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title: "Erlang"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575225/Erlang"
format: markdown
---
**Erlang(m,b) - no Crystal Ball distribution = Gamma(0,b,a) with a = m, when a is an integer**

[Erlang equations](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26576091/)

 

 

 

The Erlang distribution (or m-Erlang distribution) is a probability distribution developed by A. K. Erlang. It is a special case of the [Gamma](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575231/) distribution. A Gamma(0, b, a) distribution is equal to an Erlang(m,b) distribution with a = m, when a is an integer. Examples of the Erlang distribution are given below:

 

![image](media://cef12ebd-776b-497c-9c58-b9c8196bbc34)

 

Unlike the Gamma distribution, the Erlang does have a cumulative distribution function.

 

![image](media://9f81dd7c-9387-4efd-b6d8-cefc242dd338)

 

> Macro (mathblock)

 

#### Generation

The Erlang distribution is the same as a Gamma distribution, as long as a is an integer.

#### Uses

The Erlang distribution is used to predict waiting times in queuing systems, etc. where a [Poisson process](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575359) is in operation, in the same way as a Gamma distribution.

 

#### Comments

A.K. Erlang worked a lot in traffic modeling. There are thus two other Erlang distributions, both used in modeling traffic:

 

- Erlang B distribution: this is the easier of the two, and can be used, for example, in a call center to calculate the number of trunks one needs to carry a certain amount of phone traffic with a certain "target service".
- Erlang C distribution: this formula is much more difficult and is often used, for example, to calculate how long callers will have to wait before being connected to a human in a call center or similar situation.

 

 

 

 

 

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