A Poisson Limit Theorem for Hybrid Star Networks: the Mean Field Approximation

We present an asymptotic analysis of the equipped marked point process describing the stationary operation of a star network with hybrid switching, including elements of both message switching and circuit switching. Asymptotic formulas are given for the distribution of the delivery time of a single message. The results may be considered as a variant of the Poisson conjecture originally proposed by L. Kleinrock for message switching networks. In the language of physics, this corresponds to passage to the limit in the mean field approximation.