Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures and Robustness (1201.2698v2)

Abstract: We consider a cyber-physical system consisting of two interacting networks, i.e., a cyber-network overlaying a physical-network. It is envisioned that these systems are more vulnerable to attacks since node failures in one network may result in (due to the interdependence) failures in the other network, causing a cascade of failures that would potentially lead to the collapse of the entire infrastructure. The robustness of interdependent systems against this sort of catastrophic failure hinges heavily on the allocation of the (interconnecting) links that connect nodes in one network to nodes in the other network. In this paper, we characterize the optimum inter-link allocation strategy against random attacks in the case where the topology of each individual network is unknown. In particular, we analyze the "regular" allocation strategy that allots exactly the same number of bi-directional inter-network links to all nodes in the system. We show, both analytically and experimentally, that this strategy yields better performance (from a network resilience perspective) compared to all possible strategies, including strategies using random allocation, unidirectional inter-links, etc.

• The paper introduces and analytically proves that a "regular" allocation strategy for bi-directional inter-links, where each node has an equal number, significantly enhances the robustness of interdependent cyber-physical systems against random attacks and cascading failures.
• Analytical results and simulations demonstrate that this regular allocation strategy leads to a lower critical attack threshold compared to random allocation strategies, allowing a larger fraction of nodes to remain functional after failures.
• The findings provide practical guidance for designing more resilient critical infrastructure, such as power grids and communication networks, by optimizing the interconnections between their cyber and physical components.

Optimal Allocation of Interconnecting Links in Cyber-Physical Systems: Interdependence, Cascading Failures and Robustness

The paper explores the challenges and strategies for link allocation in interdependent networks, which are susceptible to cascading failures due to their interconnections. By focusing on cyber-physical systems comprising interacting networks, such as a cyber-network overlaid upon a physical-network, the paper investigates the robustness of these systems against random attacks.

The authors introduce a model where nodes in either network can only function if connected via inter-links to nodes in the other network. They propose an optimum inter-link allocation strategy, termed the "regular" allocation strategy, wherein each node is provided with an equal number of bi-directional inter-network links. This differs from other strategies that may employ random allocation or unidirectional links.

Analytical Insights and Numerical Results

The analysis employs random graph theory and generating functions to determine the size of functioning network components at steady state and to explore critical attack thresholds. Key findings include:

• Regular Allocation Strategy: This strategy, where each node receives an identical number of bi-directional inter-links, is shown to enhance resilience compared to random allocation models. This approach reduces the critical threshold $p_c$, above which a significant fraction of nodes remains functional in both networks.
• Comparison with Random Allocation: The paper proves analytically that regular allocation results in lower critical thresholds than random allocation strategies, for both bi-directional and unidirectional inter-links.
• Validation via Simulations: The theoretical results are supported by simulations using Erdős-Rényi (ER) networks, confirming that this allocation approach outperforms others by allowing the system to withstand more significant fractions of node failures.

For instance, scenarios where both networks have a degree distribution with average degrees of four, regular allocation with bi-directional links resulted in a critical threshold $p_c = 0.43$. Conversely, systems using random allocation of inter-links with the same average degree showed a much higher critical threshold, meaning they were less resilient to node failures.

Theoretical and Practical Implications

The implications of this work extend both theoretically and practically. Theoretically, it introduces a framework to analyze and optimize the interplay between interdependent networks, providing a basis for further studies on cascading failures. Practically, it offers strategies for designing more robust cyber-physical systems by optimizing inter-link allocations to minimize failure risks in vital infrastructures like power grids and communication networks.

Future Directions

While this work advances understanding of interdependence-induced vulnerabilities, future research may explore interdependencies involving more than two networks or incorporate specific topological insights into allocation strategies. Additional considerations might include the effect of network heterogeneity and node specific importance, factors crucial for evolving robust systems against escalating cyber-physical threats. The paper's framework can further be expanded to evaluate the implications of autonomous nodes and correlated inter-intra network topologies.

In conclusion, this paper substantiates regular allocation of inter-link edges as the robust choice for mitigating cascading failures in interdependent network systems lacking detailed topological data, highlighting its superior performance over other conventional strategies.