Defense resource allocation in road dangerous goods transportation network: A Self-Contained Girvan-Newman Algorithm and Mean Variance Model combined approach
Introduction
With the fast development of the chemical industry and social economic, the demand of dangerous goods increases year by year. In China, by the end of 2015, the survey results show that there are 502 industries in national key chemical parks or petrochemical enterprises, the total output of these 502 chemical parks reached 6.6 trillion in China yuan, accounting for 56% of the total production of the national chemical and petroleum industries, which has greatly promoted the development of dangerous goods market [11, 14]. Generally, the production places and demand places of dangerous goods are located in different regions, which makes the transportation of dangerous goods more active in various transportation networks. A large number of vehicles carrying inflammable, explosive, radioactive, infectious, toxic and corrosive dangerous goods move on the road transport network, and forms the mobile hazard sources [15]. Due to the convenient and high-efficient “door to door” transport service, most of the dangerous goods are transported by road [10].
Accidents of dangerous goods transported by road have the characteristics of strong destructiveness and wide spread, and are easy to cause secondary harm. Once the accidents happen during the transportation process, it will cause great threat to people's life and property, and will also bring extremely bad influence to the society. According to the statistical data, from 2006 to 2015, 687 dangerous goods accidents occurred in China, causing about 1267 deaths. The accidents occurred during the transportation of dangerous goods accounted for 34% of the total accidents, which has the highest proportion [12, 13]. According to a European study, there were 3222 dangerous goods accidents from 1926 to 1997, 41% of which occurred during transportation [12].
In order to provide rapid emergency rescue services after the occurrence of road dangerous goods transportation accidents, prevent the occurrence of secondary accidents and reduce casualties, property losses and environmental damage in the road transportation network as much as possible, some defense resources need to be arranged in the nodes or edges of the road dangerous goods transportation network in advance. Generally, the limited defense resources might be fixed defense facilities and equipment (e.g., fire-fighting facilities, rescue equipment) or the mobile support materials (e.g., emergency rescue vehicle), which should be allocated reasonably in the node or edges of network according to a certain proportion, and should be transported to the accident points in the shortest time after the accident happened [31], so as to improve the network robustness [34] and to mitigate the network vulnerability [1, 6, 17], such issue can be defined as the defense resource allocation [2].
A lot of previous works have been devoted to the defense resources allocation in a network (e.g., in scale-free networks, in small-world network, in multi-commodity networks) considering single or multiple intentional impacts (e.g., strategic attacks) [9], single or multiple unintentional impacts (e.g., natural disasters), or sequential intentional and unintentional impacts [32], or focusing on improving network security performance [21]. The game theory [20, 27, 35], trilevel programming [1], intelligent countermeasure [18, 24], resource allocation model considering sequential intentional and unintentional impacts [32], decision tree [3, 19], estimation of the Pareto frontier via the Non-dominated Sorted Genetic Algorithm II [17], system analysis [22], agent-based modeling and reinforcement learning [29], Power Function Allocation Model (Li et al., 2008; [6]) and stochastic game theory [31] have been devoted to model the allocation of network defense resource. Actually, the essence of defense resource allocation in networks is an optimization problem. Hence, the intelligent optimization algorithms have been applied to the network optimization in recent years, e.g., memetic algorithm (MA) applied to enhance the robustness of scale-free networks against malicious attack without changing the degree distribution [36], particle swarm optimization (PSO) to search the most favorable pattern of node capacity allocation to improve the network robustness with minimum cost [5, 34] etc. The previous defense resources allocation works are concluded and summarized in Table 1.
As the conclusion of Table 1, we can find that: most of the previous defense resources allocation works are based on the whole network structure without community partition, which considered that a network especially a complex network is composed of many communities (or groups) with the same or similar properties, the connections among nodes are relatively dense in one community, and the connections among communities are strong.
In 2002, the community structure of complex network was proposed [8], which defines the community in a complex network as a collection of some nodes in the network. Fig. 1 shows an example of community structure in a complex network, we use the actual physical average distance to measure the average distance among the nodes, and use the average node degree to measure the connection among nodes, the higher average node degree is, the stronger the connection is. From Fig. 1 we can find that in one community, the average distance among these nodes is relatively short and the average connection among nodes is relatively strong. However, according to the actual operational practice, for the whole communities, the average distance among nodes in different communities is quite long, the average connection among nodes in different communities is relatively weak (e.g., only one edge connects the two communities in a road dangerous goods transportation network). The defense resources should not be allocated based on the whole network structure, because as long as the connections between the communities are broken, the whole transportation of defense resources will be influenced [33]. In order to ensure the rationality of resource allocation in the whole network, and improve the robustness of resource allocation process in community when accident happened, and achieve the purpose of rapid emergency rescue services, the whole network should be separated into several communities, and the defense resources should be allocated based on the community structure [7, 33].
In this paper, we want to solve two key problems: (i) How to separate a network into several communities? (ii) How to allocate the defense resource in a community? Firstly, we establish the topological structure of road dangerous goods transportation network in a region. Based on the structure of the network, we use the Self-Contained Girvan-Newman Algorithm [23] to separate the whole network into several communities. After that, for each community, the defense resource allocation approach based on Mean Variance Model is introduced, which focuses on calculating the defense resources allocation proportion of each node in each community without considering attack strategies. By combining the Self-Contained Girvan-Newman Algorithm and Mean Variance Model, we hope to provide a feasible and effective method to solve the two problems mentioned above.
The remainder of this paper is organized as follows: Section 2 is devoted to the establishment of road dangerous goods transportation network. Section 3 is devoted to the community partition based on Self-Contained Girvan-Newman Algorithm. Section 4 is devoted to the defense resource allocation approach based on Mean Variance Model. In Section 5, a case study is conducted by using the road dangerous goods transportation network in Dalian City of China as the background. In order to test the effectiveness of the proposed method in this paper, in Section 6, the Power Function Allocation Model (PFAM) ([6]; Li et al., 2008) is applied to compare the defense resource allocation results, the overall rescue capability of the network is defined and applied to evaluate the defense resource allocation schemes. Section 7 is devoted to the conclusions and the future work list.
Section snippets
The establishment of road dangerous goods transportation network
Road dangerous goods transportation network belongs to a special infrastructure of transportation network which distributes dangerous goods according to the demand [25, 26], the nodes and the edges in the network are selected from the existing traffic network. In this paper, the road dangerous goods transportation network is divided into physical network and service network. The physical network is composed by the possible nodes and edges selected from the existing traffic network. The vehicles
The community partition based on Self-Contained Girvan-Newman Algorithm
The complex network is composed of many communities (or groups) with the same or similar properties. In one community, the connections among nodes are relatively strong, however, the connection between two communities is not that strong. Therefore, separating the whole complex network into several communities reflects the structure and characteristics of the physical network. In this paper, the road dangerous transport physical network is separated into different communities in order to
The defense resource allocation based on Mean Variance Model
In the financial industry, the stock market is usually regarded as a complex network, the stocks in the stock market are regarded as the nodes of the service network, the correlations among the stocks are regarded as the edges of the service network. Based on the Markowitz Mean Variance Model, the impacts of one stock's price fluctuation on the adjacent stocks can be analyzed, the optimal investment model of the stock market can be constructed, and the maximum stock return value can be
Case study
Now a case study is conducted by using the road network and the dangerous goods transportation volume of Dalian, China as the background. There are 154 nodes and 238 edges of Dalian's road network, and the dangerous goods transportation volume of each node is collected in September 2020. Using Arc-GIS to process the given road network map of Dalian, the data in reality can be visualized. As shown in Fig. 3 (a), the nodes in the network are the intersection of paths. Based on the processing
Comparison study
In order to test the effectiveness of the proposed method in this paper, in this section we conduct the comparison study. When applying the Self-Contained Girvan-Newman Algorithm and Mean Variance Model combined approach to allocate the defense resource, the structure of the network and the dangerous goods transportation volume of each node are considered, the attack strategies are not considered. Therefore, we choose Power Function Allocation Model (PFAM, see Table 1) [6] to compare the
Conclusion and further study work
In this paper, a Self-Contained Girvan-Newman Algorithm and Mean Variance Model combined approach is proposed to allocate the defense resource of road dangerous goods transportation network without considering the attack strategies. Firstly, for a specifical network, the physical network and its service network should be established. For the physical network, the length of each edge shows the weight of each edge, the established road dangerous goods transportation physical network belongs to a
Author statement
The authors claim that none of the material in the paper has been published or is under consideration for publication elsewhere.
Declaration of Competing interest
The authors declared that we have no conflicts of interest to this work.
Acknowledgements
This research was jointly supported by the National Natural Science Foundation of China (71173177), Youth Fund of National Natural Science Foundation of China (72001179), International Science and Technology Innovation Cooperation Project of Science & Technology Department of Sichuan Province (2021YFH0106) and Basic Research Fund of Central University (2682021CX052).
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