Dispatch then stop: Optimal dissemination of security patches in mobile wireless networks

The security threat posed by malware in mobile wireless networks can be countered through immunization using security patches. The distribution of patches however consumes bandwidth which is specially scarce in wireless networks, and must therefore be judiciously controlled in order to attain desired trade-offs between security risks and resource consumption. The desired tradeoffs can be attained by activating at any given time only fractions of dispatchers and selecting their packet transmission rates. We formulate the above tradeoffs as optimal control problems that seek to minimize the aggregate network costs that depend on security risks and resource consumed by the countermeasures. We prove that the optimal control strategies have simple structures. When the resource consumption cost rate is concave, the control strategies are bang-bang with at most one jump from the maximum to the minimum value. When the resource consumption cost rate is convex, the above transition is strict but continuous.