Controlling the self-organizing dynamics in a sandpile model on complex networks by failure tolerance

¹ Energy Systems Division, Argonne National Laboratory - 9700 South Cass Avenue, Lemont, IL, USA
² Department of Civil and Environmental Engineering and Grantham Institute, Imperial College London London, UK

Received: 5 March 2015
Accepted: 23 July 2015

Abstract

In this paper, we propose a strategy to control the self-organizing dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on complex networks by allowing some degree of failure tolerance for the nodes and introducing additional active dissipation while taking the risk of possible node damage. We show that the probability for large cascades significantly increases or decreases respectively when the risk for node damage outweighs the active dissipation and when the active dissipation outweighs the risk for node damage. By considering the potential additional risk from node damage, a non-trivial optimal active dissipation control strategy which minimizes the total cost in the system can be obtained. Under some conditions the introduced control strategy can decrease the total cost in the system compared to the uncontrolled model. Moreover, when the probability of damaging a node experiencing failure tolerance is greater than the critical value, then no matter how successful the active dissipation control is, the total cost of the system will have to increase. This critical damage probability can be used as an indicator of the robustness of a network or system.