About the Erlang formula

The calculation of the number of resources needed for each day and interval is based on the Erlang A model. The Erlang A model is an extension of the Erlang C model and therefore you need to understand Erlang C to understand Erlang A.

Erlang C

Erlang C is a traffic modeling formula used in call centers to determine the number of resources needed to keep the wait times within the contact center's service level targets. This method assumes that all callers stay in the queue until the call is answered, and therefore might overestimate the staff that is required. When scheduling the agents, Erlang C can also be used to calculate the predicted service level.

Erlang C bases its formula on three factors; the number of agents providing service, the number of callers waiting and the average amount of time it takes to serve each caller.

Erlang A

The difference between Erlang A and Erlang C is that Erlang A takes the average patience into account, where Erlang C assumes that callers have infinite patience. If you set the abandon rate for a skill to 0%, this is the same as using Erlang C because that means that you are saying that no one will leave the queue.

The average patience is the average time a caller is willing to wait before leaving the queue. WFM uses the abandon rate for the skill to estimate the average patience. The average patience is used to calculate the waiting probability in the formula below.

Calculation of agents needed

The calculation of the number of agents needed with Erlang A uses these measures.

  • Service level
  • Service time
  • Number of calls
  • Average handling time
  • Minimum occupancy
  • Maximum occupancy
  • Average patience with abandon rate

Calculation of predicted service level

The calculation of the predicted service level with Erlang A uses these measures.

  • Scheduled agents
  • Number of calls
  • Average handling time
  • Service time
  • Minimum occupancy
  • Maximum occupancy
  • Average patience with abandon rate

Formula

This formula is used to calculate the probability that a customer must wait for service.

where

and and

  • Pw—Probability that a customer must wait for service.
  • λ—Number of calls.
  • µ—Service rate (1/µ = Average handling time)
  • n—Number of agents.
  • θ—Individual abandon rate (1/ θ = Average patience).

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