Pattern 1
One agent off sick multiplies your average wait by five. Two, and the queue never drains.
Contact centres run on Erlang C, the queueing model behind supermarket checkouts and web servers. The worked example is a 4-person centre. The fix is an overflow agent that takes calls only while the wait is over your target.
The worked example
30 calls an hour, 4 minutes each
Work arriving
2 erlangs
120 minutes of talk time an hour
4 agents
21s
Average wait, 85% inside 20 seconds
3 agents
107s
One person off, five times the wait
2 agents
No limit
Arrivals equal capacity, the queue never drains
The maths
Erlang C at those inputs
Take a centre that receives 30 calls an hour, averaging 4 minutes per call. That is 120 minutes of talk time arriving every hour, or 2 erlangs of work.
To answer 80 per cent of calls within 20 seconds, the target most of the industry sizes to, Erlang C says you need 4 people on the phones. With 4, the average wait is 21 seconds and 85 per cent of calls are answered inside 20. With 3, the average wait is 107 seconds. With 2, arrivals equal capacity, the queue never drains, and the average wait has no value.
The numbers are the Erlang C formula at those inputs. Erlang published it in 1917, and the same formula sizes supermarket checkouts and web servers. At 2 agents the only release valve is callers giving up, and the callers who give up are the ones who waited longest.
Adding a fifth person is one way to buy down the wait. Answering the simple calls in software is another, and voice agents run in Australia are billed by the minute rather than by the shift, so the cost follows the queue instead of the roster.
Explainer
The pattern in 64 seconds
The cost
Why the roster sits above demand
Calls arrive in waves. A roster that holds the target at the peak carries idle agents for the rest of the day, and a roster sized for the average breaks at the peak. Absence makes it worse: every sick day is the 4-to-3 step in the example.
The same maths is why your line closes at five. Staffing for the peak costs money in every hour you are open, so you buy one window. That is the out-of-hours pattern.
The pattern
The overflow agent
01
Set the wait target
Pick the service level the roster is sized to, such as 80 per cent of calls answered within 20 seconds. The agent takes calls only while the queue is over it.
02
Give the agent the query types it passes
Write each query the queue carries at peak as a scenario and run it against the agent. A query type that does not pass stays with the roster (docs.meddle.sh/docs/operate/evals).
03
Forward the busy line
Forward your number to the agent only when your lines are engaged. Carrier busy-forwarding does this without changing the number your callers dial, and the forwarding codes are in the docs.
04
Hand back the rest
A caller the agent cannot finish is transferred to a person, with who is calling and why announced first. The transfer is a tool the agent calls, and the rule for calling it is written in your words.
05
Read the overflow calls
Each call the agent took at peak sits in the transcript with its score. Read the ones it escalated and the ones it should have, and change one line.
On Meddle
Building it
Number
Keep the one you have
Forward your existing number to the agent every time, after a set number of rings, or only when you are already on another call. The overflow pattern is the third option (inbound calls).
Handover
Straight or warm
The agent dials your destination and puts the caller through, or announces who is calling and why before connecting them. The ring timeout is set on the transfer tool itself.
Proof
Scenarios and a judge
Write the query types your queue carries at peak as scenarios and run them. The judge grades whether the agent finished the call or transferred when it should have (docs.meddle.sh/docs/operate/evals).
After
Transcripts and alerts
Every call is stored as a transcript with timings and scores, and alerts can tell you when a call needs attention or a metric slips.
Last updated 4 September 2026
Questions
Before the next sick day
What is Erlang C?
Why does one absent agent multiply the wait by five?
Does the overflow agent replace agents?
How do I route only the overflow to the agent?
Is this the same thing as auto scaling?
Run the overflow scenario before the next sick day.
Build the agent, script the query types your queue carries at peak, and read the graded calls. Forward the busy line to it after it passes.