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Too Many Connections Weaken Networks
itwbennett writes "Conventional wisdom holds that more connections make networks more resilient, but a team of mathematicians at UC Davis have found that that is only true up to a point. The team built a model to determine the ideal number of cross-network connections. 'There are some benefits to opening connections to another network. When your network is under stress, the neighboring network can help you out. But in some cases, the neighboring network can be volatile and make your problems worse. There is a trade-off,' said researcher Charles Brummit. 'We are trying to measure this trade-off and find what amount of interdependence among different networks would minimize the risk of large, spreading failures.' Brummitt's team published its work (PDF) in the Proceedings of The National Academies of Science."
pnas... lol.
If the neighboring connections use your connection more than you use theirs it is weakening your connection.
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The Goldie Locks network:
"As a first theoretical step, it's very nice work," said Cris Moore, a professor in the computer science department at the University of New Mexico. Moore was not involved in the project. "They found a sweet spot in the middle," between too much connectivity and not enough, he said. "If you have some interconnection between clusters but not too much, then [the clusters] can help each other bear a load, without causing avalanches [of work] sloshing back and forth."
I'm sure that in 100 years time, people will look back on our understanding of networks, information and culture in the same way as we look back on people's understanding of the body's nervous or endocrine systems 100 before now. This study hints at our lack of knowledge about what the hell is happening.
"And the meaning of words; when they cease to function; when will it start worrying you?"
If the neighboring connections use your connection more than you use theirs it is weakening your connection.
No, not necessarily. A use may be relatively costless to me, but the fact that I am a node that generates new connections may increase my value to others, for example.
-- IANAL, this isn't legal advice, and definitely isn't legal advice for you. Also, Squee!
As a telecom geek, I see many people create these vast, incredibly complex networks that end up being more difficult to troubleshoot and manage because they invoke non-standard designs which fail when people wander in and make mundane changes. And then when these links fail, go down for maintenance....surprise, there's no 100% network availability.
Three simple rules to networks...
Simple enough to explain to your grandmother.
Robust enough to handle an idiot walking in and disconnecting something.
Reasonable enough to be able to be maintained by Tier I staffing.
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I'll admit I don't understand the reasoning why more is not always better even after reading the article. Sure the calculation overhead for topology changes increase with more choices but such costs are trivial to the overall cost of most systems. Whether the system is more or less resilliant would seem to me anyway to have everything to do with the intelligence the system is able to bring to bear to plan a stable topology based on changing conditions. You can invent and constrain a dumb network with easy to calculate properties for the purpose of simulation but this would seem to have extremely limited implications to the real world where it is cost effective for networks to not be dumb.
Perhaps might be interesting to try this sort of simulation work on power transmission networks?
To their credit they do not claim their work has applicability to the Internet.. Even if BGP made poor choices the edges provides some degree of congestion avoidance which mitigates against the sloshing of snowballs... We learned that lesson the hard way :(
Forty-two.
Now we finally know the question.
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Could these types of models be applied to government or corporate hierarchies? I've often heard about the efficiencies of scale, but my experience with large organizations is that they have too much overhead and inertia. I wonder if mathematicians could could come up with a most efficient organization size and structure.
"The study, also available in draft form at ArXiv, primarily studied interlocked power grids but could apply to computer networks and interconnected computer systems as well, the authors note. The work could influence thinking on issues such as how to best deal with DDOS (distributed denial-of-service) attacks, which can take down individual servers and nearby routers, causing traffic to be rerouted to nearby networks. Balancing workloads across multiple cloud computing services could be another area where the work would apply."
The study was about the stability of power systems, which is a completely different animal. For power systems, as demonstrated by a few wide spread outages, are at the mercy of the control systems which can over or under react. Computer networks might have some similarities but trying to draw any firm conclusions from this study would be pure speculation.
I would agree though, that at some point you move beyond providing redundant paths to opening up additional areas of exposure and risk.
It's interesting that this story appeared on the same day I read an article on brain hyper-connectivity being linked to depression.
Hell ask the P2P guys because if there is anybody that has to balance craploads of connections its those guys. Look at how much overhead the first gen P2Ps used compared to now, with each version they get better at moving data without the connections getting overloaded. Give me somebody that has actually had to deal with the BS day to day than somebody that is writing a paper any day of the week. the trial by fire quickly weeds out the dumb ideas and you fix it or die.
ACs don't waste your time replying, your posts are never seen by me.
There is a network like that, it's called Freenet.
There's no -1 for "I don't get it."
So I guess this can be considered a Dunbar's number for computer networks?
http://en.wikipedia.org/wiki/Dunbar's_number
Conclusions in TFA (The Fine Article) make sense.
I remember in College, back in the Dark Ages of the 1970's. Communications Theory. That has been known since the late 1940's.
For any system, at the bottleneck points there is a saturation level. When you try to get higher throughput, it saturates the bottleneck, and the throughput either breaks down, or slow substantially.
Ever been stuck in traffic? If so, then you have experienced this effect.
Ever tried to run a large Database on a Windows box? Slowdown and crashes happen.
For every system there is a limit to the communications that can be throughput.
The Internet works by having a massively parallel structure, but every Node on the Internet can only connect to a limited number of other points. The number of connections maintainable has risen as our technology has improved, but there are limits at each step of the way. Sorry guys, that's not because of software or system design, it's a basic result of physics. We can't get unlimited performance out of any foreseeable hardware. Software will always be limited to something less than the limitations of the hardware. There are limits.
This study was about the power system, but it applies to all systems. There is going to be some point of maximum benefit. Trying to go beyond that point will be largely an exercise in frustration. It will only be by changing the physical network that further expansion will be practical. That's the bad news.
The good news is that the current Internet isn't at that point. Yes, it is beyond the capacity of 1990. But, we have changed the parameters of the Hardware. We've even outgrown the capacity of the software from the 1990's. (TCP/IP V4) That's why we are moving slowly to IP V6. but V6, while 'infinite' for today's hardware will also be outgrown someday. Until, that is, our hardware reaches the real physical limits. Only then will we be stuck with no further performance improvements.
Research labs have already reached the physical limits. we know what they are. Fortunately, we probably won't be there for around 10 to 20 years.
Diamond semiconductors, Graphene, circuit elements that consist of fewer than 20 atoms. All these things have been done. Just not economically or reliably. That will come in the future. It'll be fun to see.
I wonder what we will be doing with Petabyte thumb drives and 1000 processor tablet systems?
My Grand-kids will be finding out.
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Luis von Ahn says that past collavorations like putting men on the moon and the A-Bomb project were all done by about 100,000 because tech constraints limited effective organization to groups of that size. But projects like reCAPTCHA, DuoLingo and Wikipedia use massive human computation and organize millions of people. We'll see many more massivly co-ordinated projects and the ideal size of organizations for each kind of project will become more clear as the number of these projects increases.
...at the low amount of comments on this paper. I read it over the weekend, and it offers some insights into network theory as applied "to the everyday world" that engineers have to deal with, that are not all trivial or unimportant. Is it because the article has a "pure" mathematics approach, in spite of using a model of the US power grid for illustration purposes ?
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