Defense Resource Distribution Between Protection and Redundancy for Constant Resource Stockpiling Pace
ABSTRACT The article considers the optimal resource distribution in a parallel system between increasing protection and providing redundancy in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed along this horizon. The defender optimizes the resource distribution in order to minimize the system destruction probability during the time horizon. First, we find the optimal pace of construction of the new redundant elements assuming that the construction must start in the initial stage of the stockpiling process. We show that starting construction of new elements in the beginning of the system's existence results in its high initial vulnerability. Introducing the time delay before starting the construction can reduce the initial system vulnerability and the entire system destruction probability. The problem of optimization of time delay and new element construction pace is considered with and without constraint on the initial system vulnerability. Examples illustrating the methodology of the optimal defense strategy analysis are presented.
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ABSTRACT: The paper compares the efficiency of single and double attack against a system consisting of identical parallel elements. An attacker maximizes the system vulnerability (probability of total destruction). In order to destroy the system, the attacker distributes its constrained resource optimally across two attacks and chooses the number of elements to be attacked in the first attack. The attacker observes which elements are destroyed and not destroyed in the first attack and allocates its remaining resource into attacking the remaining elements in the second attack. The paper considers two types of identification errors: wrong identification of a destroyed element as not destroyed, and wrong identification of a not destroyed element as destroyed. First, the influence of the identification error probabilities on the optimal attack strategy against a system with a fixed number of elements is analysed. Thereafter, a minmax two-period game between the attacker and the defender is considered, in which the defender in the first period distributes its constrained resource between deploying redundant elements and protecting them against the attack in the second period. It is shown how the identification error probabilities affect the defence strategy.Journal of the Operational Research Society 11/2012; 63(11). DOI:10.1057/jors.2012.4 · 0.91 Impact Factor
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ABSTRACT: The paper considers the optimal resource distribution between increasing protection of genuine elements and deploying decoys (false targets) in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed over this horizon. Series and parallel systems are considered. The defender optimizes the resource distribution in order to minimize the system vulnerability. The attacker cannot distinguish genuine and false elements and can attack a randomly chosen subset of the elements.Journal of the Operational Research Society 09/2013; 64(9). DOI:10.1057/jors.2012.117 · 0.91 Impact Factor
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ABSTRACT: 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.European Journal of Operational Research 12/2014; 243(1). DOI:10.1016/j.ejor.2014.12.006 · 1.84 Impact Factor