Palm–Khintchine theorem
Encyclopedia
In probability theory
, the Palm–Khintchine theorem, believed to be 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 Han et al. (2006), 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.
Cox and Miller provide a more formal description.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, the Palm–Khintchine theorem, believed to be the work of Conny Palm
Conny Palm
Conrad "Conny" Palm was a Swedish electrical engineer and statistician, known for several contributions to teletraffic engineering and queueing theory....
and Aleksandr Khinchin, expresses that a large number of not necessarily Poissonian
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
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 Han et al. (2006), 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.
Cox and Miller provide a more formal description.