Optimal propagation of security patches in mobile wireless networks: extended abstract

Reliable security measures against outbreaks of malware is imperative to enable large scale proliferation of wireless technologies. Immunization and healing of the nodes through dissemination of security patches can counter the spread of a malware upon an epidemic outbreak. The distribution of patches however burdens the bandwidth which is scarce in wireless networks. The trade-offs between security risks and resource consumption can be attained by activating at any given time only fractions of dispatchers and dynamically selecting their packet transmission rates. We formulate the above trade-offs as an optimal control problem that seek to minimize the aggregate network costs that depend on security risks and resource consumed by the countermeasures. Using Pontryagin's maximum principle, we prove that the dynamic control strategies have simple structures. When the resource consumption cost is concave, optimal strategy is to use maximum resources for distribution of patches until a threshold time, upon which, the patching should halt. When the resource consumption cost is convex, the above transition is strict but continuous.