Research On The Network Fortification Model Based On R-Interdiction

Research on the fortification of the critical infrastructure, there are three main aspects. First, the facility location problem, namely, how to determine the initial network; Second, identity the critical infrastructure. In the existing network, which one or a few facilities interrupted, then the operating losses of the whole system is the largest. The facilities are the critical infrastructures; Third, distribution of limited defensive resources. Because in the reality social, the defensive resources are always limited, we can’t protect all facilities in the system. So, how to allocate the limited defensive resources, making the overall operating cost minmun after attacks, in order to achieve the optimal allocation of resources.In this paper, the complex supply system is simplified to a general network with several facility points, some demand points and the specific transportation paths. Using P-median location model solves the facility location problem, so we get the initial supply network. On this basis, we study the fortification of critical infrastructure.The manager of supply system is the defender, and the random attack and deliberate attack is the destroyer. Using Stackelberg game analyzes the relationship between the defender and the destroyer. First, the top-level defender determines defensive strategy after analysis and forcast to the destroyer, to minimize the system operation cost after attacks. Then, the lower-level destroyer determines the disruptive strategy, based on the knowledge of defensive strategy, to maximize the the system operation cost after attacks. In this paper, the network operation cost is the sum of weighted distance between demand points and infrastructure points.In this paper, we proposed a new method to measure the limited defensive and disruptive resources. The defensive resources are measured to some defensive units. The defender can layout one or a few defensive units to a infrastructure. The disruptive resources are measured to a number of attacks. The destroyer can attack to a infrastructure one time or several times. We also consider the successful probability of individual defensive unit intercepting an attack. And we also consider the extra cost when the demand points change the supply infrastructure, after attacks. Based on this, we present the formulation of critical infrastructures fortification based on R-interdiction. Then we make the example analysis. By comparing the best disruptive strategy without defender and the best defensive strategy after defender-destroyer game, the scientificity and the necessity of the study in this paper are. proved. Besides, the calculation results show that the two parameters, the successful probability and the extra cost, both can effectively influence the best defensive strategy. The successful probability determines the defender weather maximizing the number of defensive infrastructures, or concentrating defensive resources to a few critical infrastructures. The extra cost will lead to the adjustment of the best defensive strategy. This research has certain guiding significance to the real network managers.