Erlangfordeling

Erlangfordeling, also known as the Erlang distribution, is a probability distribution used in queueing theory to model the number of calls or customers arriving at a service facility. It is named after the Danish mathematician Agner Krarup Erlang, who developed the distribution in the early 20th century to analyze telephone traffic.

The Erlang distribution is a special case of the gamma distribution and is characterized by two parameters: the shape parameter k (a positive integer) and the rate parameter λ (a positive real number). The shape parameter k represents the number of independent Poisson processes that contribute to the distribution, while the rate parameter λ represents the average rate of arrivals.

The probability mass function (PMF) of the Erlang distribution is given by:

P(X = x) = (λ^k * x^(k-1) * e^(-λx)) / (k-1)!

where x is a non-negative integer, and e is the base of the natural logarithm.

The Erlang distribution is commonly used in telecommunications, computer science, and operations research to model the number of arrivals in a fixed time interval, the time between arrivals, and the number of customers in a queue. It is particularly useful in analyzing the performance of systems with multiple servers and finite waiting spaces.