm sure the conservapedia might offer solace.--Kmhkmh (talk) 16:51, 11 October 2010 (UTC)


 * That it appears to be an "obvious hoax", but is still true, is the whole point making it a paradox, and interesting. Understand the example with the diagram - it's a little bit mind bending, but just a little. Volker Siegel (talk) 22:50, 25 April 2019 (UTC)

Wrong notation in "Existence of an equilibrium"
The term $$x_e$$ has not been previously defined in the section. If it refers to total number of people on edge e then it should be $$e_x$$. Secondly, the variable x refers to the number of people: "Let $$L_e(x)$$ be the formula for the cost of $$x$$ people" as well as the route: "$$x_0, x_1, \ldots, x_n$$". — Preceding unsigned comment added by 155.69.2.12 (talk) 09:19, 16 February 2014 (UTC)
 * I noticed that this proof was using both x_e and e_x inconsistently, and fixed it. I prefer x_e, since it's a quantity x (consistent with prior uses of x as a number of travelers) dependent on an edge e. This is more naturally denoted x_e than e_x. I also changed the routes to e_i (before) and e'_j (after) so that e with subscript now consistently means an edge and x with subscript now consistently means a number of travelers. The disadvantage is there are now double-subscripts in a few places (e.g. $$x_{e_i}$$), but I think the result is easier to follow overall. I also did a few other proof-rewrites to make the proofs easier to follow and more precise. (By the way, the edits to this page from 207.198.105.22 were mine.) --skeptical scientist (talk) 04:40, 14 November 2015 (UTC)

Requested move 21 May 2015

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section. 

The result of the move request was: Moved. There is a narrow majority favoring the move, but there is no agreement on whether WP:UCN applies to grammar points like this one. Other articles raise a similar question but they don't always follow one pattern. We do have Olbers' paradox and Charles's law, but it would be unwise to generalize from this outcome on how those other articles should be treated. Those who were arguing from Google searches would have been more persuasive if they had offered the actual search strings so we could verify they were effective in finding only the desired pattern. EdJohnston (talk) 22:34, 15 June 2015 (UTC)

Braess's paradox → Braess' paradox – Per WP:COMMONNAME. "Braess' paradox" outnumbers "Braess's paradox" 6:1 on Google Scholar, and between 2:1 and 3:1 on Web, Books and News. --Relisted. George Ho (talk) 05:50, 30 May 2015 (UTC) 85.178.214.229 (talk) 13:38, 21 May 2015 (UTC)
 * Comment - seems like good evidence that Braess' paradox is in wider use. Jonpatterns (talk) 13:27, 22 May 2015 (UTC)
 * But calling it that it is wrong; unless there were a bunch of fellows of that name who came up with the paradox. By the way, I am going to take a run at making the article more accessible and relevant Overagainst (talk) 10:53, 29 May 2015 (UTC)
 * I don't see how that is a grammatical error. Also Olbers' paradox. Finally, which policy overrides WP:COMMONNAME? 85.178.196.26 (talk) 12:46, 29 May 2015 (UTC)


 * AFAIK, when a name ends with an 's', for the possessive one can either write (s') or (s's), both are acceptable. However, (s') is far more common. For example, if you google search for "Prince Charles' wife", you'll get far more hits than if you search for "Prince Charles's wife". The same is true for "Elvis' birthday" vs "Elvis's birthday". I say move it to Olbers' paradox per WP:COMMONNAME. LK (talk) 10:00, 30 May 2015 (UTC)
 * I would prefer a more reliable authority, such as User:Rothorpe.Overagainst (talk) 13:46, 30 May 2015 (UTC)
 * If Rothorpe wants to weigh in, he's certainly welcome. But the verdict of the "reliable authorities" is already in: 6:1 in favor of the move. It doesn't matter whether the name is grammatically correct. "Wikipedia [...] prefers to use the name that is most frequently used to refer to the subject in English-language reliable sources." In any case, "practice varies as to whether to add ‍‍ '​‍s or the apostrophe alone", so it is a matter of opinion whether the one or the other is "correct". 85.178.210.61 (talk) 15:20, 30 May 2015 (UTC)
 * Thanks for the mention. Yes, I would put 'Braess's', but the common name policy trumps all linguistic conventions. Rothorpe (talk) 16:54, 30 May 2015 (UTC)
 * It may matter for one policy whether the name is commonest, but that is not a conclusive argument in the total context, there are other considerations. "Wikipedia [...] prefers to use the name that is most frequently used to refer to the subject in English-language reliable sources", but in this case the existing name is correct and well understood and the proposed change is to bring it into line with what is but an extremely common mistake by people unaware of a well established rule's application being limited to the plural. They're actually applying a rule which does not exist, that you don't add the s to plural or non plural words that end in s. We shouldn't. It's a bad policy for the credibility of Wikipedia to think a policy which has the aim of clarifying names can be extended to warp acceptable usage and blur meaning by citing a world wide internet search. Common name is not a licence for changing the rules of the language and expert opinion counts for something.  Moreover, the common name and the less common name have the difference that  the meaning is different, and as both the ignorant and  correct usage is extremely common  there is no way to know which is intended. In this context the proposed renaming of fails WP:PRECISE Precision – The title unambiguously identifies the article's subject and distinguishes it from other subjects. (See § Precision and disambiguation). I think this and similar titles should be left alone. I will bet you anything when the common name policy was created it was never envisioned it would be applied in the way it is being used here, to bulldoze distinctions and the language ._Overagainst (talk) 20:18, 30 May 2015 (UTC)
 * WP:PRECISE does not apply, both titles refer to the exact same topic.
 * "the existing name is correct" The authority you appealed to stated that this is overruled by WP:UCN.
 * "It's a bad policy" Proposing changes to policy is outside the scope of article talk. You can do that at WP:VP/P, or go to the policy's talk page. 85.178.210.61 (talk) 00:13, 31 May 2015 (UTC)


 * I do sympathise. I think "Prince Charles's" wife is much more common than "Prince Charles' wife", and infinitely preferable. Is this a British/American thing? User:CorinneSD, any comments? Rothorpe (talk) 21:55, 30 May 2015 (UTC)
 * I'm afraid you're mistaken. Google Books "Prince Charles' wife":952 "Prince Charles's wife":216 85.178.210.61 (talk) 23:51, 30 May 2015 (UTC)
 * I didn't mean there. Rothorpe (talk) 00:29, 31 May 2015 (UTC)


 * Support per WP:UCN and WP:CONCISE. The rule, fwiw, says to do this for historical names.  Red Slash 22:30, 30 May 2015 (UTC)
 * Where exactly? TMK, UCN applies generally. 85.178.210.61 (talk) 23:55, 30 May 2015 (UTC)


 * I've been reading the article Apostrophe carefully. Near the beginning, in the section Apostrophe, in the section "Basic rule (singular nouns)", it says, :For most singular nouns the ending 's is added; e.g., the cat’s whiskers.


 * If a singular noun ends with an s-sound (spelled with -s, -se, for example), practice varies as to whether to add '​s or the apostrophe alone. A widely accepted practice is to follow whichever spoken form is judged better: the boss’s shoes, Mrs Jones’ hat (or Mrs Jones’s hat, if that spoken form is preferred). In many cases, both spoken and written forms differ between writers. (See details below.)

Further down, in the section Apostrophe, it says,


 * Many respected authorities recommend that practically all singular nouns, including those ending with a sibilant sound, have possessive forms with an extra s after the apostrophe so that the spelling reflects the underlying pronunciation. Examples include Oxford University Press, the Modern Language Association, the BBC and The Economist. Such authorities demand possessive singulars like these: Senator Jones’s umbrella; Tony Adams’s friend. Rules that modify or extend the standard principle have included the following:


 * If the singular possessive is difficult or awkward to pronounce with an added sibilant, do not add an extra s; these exceptions are supported by The Guardian, Yahoo! Style Guide, and The American Heritage Book of English Usage. Such sources permit possessive singulars like these: Socrates’ later suggestion; or Achilles’ heel if that is how the pronunciation is intended.


 * However, some contemporary writers still follow the older practice of omitting the extra s in all cases ending with a sibilant, but usually not when written -x or -xe. Some contemporary authorities such as the Associated Press Stylebook recommend or allow the practice of omitting the extra "s" in all words ending with an "s", but not in words ending with other sibilants ("z" and "x"). The 15th edition of The Chicago Manual of Style recommended the traditional practice, which included providing for several exceptions to accommodate spoken usage such as the omission of the extra s after a polysyllabic word ending in a sibilant, but the 16th edition no longer recommends omitting the extra "s".


 * Similar examples of notable names ending in an s that are often given a possessive apostrophe with no additional s include Dickens and Williams. There is often a policy of leaving off the additional s on any such name, but this can prove problematic when specific names are contradictory (for example, St James’ Park in Newcastle [the football ground] and the area of St. James’s Park in London). For more details on practice with geographic names, see the relevant section below.

It's obvious there is a lot of variation in usage. Personally, I don't understand the need for the extra "s" after singular nouns or names ending in "s": "Braess' paradox" will be read as "Braess's paradox" by native speakers of English. Non-native speakers may be confused and read it as "Braess paradox", so the addition of the "s" after the apostrophe would help them. CorinneSD (talk) 01:58, 31 May 2015 (UTC)


 * This is going offtopic. The question of the "proper" possessive form is not relevant here. As far as I can tell Overagainst seems to acknowledge that our policy mandates the move. I realize Overagainst is not happy with that. If he or she wishes, I'm willing to discuss the wisdom of WP:UCN, or the lack thereof, on User talk:Overagainst, but an article talkpage is not the right forum to address this problem. 85.178.210.61 (talk) 02:59, 31 May 2015 (UTC)


 * Just for comparison, see Talk:Charles's law. CorinneSD (talk) 15:32, 31 May 2015 (UTC)

"As far as I can tell Overagainst seems to acknowledge that our policy mandates the move." I don't think common name is irrelevant but I don't think it mandates the change. Common name is not the only policy relevant, and it doesn't trump common sense. It's about the name of the article but it's also the application of a rule, and hence what that rule consists of is on topic. There should be no ambiguity in the language in articles, or used to name articles. Yet the the language used on Wikipedia is having ambiguity introduced through this change. There are all sorts of folk beliefs that could be cited as 'acceptable' using the methodology of an internet search. Loosening the standards in this way is not a good idea. We could, and should, just leave these names as they are. When the world becomes standardised on the rule all article names can be brought into line with that._Overagainst (talk) 17:48, 31 May 2015 (UTC)


 * Yes, that[CorinneSD's post]'s interesting. User:Ben Best, at 13:02, says 'although sometimes "Charles'" is used to simplify pronunciation', confirming my British confusion about how Americans pronounce "Charles'" or "Braess'". Rothorpe (talk) 17:49, 31 May 2015 (UTC)


 * You have not answered the objections made to your position. Please address these points.
 * "not the only policy relevant" Which other policy is? Please link and quote the relevant passus, otherwise your claim is unsupported.
 * "no ambiguity in the language in articles" Again, there is none. You just claim this, but you have so far not produced facts that show the ambiguity. Both "Braess' paradox" and "Braess's paradox" refer to the exact same thing.
 * "and it doesn't trump common sense" WP:COMMONSENSE: "When advancing a position or justifying an action, base your argument on existing agreements, community foundation issues and the interests of the encyclopedia, not your own common sense."
 * 85.178.201.66 (talk) 19:42, 31 May 2015 (UTC)
 * The problem with Wikipedia is it lacks protection for expert opinion. People don't get to mess with maths just because their favoured mistakes are common. Something is being lost with this change, because it is a precedent for bulldozing every single article title, and then the language in articles. The five out of six cats onna net rationale for pushing it through is dangerous methodology. The correct use means only one thing to everyone. The common mistake is ambiguous, and there is a policy to avoid ambiguity. Leave it be._Overagainst (talk) 20:16, 31 May 2015 (UTC)
 * "The problem with Wikipedia" Fine, discuss it at WP:VP/P. Here is not the place.
 * "Leave it be." What, trying to build an encyclopedia?
 * You are still not addressing the points raised. You can't build consensus by simply ignoring the objections and arguments of others. 85.178.201.66 (talk)
 * The onus is on those proposing a change to established language rule and claiming that it is mandated by a Wikipedia policy that was never intended to be used in that way.   There are people who will go through Wikipedia altering every single article to conform with this nonetheless. Not just the article names, the actual text of the articles will be altered and distinct meanings will be lost. Braess's paradox is unambiguous to everyone. The proposed change isn't.Overagainst (talk) 21:14, 31 May 2015 (UTC)


 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

lede
Someone keeps chopping the lede down to below the bare minimum while including inappropriate language such as "proved" and the phrase "in real life". It's also repetitive about electricity "decentralized power grids or mesoscopic electron systems" and traffic "reduced congestion or increased traffic speed,". The lede is an overview not supposed to be stand alone definitive and while words like "observed" may be understood in a technical sense in a technical paper the word 'proved' is quite a bit worse. This is coming from a single use account i think 85.178.210.61 should read Manual of Style/Lead section before doing anything else.Overagainst (talk) 17:06, 31 May 2015 (UTC)
 * I suggest you do a little reading, too.
 * Your words: "The lede is an overview not supposed to be stand alone"
 * WP:LEAD: "The lead should be able to stand alone as a concise overview."
 * You clearly had no WP:CONSENSUS for your last edit to the lead, and there is no edit summary in its support. Please adress the issues raised in the various edit summaries in my step-by-step edit of the lead. 85.178.201.66 (talk) 20:21, 31 May 2015 (UTC)
 * My efforts yesterday were not very good but they were at least comprehensible to non specialists. You didn't revert to what you had been happy with right up until before I arrived. The lede can't say everything, it is supposed to make you want to read on, and give an overview if you don't want to read the full article.  But you were step by step holding each word of mine to the fire with technical senses of words. And you chopped it ridiculously short in actual content while adding stuff like "increase travel times, rather than reducing them" and "reduced congestion or increased traffic speed," which is atrocious waffle and padding. Anyway the lede yesterday is here and it is much better than that now, as all can see. I happen to think my last edit is trying to make the article lede accessible as I said in original edit summary. I'll be more attached to latest edit, thought not dogmatic. I have also brought the accessible parts of the article to the fore added a little relevant detail with refs and put the abstruse mathematics further down. Overagainst (talk) 20:45, 31 May 2015 (UTC)

Inexact analogies
Among the so-called "Possible instances of the paradox in action", only the first few traffic examples are actual examples of Braess's paradox. People moving to public transport or staying at home is not an example.

Also, for the other fields, few, if any, of the examples are analogous. Some of them are related to the prisoner's dilemma and Nash equilibria, though.

The article could definitely benefit from having a clearer definition in the introduction, accompanied by an illustration of a minimal example.2001:700:1200:5118:95BA:2753:A33A:2A52 (talk) 14:05, 1 November 2018 (UTC)

Citation Error?
Is there an error on the first citation in the bibliography? It says (1969) but when I follow the link the publication says 1968 on it.

Edit: actually even the text for [1] says that it was observed in 1920, but the reference provided points to a chapter in a book from 2002 or so. — Preceding unsigned comment added by 131.155.69.19 (talk) 19:03, 22 November 2023 (UTC)

Possible source of additional references
I came across a discussion of Braess's paradox at: https://www.quora.com/What-are-examples-of-Braess-Paradox-in-real-life/answer/Sridhar-Mahadevan-6?ch=99&share=68016dc7&srid=u30T This may provide additional examples or references that can be used to improve this article. (I hope I am not being redundant, again!) Thanks! --Lbeaumont (talk) 15:29, 26 December 2020 (UTC)

Prisioner dilemma games are always multiplayer.
The article states that the situation in which the paradox appears is a multiplayer prisoner dilemma. However prisoner dilemmas are always multiplayer, since they involve at least two players. The redaction should therefore be changed to something like "a prisoner's dilemma with more than 2 players". Carllacan (talk) 09:15, 9 July 2022 (UTC)

Application to Google Map navigation?
Now that a centralized (well, distributed within a central company) algorithm is suggesting optimal routes to a significant fraction of drivers, have the operators of the Google vehicle navigation service observed Braess' Paradox and attempted to improve their routing algorithms to reduce its impact? For example, if there are three routes, they could suggest that 70% of the cars go the "fast way" and suggest 10% go another way and 20% a third way. This seems like an interesting research area, has it been investigated somewhere that Wikipedia could cite? Gnuish (talk) 03:44, 11 October 2022 (UTC)

Assumptions of the traffic example
Why are the travel times of only two legs of the network dependent on the current number of users while the other two are fixed regardless of users? Am I to imagine an expansive, underutilized road of many lanes, with a strictly enforced speed limit? And the other segment is an unpoliced, undersized highway that can provide instantaneous transportation? And both paths from start to end use each type, alternating type at the point where both paths tangentially contact, but only allow for a one-way transfer?

I fail to see how this is a relevant model to any actual city's traffic grid. The parameters of the model appear to be carefully designed to produce an unusual result. After giving it thought myself, I challenge someone to sketch a pipe network or electronic circuit with equivalent behavior. For the arguably cherry-picked/myopic phenomenon of traffic improving upon road closure (as referenced in the article), I would expect the chilling effect to be the primary cause. 192.33.240.46 (talk) 16:38, 2 August 2023 (UTC)