Robust Capacity of Wireless Networks Under Cascading Failures

In this paper, we study the impact of node cascading failures and network structure robustness on the capacity of wireless networks. Especially, in order to quantify how much information can be conveyed by wireless networks under node cascading failures, robust capacity is defined to capture the influence of the intensity of the initial failure nodes
$m$
and the connectivity parameter
$k$
on capacity. Note that increasing
$k$
could provide
$k$
disjoint data paths for any two nodes, thereby combating the cascading failure. Denoting the intensity of the nodes as
$n$
and
$m=n^{\frac{1}{\beta}}$
, it is shown that robust capacity
$O\left(\sqrt{\frac{n}{k\log n}}\right)$
can be achieved when the initial failure exponent
$\beta > 2$
. In contrast, robust capacity would converge to zero with increasing
$n$
when
$1 < \beta\leq 2$
since the data paths of most source-destination pairs are interrupted due to the cascading failures. Moreover, increasing the connectivity parameter
$k$
, although capable of enhancing the network structure robustness, is shown to degrade cascading failures and robust capacity.