What is an Erlang Calculator?

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An Erlang C calculator is a mathematical tool used in call centre management and workforce planning to estimate the required staffing levels needed to meet specific service level agreements (SLAs). It is based on the Erlang C formula, developed by Danish mathematician Agner Krarup Erlang, and is widely used in operations research and queuing theory.

The primary purpose of the Erlang C calculator is to predict the probability of a customer having to wait to be served, based on factors such as call volume, handling times, and the number of available agents. It is particularly valuable in environments where customer interactions are handled in real-time, such as call centres, service desks, and technical support teams.

How Does the Erlang C Formula Work?

The Erlang C formula evaluates queuing scenarios and assumes that:

  • Calls arrive randomly but follow a Poisson distribution.
  • All agents work at a consistent rate.
  • Calls are held in a queue if no agents are available.
  • There are no abandoned calls; customers wait indefinitely until an agent becomes available.

Using these assumptions, the Erlang C formula calculates the probability that a call will have to wait before being answered, which can then be translated into other metrics, such as the average waiting time or service level.

Inputs to an Erlang C Calculator

An Erlang C calculator requires several key inputs to produce results:

  1. Call Volume (A): The number of customer interactions or calls expected during a specific period.
  2. Average Handling Time (T): The average time (in seconds or minutes) it takes an agent to handle a single call or interaction.
  3. Number of Agents (N): The number of agents or staff available to handle the workload.
  4. Target Service Level: The percentage of calls answered within a specific time (e.g., 80% answered within 20 seconds).

With these inputs, the calculator provides critical data, including:

  • The probability of callers waiting in a queue.
  • The average waiting time for calls.
  • The agent occupancy rate, i.e., how busy agents are during the period.

Limitations of the Erlang C Model

While the Erlang C calculator is highly useful, it has limitations:

  • No Abandonment Considered: It assumes customers will wait indefinitely, which may not reflect real-world scenarios.
  • Assumes Constant Work Rates: Variations in agent performance or multitasking are not accounted for.
  • Ignores Variability in Call Arrival Patterns: It assumes a random arrival pattern but may not account for peaks and troughs during the day.

Published On: 20th Jan 2025 - Last modified: 22nd Jan 2025
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