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Population processes in cyber system variability.

Marc Mangel1,2,3, Alan Brown4

  • 1Department of Applied Mathematics, University of California, Santa Cruz, Santa Cruz, CA, United States of America.

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This study applies population biology models to cyber systems, analyzing component functionality and operating system (OS) updates using Markov processes and simulations. Findings offer new insights into cyber system variability and performance scaling.

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Area of Science:

  • Cyber-physical systems
  • Stochastic modeling
  • Systems biology

Background:

  • Cyber systems exhibit inherent variability, impacting reliability and performance.
  • Understanding this variability is crucial for designing robust and scalable systems.
  • Traditional approaches may not fully capture the dynamic nature of cyber component states and updates.

Purpose of the Study:

  • To apply stochastic population biology concepts to model cyber system variability.
  • To analyze the functional states of cyber components and the dynamics of operating system (OS) updates.
  • To develop scalable methods for assessing the performance and security of large cyber systems.

Main Methods:

  • Modeled component state transitions (functional/nonfunctional) as a Markov process.
  • Derived equations for component functionality probability and system performance metrics.
  • Utilized stochastic simulation and solved the forward Kolmogorov (Fokker-Planck) equation.
  • Developed a Gaussian approximation for large-scale system analysis.
  • Modeled OS update schedules and transition probabilities, incorporating OS compromise.

Main Results:

  • Derived an equation for individual cyber component functionality probability.
  • Developed a performance metric dependent on functional and nonfunctional component counts.
  • Obtained a Gaussian approximation for system properties, enabling scalability to large systems.
  • Modeled OS update dynamics and derived the forward equation for OS status over time.
  • Quantified the probability of a cyber component having an unexploited OS.

Conclusions:

  • An interdisciplinary approach, integrating population biology with cyber systems, provides novel perspectives.
  • Stochastic modeling offers powerful tools for understanding and predicting cyber system behavior.
  • The developed methods allow for the analysis and scaling of complex cyber systems with inherent variability.