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Large deviations for the capacity in dynamic spatial relay networks
We derive a large deviation principle for the space-time evolution of users
in a relay network that are unable to connect due to capacity constraints. The
users are distributed according to a Poisson point process with increasing
intensity in a bounded domain, whereas the relays are positioned
deterministically with given limiting density. The preceding work on capacity
for relay networks by the authors describes the highly simplified setting where
users can only enter but not leave the system. In the present manuscript we
study the more realistic situation where users leave the system after a random
transmission time. For this we extend the point process techniques developed in
the preceding work thereby showing that they are not limited to settings with
strong monotonicity properties.Comment: 24 pages, 1 figur
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