Pick the Right Queueing Model

Erlang C assumes every caller waits forever; Erlang A adds a patience clock so the model stays realistic when people abandon.

Erlang C — what it is

  • M/M/n queue, infinite queue, no abandonment.
  • Poisson arrivals, exponential service, identical agents, FCFS.
  • Outputs: wait probability, SL at target wait, ASA, occupancy, staffing.

Use when

  • Waits are short and abandon <≈5%.
  • You need a quick sizing upper bound or education aid.
  • Channels where customers virtually never abandon.

Pros

  • Simple, fast, widely known.
  • Great for quick SL/ASA checks with minimal data.

Cons

  • No abandonment → can overstate queues and ASA.
  • Unstable under overload; suggests unrealistic staffing.
  • Ignores lost demand and CX impact from abandons.

Erlang A — what it is

  • M/M/n+M queue: same core assumptions plus exponential patience.
  • Callers may abandon before agents answer; abandonment is explicit.
  • Outputs: everything from Erlang C plus abandon %, effective demand, stabilized ASA.

Use when

  • Abandonment is material or varies by queue/time.
  • You compare staffing vs callbacks, virtual hold, or digital deflection.
  • You need realistic peak forecasts or ROI trade-offs.

Pros

  • Realistic under stress; queue self-regulates.
  • Quantifies lost demand and CX when understaffed.
  • Supports per-channel patience assumptions.

Cons

  • Requires patience data or calibration.
  • More complex to explain; wrong patience drifts results.

Key differences at a glance

Abandonment

Erlang C: none. Erlang A: explicit patience parameter.

Overload behaviour

Erlang C: ASA explodes. Erlang A: stays finite thanks to abandonment.

Inputs

Erlang C: λ, AHT, agents, target wait. Erlang A: same plus patience.

KPI coverage

Erlang C: SL/ASA/occupancy only. Erlang A: adds abandon %, effective demand.

Practical tip: default to Erlang A for production planning. Keep Erlang C for quick checks or truly no-abandon queues.

One-liner: Erlang C is fast and simple but blind to abandonment; Erlang A adds patience so forecasts stay honest in modern contact centers.

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