# On Defense Strategies for Recursive System of Systems Using Aggregated Correlations

## Abstract

We consider a class of Recursive System of Systems (RSoS), wherein systems are recursively defined and the basic systems at finest level are composed of discrete cyber and physical components. This formulation captures the models of systems that are adaptively refined to account for their varied structure, such as sites of a heterogenous distributed computing infrastructure. The components can be disrupted by cyber of physical means, and can also be suitably reinforced to survive the attacks. We characterize the disruptions at each level of recursion using aggregate failure correlation functions that specify the conditional failure probability of RSoS given the failure of an individual system at that level. At finest levels, the survival probabilities of basic systems satisfy simple product-form, first order differential conditions using the multiplier functions, which generalize conditions based on contest success functions and statistical independence of component survival probabilities. We formulate the problem of ensuring the performance of RSoS as a game between an attacker and a provider, each with a utility function composed of a survival probability term and a cost term, both expressed in terms of the number of basic system components attacked and reinforced. We derive sensitivity functions at Nash Equilibrium that highlightmore »

- Authors:

- ORNL
- Hang Seng Management College, Hon Kong
- Texas A&M University, Kingsville, TX, USA

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1468113

- DOE Contract Number:
- AC05-00OR22725

- Resource Type:
- Conference

- Resource Relation:
- Conference: International Conference on Information Fusion (FUSION 2018) - Cambridge, , United Kingdom - 7/10/2018 8:00:00 AM-7/13/2018 8:00:00 AM

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Rao, Nageswara S., Ma, Chris Y. T., and He, Fei.
```*On Defense Strategies for Recursive System of Systems Using Aggregated Correlations*. United States: N. p., 2018.
Web. doi:10.23919/ICIF.2018.8455421.

```
Rao, Nageswara S., Ma, Chris Y. T., & He, Fei.
```*On Defense Strategies for Recursive System of Systems Using Aggregated Correlations*. United States. doi:10.23919/ICIF.2018.8455421.

```
Rao, Nageswara S., Ma, Chris Y. T., and He, Fei. Sun .
"On Defense Strategies for Recursive System of Systems Using Aggregated Correlations". United States. doi:10.23919/ICIF.2018.8455421. https://www.osti.gov/servlets/purl/1468113.
```

```
@article{osti_1468113,
```

title = {On Defense Strategies for Recursive System of Systems Using Aggregated Correlations},

author = {Rao, Nageswara S. and Ma, Chris Y. T. and He, Fei},

abstractNote = {We consider a class of Recursive System of Systems (RSoS), wherein systems are recursively defined and the basic systems at finest level are composed of discrete cyber and physical components. This formulation captures the models of systems that are adaptively refined to account for their varied structure, such as sites of a heterogenous distributed computing infrastructure. The components can be disrupted by cyber of physical means, and can also be suitably reinforced to survive the attacks. We characterize the disruptions at each level of recursion using aggregate failure correlation functions that specify the conditional failure probability of RSoS given the failure of an individual system at that level. At finest levels, the survival probabilities of basic systems satisfy simple product-form, first order differential conditions using the multiplier functions, which generalize conditions based on contest success functions and statistical independence of component survival probabilities. We formulate the problem of ensuring the performance of RSoS as a game between an attacker and a provider, each with a utility function composed of a survival probability term and a cost term, both expressed in terms of the number of basic system components attacked and reinforced. We derive sensitivity functions at Nash Equilibrium that highlight the dependence of survival probabilities of systems on cost terms, correlation functions, and their partial derivatives. We apply these results to a simplified model of distributed high-performance computing infrastructures.},

doi = {10.23919/ICIF.2018.8455421},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {7}

}