Extended Erlang C formular

The Erlang C formula was established in the early 20th century by the Danish mathematician Agner Krarup Erlang, to optimize the performance of the then manually occurring telephone connections. While the original Erlang C formula assumes that the clients are willing to wait any length of time, the here offered extended Erlang C formula also respects the impatience of the clients.

In the Erlang model it is assumed that the inter-arrival times of the clients, the service times and the waiting time tolerances of the clients are distributed exponentially. In addition, it is assumed that the system is in steady state.

To calculate the parameters of queuing system, only the arrival rate, the service rate, the average waiting time tolerance and the number of parallel operators has to be specified.

Arrival process Service process Parameter
Arrival rate (in clients per minute)
Average waiting time tolerance (in minutes)
Average service and post processing time (in minutes)
Number of agents
Waiting time (in secunds)
The probability of a client to have to wait at maximum als long as here specified will be displayed.

Calculate performance indicators

Key performance indicators of the queueing model

Erlang calculator for spreadsheets

Via the next two links example tables allowing to calculate all common Erlang queueing models can be downloaded:

Criticism of the Erlang-C model

At its time of the early 19th century the Erlang formulas opened the first opportunity to model and calculate queueing processes analytically. However, the formulas do not take into account many of the relevant properties today:

  • The exponential distribution is used for the distribution of the service times which usualy is not very realistic.
  • The exponential distribution is used for the distribution of the waiting time tolerances which usualy is not very realistic.
  • It is assumed that the system is in steady state, i.e., that the arrival rate does not change.
  • Customers who start a repeated attempt after a waiting cancelation are not mapped in the model.
  • More complex features, such as different types of customers (and the resulting possibly of multi-skill agents), forwarding, post processing times of the agents, prioritization strategies, etc. are not mapped.

To meet these new demands, the analysis and optimization of queueing systems is now mostly done using simulation methods.

Applications of Queueing Theory in Call Center Management


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