Palm–Khintchine theorem

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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.[1]

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.[2]

Cox and Miller provide a more formal description.[3][not in citation given]


  1. ^ Daniel P. Heyman, Matthew J. Sobel (2003). "5.8 Superposition of Renewal Processes". Stochastic Models in Operations Research: Stochastic Processes and Operating Characteristics. 
  2. ^ Han, Yijie; La, Richard J.; Makowski, Armand M.; Lee, Seungjoon (2006). "Distribution of path durations in mobile ad hoc networks—Palm’s Theorem to the rescue". Computer Networks 50 (12): 1887–1900. doi:10.1016/j.comnet.2005.10.005. 
  3. ^ Cox, D. R. & Miller, H. D. (1977). The Theory of Stochastic Processes. Chapman and Hall/CRC. Retrieved 2010-05-23.