# On Strategic Defense of Stochastic Networks

## TL;DR

This paper models the accumulation of cyber attack damages on vital networks using a 2D monotone random walk, providing predictions for critical threshold crossings related to node failures and associated costs.

## Contribution

It introduces a stochastic model for network attack impacts, analyzing joint functionals of attack progression and thresholds crossing times.

## Key findings

- Predicts time to critical network failure thresholds.
- Provides joint distribution of node failures and costs at threshold crossing.
- Offers analytical tools for network defense planning.

## Abstract

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.