## 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:

http://www.internode.on.net/customer-service/

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.

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