By Franceschetti M., Meester R.
ISBN-10: 0521854423
ISBN-13: 9780521854429
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Additional resources for Random networks for communication
Sample text
It is easy to see that the integrability condition is required to avoid a trivial model. Indeed, let Y denote the (random) number of points that are directly connected to the origin. 48) k! where this expression is to be interpreted as zero in the case 2 g x dx = . s. s. As usual, we write the number of vertices in the component at the origin as C and =P C = ; we sometimes omit the subscript when no confusion is possible. 2 (see the exercises). We also have the following phase transition theorem.
It is also reasonable to assume that this link can sustain a certain information flow, which is proportional to the SNR. 16) N A physical justification for this formula will be given in Chapter 5. The formula shows that every pair of nodes in the network is connected by a link that can sustain a constant information rate, whose value depends on the loss factor between xi and xj , and hence by their random positions on the plane. 16) to account for the case of simultaneous communication of different nodes in the network.
Again, in order to talk about these we need some information theory background that we provide in Chapter 5. For now it is sufficient to keep in mind that the geometry of the information-theoretic network model is that of an infinite, fully connected graph, where vertices are Poisson points and the flow of information on each link is limited by the random spatial configuration of the nodes and by their transmission strategies. 4 Historical notes and further reading The random tree network is known as a Galton–Watson branching process, after Watson and Galton (1874).
Random networks for communication by Franceschetti M., Meester R.
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