Can I get a Little MORE support around here?

In November last year, I blogged about the phone queue reporting and graphing page beta-released by my ISP, Internode.  The aim was to use the data presented on that page, with some basic queuing theory (Little’s Law), to determine the size of their helpdesk.  I theorised that a rough estimate for how many Internode support staff are on duty at any particular point in time could be given by:

Calls in Queue x 12.5 / Wait Time

Looking at the hourly averages, I concluded that, on the Saturday of my analysis, Internode helpdesk had 8 or so people on hand to assist with customers’ technical problems.  I have been informed that my estimate for that period was surprisingly accurate.

The graphs and hourly averages data were taken offline for a little bit, but they’ve recently been reinstated.  I thought it would be timely and interesting to have another look and see what’s changed over the intervening months.  Last Saturday evening I went through and analysed the hourly averages covering the time period from 8pm Friday (17 July 2009) to 8pm Saturday (18 July 2009).  Note that Internode’s residential technical support helpdesk is staffed from 7am to midnight, 7 days a week.  I then applied the same methodology from Can I get a Little support around here to estimate the number of support staff on duty (last column).

Table 1: Internode helpdesk phone queue – hourly averages

Time period Avg. wait time
Avg. calls queued
Support staff on duty
Friday, 8pm-9pm 00:21 0.1 4
9pm-10pm 00:22 0.1 3
10pm-11pm 00:21 0.0 not enough data
11pm-midnight 00:22 0.0 not enough data
Saturday, 7am-8am 00:22 0.1 3
8am-9am 00:30 0.2 5
9am-10am 00:22 0.2 7
10am-11am 00:26 0.3 9
11am-noon 00:22 0.2 7
noon-1pm 00:22 0.2 7
1pm-2pm 00:23 0.2 7
2pm-3pm 00:23 0.2 7
3pm-4pm 00:58 0.7 9
4pm-5pm 00:22 0.2 7
5pm-6pm 00:23 0.2 7
6pm-7pm 00:22 0.1 3
7pm-8pm 00:21 0.1 4

Looking through my small window of analysis, it appears that Internode have largely resolved any problems they were experiencing late last year/early this year in terms of extraordinarily long wait times.  Time spent in the phone queue has collapsed from around 10 minutes to less than 30 seconds.  However, this dramatic improvement doesn’t appear to be due to any significant increase in staff numbers.



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“.

The Simon Hackett Law of Productivity

Simon Hackett is the Managing Director of my Internet Service Provider of choice, Internode.  Simon is also a long-time member of, and a (very, very) regular participant on my favourite Internet site, the Australian broadband and technology-related discussion forum Whirlpool.  I think it’s great that a company owner and boss makes himself so open and accessible to his customers.  Simon’s Whirlpool posting is also interesting from a statistical point of view.  Based on a recent observation, a totally hare-brained theory, and the liberal application of gonzo statistics, I’m going to formulate what I’ll dub “The Simon Hackett Law of Productivity”

As Simon Hackett’s Whirlpool posting frequency approaches zero, the probability of Internode launching an amazing product or service approaches one.

Yes, you asked for it.  Here comes the science.

The Poisson distribution, named after its discoverer Siméon-Denis Poisson, is a statistical model.  It is used to describe the probability of a number of random, independent events occurring over a fixed period of time, and is a useful tool in queuing theory (where the “events” are arrivals onto the system).  You could argue that posts made to an online discussion forum follow a Poisson distribution, for example.

So let’s say the probability with which a Whirlpool member posts to the discussion forums is random and independent, and follows the Poisson distribution with a mean of λ=post rate.  Up until the 60 days prior to 9 December 2008 (when I came up with this crazy theory), Simon Hackett’s λ was 9.6 posts per day (ppd).

But then something remarkable happened.

From 10 October Simon’s λ crashed from 9.6 ppd to a meagre 5.7 ppd.  From the Poisson probability mass function, the chances of this happening is just 4.5%. Significant at the α=0.05 level.  Perhaps something other than just random variation was afoot.  Early on in Statistics I they warn you not to confuse correlation with causation, but by sheer “coincidence” at the moment Simon’s Whirlpool posting took a nose dive, Internode’s output of cool stuff its customers love to use sky-rocketed. Here’s a list of the headlines covering the 60 days that Simon dropped his lambda:

  • Major Product Updates for ADSL and NodePhone
  • Yorke Peninsula caravan parks get free WiFi access
  • Powers ahead with 100% green energy
  • Tops customer success poll: Roy Morgan
  • Signs new deal with Telstra Wholesale
  • Opens new Sydney office
  • Elbows aside rivals with new Ultra service
  • Launches Chumby in Australia
  • Offers customers free ADSL setup
  • Extreme, NakedExtreme and SOHO ADSL updates
  • Home ADSL2+ sales resume in Tasmania
  • Royal Navy veteran appointed as first CIO
  • Chumby contest to boost Aussie content
  • Internode sponsors telecoms thinkfest
  • Launches unmetered ABC iView


When you look at the average news and media releases per month, the period October to December has been an unprecedented Poissonian burst of quite groovy announcements.

So could it just be happenstance?  Well… yes.  But that would not make for a very interesting blog entry!  So consider if I’m right.  When Simon logs off Whirlpool, Internode get to work.  Keep an eye on Simon’s activity on Whirlpool.  If his participation rate drops below 6 ppd for a period of time then something awesome out of the Internode labs is on the way.

Or perhaps he’s just on the loo.


Can I get a Little support around here?

Yesterday my Internet Service Provider, Internode, released a public beta of its phone queue reporting and graphing software.  You can view it here:

It’s somewhat hypnotic watching the results being updated every 60 seconds.  And there’s quite a few interesting statistics presented on the page, especially if you’re into queuing theory.  In fact I’d like to use queuing theory, and Little’s Law in particular, to have a guess at how many Internode Residential Technical Support Staff are on duty at a given point in time.

Little’s Law (from Wikipedia) states that: The long-term average number of customers in a stable system (N) is equal to the long-term average arrival rate (λ) multiplied by the long-term average time a customer spends in the system (T).  That is, N = λT.

Let’s turn things around a bit so that they apply to Internode’s support desk.  N in Little’s Law will become the number of support staff on duty, λ the rate at which callers come off the queue, and T the time taken to resolve technical problems.

But first things first.  And first we must estimate λ.

Luckily Internode makes this fairly easy.  We are given total wait time and total calls in the queue at a particular point in time.  So callers are arriving on the desk at a rate of (total calls in queue)/(total wait time in queue) every minute.  This is λ.

T is a bit trickier to estimate.  How long does it typically take for support staff to resolve a customer’s technical problem over the phone?  I don’t know.  All I really have to go on is this post from Exetel’s John Linton’s personal blog.  Specifically:

Given an average of 5 minutes of initial talk time per ‘live’ call and the requirement to spend a further 7 – 8 minutes for each call in either call back or other actions…

So it would seem it takes somewhere in the vicinity of 12 or 13 minutes for helpdesk to work through a customer’s technical issue on average.  That sort of feels right based on my very limited experience when it comes to contacting customer support.  Meh, I’ll split the difference and say T=12.5.

Therefore a rough estimate for how many Internode support staff are on duty at any particular point in time could be given by ( “Calls in Queue” x 12.5 ) / “Wait Time”.  For example, as I write this, there are 3 calls in the residential technical support queue and total wait time is 5.01 minutes.  So there must be 12.5×3/5.01=7 staff on helpdesk at the moment.

Earlier this afternoon I went through and analysed the hourly averages covering the time period from 5pm yesterday to 5pm today.  Note that Internode’s residential technical support helpdesk is staffed from 7:30am to midnight, 7 days a week.

Time period Avg. wait time (mins) Avg. calls queued (no.) Est. support staff on duty
Friday, 17:00-17:59 24.39 14.04 7
18:00-18:59 16.45 8.35 6
19:00-19:59 8.36 7.25 11
20:00-20:59 5.3 3.57 8
21:00-21:59 0 0.12 not enough data
22:00-22:59 0 0 not enough data
23:00-23:59 0 0 not enough data
Saturday, 7:00-7:59 3.2 1.27 5
8:00-8:59 5.51 4.17 9
9:00-9:59 14.5 7.08 6
10:00-10:59 16.17 9.03 7
11:00-11:59 6.51 3.52 7
12:00-12:59 6.59 4.18 8
13:00-13:59 12.25 6.67 7
14:00-14:59 8.36 5 7
15:00-15:59 1.1 0.9 10
16:00-16:59 0 0.13 not enough data

Things bounce around a bit because we’re dealing with averages and estimates and other problems such as small amounts of data.  However, looking through my small window of analysis (5pm Friday to 5pm Saturday), it looks like Internode helpdesk usually has 7 or 8 staff on hand to answer customer calls.  Totally unsurprisingly, extra personnel are available to cover peak periods.

I should repeat the analysis covering a busier time when sales and accounts staff are also on duty such as the mid-week period.


Thanks for reading.