  Robustness and cascading failures in interdependent systems has been an
active research field in the past decade. However, most existing works use
percolation-based models where only the largest component of each network
remains functional throughout the cascade. Although suitable for communication
networks, this assumption fails to capture the dependencies in systems carrying
a flow (e.g., power systems, road transportation networks), where cascading
failures are often triggered by redistribution of flows leading to overloading
of lines. Here, we consider a model consisting of systems $A$ and $B$ with
initial line loads and capacities given by $\{L_{A,i},C_{A,i}\}_{i=1}^{n}$ and
$\{L_{B,i},C_{B,i}\}_{i=1}^{n}$, respectively. When a line fails in system $A$,
$a$-fraction of its load is redistributed to alive lines in $B$, while
remaining $(1-a)$-fraction is redistributed equally among all functional lines
in $A$; a line failure in $B$ is treated similarly with $b$ giving the fraction
to be redistributed to $A$. We give a thorough analysis of cascading failures
of this model initiated by a random attack targeting $p_1$-fraction of lines in
$A$ and $p_2$-fraction in $B$. We show that (i) the model captures the
real-world phenomenon of unexpected large scale cascades and exhibits
interesting transition behavior: the final collapse is always first-order, but
it can be preceded by a sequence of first and second-order transitions; (ii)
network robustness tightly depends on the coupling coefficients $a$ and $b$,
and robustness is maximized at non-trivial $a,b$ values in general; (iii)
unlike existing models, interdependence has a multi-faceted impact on system
robustness in that interdependency can lead to an improved robustness for each
individual network.
