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.
Highlights
Infrastructures for cloud computing, science experiments and computations and smart energy grid consist of complex, geographically-dispersed systems that are connected over long-haul networks.In these infrastructures, the communications network plays a critical, asymmetric role of providing the vital connectivity between the systems such as cloud computing sites, or supercomputers, or energy distribution centers
The multi-site cloud computing infrastructure was discussed as an example for sum-form and product-form utility functions in [1] and composite utility functions in [3], wherein the network plays a critical asymmetric role
While the reinforcements to individual server sites or networks are not directly reflected in other systems, their failures may still be correlated due to the underlying system structures as reflected in the aggregated correlation function of the network CN +1. These system-level considerations for the provider are captured by the following condition, which is obtained by differentiating PI in Condition 1 with respect to xi and ignoring the terms corresponding to Parts (i) and (ii) above
Summary
Infrastructures for cloud computing, science experiments and computations and smart energy grid consist of complex, geographically-dispersed systems that are connected over long-haul networks. The sum-form represents a weak coupling between gain and cost terms, since the effect of their minimization on the utility function is independent For a provider, this form is used when explicit “gain” in keeping the infrastructure up can be identified and balanced against the cost. The product-form represents a strong coupling between probability and cost terms, since the effect of minimization of one term gets multiplied by the other This utility is used when the main goal of the provider is to keep the infrastructure up with the cost incurred, since there is no explicit ”gain” term. We present our game-theoretic formulation using sum-form, product-form and composite utility functions in Section 4 and derive NE conditions and estimates for the system survival probabilities and expected capacity.
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