Hyper-Erlang distribution

In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution E_i with probability p_i. A hyper-Erlang distributed random variable X has a probability density function given by

Diagram showing queueing system equivalent of a hyper-Erlang distribution

${\displaystyle A(x)=\sum _{i=1}^{n}p_{i}E_{l_{i}}(x)}$

where each p_i > 0 with the p_i summing to 1 and each of the E_li being an Erlang distribution with l_i stages each of which has parameter λ_i.^[1][2][3]

See also

• Phase-type distribution

References

1. Bocharov, P. P.; D'Apice, C.; Pechinkin, A. V. (2003). "2. Defining parameters of queueing systems". Queueing Theory. doi:10.1515/9783110936025.61. ISBN 9783110936025.
2. Yuguang Fang; Chlamtac, I. (1999). "Teletraffic analysis and mobility modeling of PCS networks". IEEE Transactions on Communications. 47 (7): 1062. doi:10.1109/26.774856.
3. Fang, Y. (2001). "Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks". Wireless Networks. Kluwer Academic Publishers. 7 (3): 211–219. doi:10.1023/A:1016617904269.