Does one in four equal fifty percent?

… perhaps for sufficiently small values of “four”…

In February 2008 two of Australia’s leading Internet Service Providers, iiNet and Internode, released an ADSL2+ broadband “heatmap”.  It illustrated what a sample of 16,000 customers within the Sydney area were achieving in terms of real ADSL2+ broadband download speeds.  The heatmap can be downloaded from the Internode website here and I’ve reproduced it below.


The map itself commits a few GIS sins including no scale or north arrow.  And personally I find the chosen colour grading makes it difficult to differentiate between the top two speed cohorts.  These criticisms aside however, the point that iiNet and Internode wanted to make is that 50% of metropolitan dwellings are technically capable of speeds of ~12Mbps or faster right now.  And certainly the map seems to support their contention (ISP… contention… boom, tish!… *sound of crickets chirping in the background*).

It’s worth mentioning that the map is a political statement.  iiNet and Internode believe there is no justification for laying down a new and very expensive Fibre To The Node National Broadband Network.  They want to show that the existing copper infrastructure can deliver NBN-like speeds to a large swathe of the population today.  Of course the irony is that both companies are part of a consortium (known as Terria) bidding to actually build the NBN – an NBN that neither actually want.  I guess they decided it’s preferable to be Victor Frankenstein rather than one of The Creature’s innocent victims.  Not that they have much to worry about.  As at January 2009 the NBN appears no closer to being built than it was back in February 2008.

But back to the map.  I have a problem with the map.

Let’s start with this graph on Internode’s website.  It shows how fast ADSL2+ speeds can be, based on your distance from the exchange:


ADSL2+ download speeds drop off exponentially as distance from the exchange increases.  12Mbps or faster is possible at distances of up to 2.5kms.  From that point onwards bitrates rapidly skid off the rails.  Any kind of meaningful ADSL2+ “broadband” (i.e. >1.5Mbps) seems to crap out at approximately 5kms or so.

Now consider the ideal case.  Imagine if dwellings are distributed randomly and uniformly around their exchange inside a perfect circle of radius=5km.  Also assume (I admit unrealistically) that the dwellings are connected to the exchange via perfect, straight, radial lines.  Dwellings within 2.5km of the exchange can download at 12Mbps or faster.  Households located 2.5km to 5km can still get ADSL2+, albeit at lower bitrates.  Any poor saps living beyond the 5km limit cannot get ADSL2+ at all.


OK, that’s a lot of assumptions.  But proportionally π2.52/π5.02=25% of the dwellings are inside the 12Mbps-or-better red zone.  A far cry from the 50% that iiNet and Internode are claiming.

Either I’ve made a hash of the whole analysis (highly likely) or something odd is going on.  One possible explanation is that households who cannot get very fast ADSL2+ speeds simply don’t bother signing up for ADSL2+ at all.  Many households outside the theoretical 12Mbps limit seem quite happy to stick with ADSL1 or some other product.

Something for me to ponder.

P.S. Here’s an excellent mashup of the heatmap and Google Maps courtesy of Whirlpool member “Switters“.


11 Responses

  1. The assumption that you made in your calculations to give the 25% figure is that exchanges are 10km apart, and that there are no or little overlaps of the 5km circles. That assumption is definitely untrue.

    Looking at Brisbane’s exchange distribution (because I can guess the distance better), a 15km straight line from the centre of the city goes through approximately areas served by 10 exchanges. I believe that you will find exchanges to be approx 7km apart, which makes the maths 2.5^2/3.5^2 = 51%

  2. Hi, AustCC. Thanks for the feedback. Not considering overlap was really stupid of me. You are right that it is the overlap that is raising the proportion of households on 12mbps+ in the Sydney area that iiNet and Internode analysed.

    But I was thinking about your example. Overlapping circles of radius=5km, spaced 7km apart from centre to centre along a line would look something like this (to scale)

    Since a household can only be connected to one exchange circles 2 to 5 lose about 20% of their area (by the “look” of it… there’s a geometrically precise way of calculating it). So you get

    [5*2.5^2] / [5^2+4*(5^2-0.2*5^2)]

    =5*2.5^2 / 5^2+4*0.8*5^2
    =5*2.5^2 / 4.2*5^2
    = approx. 30%

    Overlapping would have to be tight to get close to the figure of 50% that iiNet and Internode claim. This is true for the Sydney area that they surveyed, but what about other capital cities?

    It would be useful to see a random sample of Australia as a whole, rather than a select, and possibly biased, area of Sydney.

  3. The key failure with your analysis is to assume that attenuation is constant. Different copper cables have different levels of attenuation. As you get further from the exchange typically the main trunk cables are specified to have lower attenuation so that the speed drop off isn’t actually the same as that graph. So, inner people may have an all 0.4mm Cu cable, outer may have higher gauges (eg. 0.64mm, in the regional areas it goes upto 0.9mm which has very low attenuation – meaning you can get ADSL upto 10km).

    The heatmap is based on actually data (I helped extract ours) – so implying that we’re lying is pretty rude.

    • Of course the heatmap is based on actual data! Nowhere did I imply that you were lying or fabricating results. As I said in my comment above, “it would be useful to see a random sample of Australia as a whole, rather than a select, and possibly biased, area of Sydney.”

      However, I still maintain that the real world *median* ADSL2+ speed is significantly *less* than 12Mbps (probably closer to 8Mbps), if you look Australia/ISP-wide. In fact, latest results from the 2008 Whirlpool survey tends to support that view.

      • You’ve seen our data based on the real world which represents the reality of it. You can maintain whatever you want, but for Metro Australia the median is around 12Mbps – which is all that heatmap is trying to show. It may not match to your perfect theoretical model, so maybe your theoretical model is not right (see my above post as to why).

        iiNET did do versions for Melbourne, Perth IIRC which was in some of their investor presentations which show similar results. This was all about metro and showing that a 12Mbps NBN was a marginal improvement only.

        If you’re going to dismissed real world results as “selected and biased” then you’re calling us liars.

        • IIRC those iiNet results were based on one or two particular exchanges, not a random sample of their ADSL2+ customers across Australia. Nearly 10,000 very tech savvy respondents to the 2008 Whirlpool survey reported their own actual ADSL2+ speeds… and the median was firmly in the 5-10Mbps range. These *are* real world results.

          And for the nth time I’m not calling Internode or iiNet liars, or accusing you of selectively choosing results. However, your data collection methodology could potentially be updated and be made more representative. Results from an Australia wide representative random sample would be very interesting. Criticism is not the same thing as accusation here.

          Having said all that I’m fine with being proved wrong. If you say that the (Internode) median is 12Mbps then that’s OK with me. When did you do the analysis and how were the data collected?

  4. The heat map, if you look, covers almost the entirety of metro sydney – about 40 exchanges and combines Internode AND iiNET port results. Each black dot represents an exchange (you can see the grey boundaries).

    The data was ALL ports running ADSL2+ in those exchanges from iiNET and Internode. ALL Ports remember.

    • Are the exchanges in that area of metro Sydney representative of Australia? If you took a roll of *all* your residential ADSL2+ customers, randomly selected 1000 of them, would you expect the median speed to still be as high as 12Mbps?

      Actually, how easy would this sample be to take?

      • Hard as most in regional areas are wholesale.

        I don’t quite see the point of your argument – we can generate the actual median (rather than sampled) on our own ports for each exchange. You still seem to be arguing that your theoretical model is better than actual complete data (non-sampled).

        • Sorry, I thought you took samples because it’s simply impractical to take a census. For example, on Internode’s website: “…we took a random sample (of) 7,305 Internode Extreme® ADSL2+ broadband services…” Other ISPs that I’ve looked at also seem to base their results on samples too. I just assumed that’s the way it has to be done. If you can generate the actual median off every single port at every single exchange then obviously that is much better. If it is possible, why not report that median rather than the sampled one (and what is the median, out of interest)?

          There’s no real point to any of this. My blog is simply a product of a meandering mind. While I acknowledge the many deficiencies in the model, it’s interesting to me that it roughly matches what customers are actually achieving in the real world. Whirlpool survey respondents are reporting a median ADSL2+ speed of around 8Mbps. Internode and iiNet are saying it should be around 12Mbps. To be clear I’m not accusing anyone of inflating results. But I’d like to understand the difference.

  5. It occurs to me that what you need to focus on is median line attenuation (the database numbers are useful enough) rather than reported speed. Speed varies too much because of issues within people’s houses, CPE choice, choice of line profile (eg. no interleave gives lower download, AnnexM trades download for upload etc). There is also the problem that you get no info from ADSL1 customers.

    If the median line attenuation is 35db or lower (see above chart) then 12Mbps median for ADSL2+ is possible. If it’s higher then it’s not. As I said above outer people tend to have better main cable copper (lower per km attenuation) which will change the reality vs your theoretical model quite a bit.

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