In probability theory, the Palm–Khintchine theorem, the work of Conny Palm and Aleksandr Khinchin, expresses that a large number of not necessarily Poissonian renewal processes combined will have Poissonian properties.
It is used to generalise the behaviour of users or clients in queuing theory. It is also used in dependability and reliability modelling of computing and telecommunications.
According to Heyman and Sobel (2003), the theorem describes that the superposition of a large number of independent equilibrium renewal processes, each with a small intensity, behaves asymptotically like a Poisson process:
Let
If the following assumptions hold
1) For all sufficiently large
2) Given
then the superposition