Noisy mean field game model for malware propagation in opportunistic networks

H. Tembine, P. Vilanova, and M. Debbah

Mean field games, opportunistic networks.

2012

In this paper we present analytical mean eld techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean eld optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean eld limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realisticfor such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean eld propagation models which focus on deterministic equations, we show that the mean eld limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean eld limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems.