## Abstract

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.

Original language | English |
---|---|

Article number | 1421 |

Journal | Sensors (Switzerland) |

Volume | 18 |

Issue number | 5 |

DOIs | |

State | Published - May 3 2018 |

### Funding

Acknowledgments: The authors thank the detailed and constructive comments of an anonymous reviewer that greatly improved the presentation of the results in this paper. This work is funded by the Mathematics of Complex, Distributed, Interconnected Systems Program, Office of Advanced Computing Research, U.S. Department of Energy, and by Extreme Scale Systems Center, sponsored by the U. S. Department of Defense, and performed at Oak Ridge National Laboratory managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. The authors thank the detailed and constructive comments of an anonymous reviewer that greatly improved the presentation of the results in this paper. This work is funded by the Mathematics of Complex, Distributed, Interconnected Systems Program, Office of Advanced Computing Research, U.S. Department of Energy, and by Extreme Scale Systems Center, sponsored by the U. S. Department of Defense, and performed at Oak Ridge National Laboratory managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Funders | Funder number |
---|---|

Office of Advanced Computing Research | |

U. S. Department of Defense | |

U.S. Department of Energy | DE-AC05-00OR22725 |

Oak Ridge National Laboratory |

## Keywords

- Aggregated correlation functions
- Cyber-physical infrastructures
- Networked systems
- Product-form and composite utility functions
- Sum-form