  Network redundancy is one of the spatial network structural properties
critical to robustness against cascading failures in power networks. The
waiting-time distributions for network partitions in cascading failures explain
how the spatial network structures affect the cascading behaviors. Two waiting
time events associated with the first and largest network partitions are
studied for cascading failures under different network redundancies. With the
synthetic power networks, the waiting-time distributions of network partitions
can be systematically analyzed for various network redundancies. Waiting-time
distributions shift to the right accordingly when network redundancies
increase. Meanwhile, the sizes of the largest partitions decrease while the
numbers of them increase statistically. The realistic power networks of France,
Texas, and Poland also show the same trend for waiting-time distributions.
