  This paper deals with the detection and prediction of losses due to cyber
attacks waged on vital networks. The accumulation of losses to a network during
a series of attacks is modeled by a 2-dimensional monotone random walk process
as observed by an independent delayed renewal process. The first component of
the process is associated with the number of nodes (such as routers or
operational sites) incapacitated by successive attacks. Each node has a weight
associated with its incapacitation (such as loss of operational capacity or
financial cost associated with repair), and the second component models the
cumulative weight associated with the nodes lost. Each component has a fixed
threshold and crossing of a threshold by either component represents the
network entering a critical condition. Results are given as joint functionals
of the predicted time of the first observed threshold crossing along with the
values of each component upon this time.
