Erlang X

Erlang X extends Erlang C with customer abandonment (patience) and a retrial feedback loop: some customers who abandon or cannot get through redial and re-enter the arrival stream.

Erlang X is a queueing model for contact center staffing that extends the classical Erlang C formula with two behaviours that real customers exhibit: abandonment (callers leave the queue if they wait beyond their patience) and retrials (a portion of callers who abandon, or who get a busy signal, redial after a delay and re-enter the system). It sits at the top of the Erlang family used in workforce management: where Erlang B models loss systems and Erlang C assumes infinitely patient customers and no redials, Erlang A adds abandonment, and Erlang X adds the retrial loop on top of abandonment.

Why retrials and patience matter

Erlang C systematically misstates staffing because its assumptions are false in practice. It assumes no one abandons, so it over-counts the work that must be answered and can over-staff lightly loaded queues; at the same time it ignores retrials, which add load that a naive model misses. Abandonment and redialling interact: a caller who abandons and redials appears in the data as two contacts, inflating apparent volume, while the underlying demand is one customer with one need. Modelling these behaviours explicitly produces staffing requirements and predicted service levels that match observed operations more closely than Erlang C, particularly in understaffed or volatile conditions.

How it works

Erlang X adds parameters to the Erlang C structure for the rate at which waiting customers abandon (a patience distribution) and the probability and timing of a retrial after abandonment. Because retrials feed back into arrivals, the effective load is not simply the offered load: it depends on the service level itself, since worse service produces more abandonment and therefore more redials. This feedback makes the model non-trivial to solve in closed form; in practice it is evaluated numerically. The result is a relationship between agent count, service level, abandonment rate, and effective load that is more realistic than Erlang C across the full volume range.

The model is implemented in several commercial and open tools. The CCmath Erlang engine, developed under co-founder Ger Koole, includes Erlang X alongside Erlang C and blending models, and CCmath's 2026 "Erlang v4" release reported improvements to low-volume interpolation and blending in that engine.

WFM applications

• Accurate staffing under abandonment. For queues where customers do abandon — most voice queues — Erlang X gives a less wasteful requirement than Erlang C, which assumes everyone waits.
• Untangling repeat contacts. Retrial modelling helps separate true demand from redial-inflated volume, improving both forecasting and the interpretation of resolution metrics. It is closely related to the operational problem of not double-counting the same underlying work.
• Realistic service-level prediction. Because the model captures the abandonment–redial feedback, its predicted service levels are more dependable in the understaffed regime where Erlang C is least accurate.

Limitations

• More parameters to estimate. Erlang X requires a patience distribution and retrial parameters, which must be measured from data; poor estimates degrade the benefit.
• Still a model. Like all Erlang models it assumes stationary arrivals within an interval and a single skill; multi-skill and time-varying behaviour require simulation.
• Data and tooling. Capturing abandonment and retrial behaviour requires instrumentation many operations lack, so the model is sometimes run on assumed rather than measured parameters.

Maturity Model Position

In the WFM Labs Maturity Model™, the Erlang variant an operation actually uses is a staffing-sophistication signal.

• Level 1–2 (Emerging / Foundational) — staffing uses Erlang C with its no-abandonment, no-retrial assumptions, accepting the resulting bias.
• Level 3 (Progressive) — abandonment-aware models (Erlang A, Erlang X) are used where customers demonstrably abandon and redial, with patience and retrial parameters estimated from data.
• Level 4–5 (Advanced / Pioneering) — retrial and abandonment behaviour is measured and fed into staffing, and where the single-skill assumption fails the operation moves to simulation rather than forcing a formula.

See also

• Erlang C
• Erlang A
• Erlang B
• Queueing Theory Fundamentals
• Ger Koole
• CCmath
• Fractional Agents and Staffing Interpolation