The most realistic Erlang model — and it isn't C
Most planners reach for Erlang C, trust the number it gives back, and move on. This issue is about the one time that number quietly lets you down — and the model that fixes it.
The model nobody taught you: Erlang X
Erlang C makes one heroic assumption: that every caller waits forever. Real callers don't. Some hang up when their patience runs out (abandonment), some hit a busy tone when every line is full (blocking), and a good share of both simply call back (redials). Erlang X — assembled by the Dutch mathematician Ger Koole in the 1990s — folds all three into a single model.
There's a catch that makes it genuinely interesting: redials feed back into the load, which causes more abandonment and blocking, which generates more redials. It's circular, so there's no tidy closed-form formula — you solve it by iteration.
Why it matters on the floor: Erlang C over-staffs an impatient, line-limited queue — the "restaurant table effect," where it has 70 couples all waiting indefinitely for 50 tables, when in reality some take one look and leave and a few drift back later. Erlang X models that attrition and the redials, so it sizes the operation more honestly — usually fewer agents, though not always.
The full story, free
I've just published From Erlang to Excel — contact-centre queueing theory from beginner to expert, with every formula rebuilt cell-by-cell in a spreadsheet you control. It now includes a full Erlang X section, a diagram of the redial loop, and a live companion workbook with Erlang B, C, A and X built as real formulas. The X sheet uses iterative calculation, so you can change patience, line count and the redial rate and watch blocking and abandonment settle.
→ Read it and grab the workbook: From Erlang to Excel
Five minutes, one calculator
New this fortnight: a free Erlang X calculator. Enter your volume, patience, line count and redial rate, and it returns abandonment, blocking, occupancy and the extra load those redials create. Worth a look even if you only ever staff with Erlang C — it shows you exactly where the two diverge for your numbers.
The takeaway
You don't need Erlang X every day. For a patient, uncapped queue, Erlang A — or even plain Erlang C — is fine. Reach for X when waits regularly creep past about 90 seconds, when abandonment is real, when lines are genuinely capped, or when you want to see what a busy signal is actually costing you in redials. Knowing when a model stops being trustworthy is the deeper skill.
Until next time,
John ccPlanning
