Optimal resource distribution between protection and redundancy considering the time and uncertainties of attacks

•We study the optimal resource allocation strategy considering intentional attacks.•We model attacks with truncated normal distribution.•We propose a dynamic strategy where construction pace is geometric.•The influence of most probable attack time and uncertainties on strategy is studied.•The proposed strategy is more effective in reducing destruction probability.

This paper presents a study of the problem of resource allocation between increasing protection of components and constructing redundant components in parallel systems subject to intentional threats. The defender aims at minimizing the entire system destruction probability during certain time horizon by using the best resource allocation strategy which is determined by redundant components construction pace. Different from previous works which focus on the static resource allocation strategy, we propose a dynamic resource distribution strategy with geometric construction pace model and show its advantage over constant construction pace. The vulnerability model considering a most probable attack time and uncertainties of attack time estimates is provided and a destruction probability is evaluated to quantitatively define the ability of the system to survive an intentional attack. The random time of intentional attack is represented by truncated normal distribution. Through the modeling of the most probable attack time and quantifying the uncertainty of the knowledge of defender about this time, the influence of these factors on the optimal resource allocation strategy is investigated. Proper decision regarding the resource allocation is crucial in protecting safety-critical systems, i.e. nuclear power plant, communication base station, power network. Case studies are presented to illustrate the influence and strategy.