Controllability Robustness Against Cascading Failure for Complex Logistics Networks Based on Nonlinear Load-Capacity Model

Abstract

In order to achieve good connectivity after the cascading failure of a logistics network, this paper studies the controllability robustness of complex logistics network based on the nonlinear load-capacity (NLC) model. Firstly, the extended Baraba' si and Albert (BA) network is constructed as a complex logistics network for experiments, based on the power law distribution and the agglomeration and sprawl evolution mechanism. Secondly, the existence of the NLC relationship of the real logistics network is proved, and then the NLC model of complex logistics networks is proposed. Furthermore, a simulation analysis of the controllability robustness and influencing factors of the complex logistics network is carried out under four different cascading failure models. In those models, different scenarios of the NLC and the classical linear load-capacity (LLC) model with initial load (IL)/initial residual capacity (IRC) load-redistribution strategies are combined. The research results show that the main influencing factors of the cascading failure of complex logistics networks for the controllability robustness P' are the tolerance parameters β and γ. Moreover, the effect of γ on the load-capacity relationship under the NLC model is more significant than that of β. Among the four cascading failure models, the one based on the NLC model with IRC strategy is the optimal for controllability robustness. Based on the optimal model, the simulation considering the perspective of the logistics economy shows that the relationship among the network cost e, P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and γ is as follows: under a fixed cost, the greater is γ, the stronger is P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> . Also, when 2 <; γ ≤ 9, the robustness of the network is controllable. According to the requirements of real logistics networks, both controllability robustness and the logistics cost can be controlled, and a solution that against cascading failure can be obtained by adjusting the minimum residual load.