1. bookVolume 7 (2022): Edizione 2 (July 2022)
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Research on an intelligent game simulation system based on road network

Pubblicato online: 12 Dec 2022
Volume & Edizione: Volume 7 (2022) - Edizione 2 (July 2022)
Pagine: 1181 - 1192
Ricevuto: 08 Oct 2022
Accettato: 19 Nov 2022
Dettagli della rivista
License
Formato
Rivista
eISSN
2444-8656
Prima pubblicazione
01 Jan 2016
Frequenza di pubblicazione
2 volte all'anno
Lingue
Inglese
Introduction

Presently, public safety events are mainly divided into four categories, namely natural disasters, accidental disasters, public health events and social security incidents [1]. Natural disasters mainly involve flood and drought, earthquake and meteorological, geological, marine and biological disasters while accidental disasters mainly include production and environmental disasters in mining, commerce and trade industries. Public health events mainly include infectious diseases, transmission of mass diseases of unknown cause to humans, animal epidemics and other events that seriously affect public health and life safety while social security incidents mainly involve aggressive events, economic security incidents, foreign emergencies, etc. The related content to the management of regional road network public security incidents studied in this paper belongs to the management of aggressive events in social security incidents. Since the ‘911’ event that caused great losses to the American society, public safety governance has gradually become the focus of researchers from all over the world, and domestic researchers have also begun to involve in studying emergencies and participate in the discussion of emergency problems. Then, after the SARS occurrence, domestic scholars have conducted [2] more research studies on public security incidents, and their results are also interesting. In recent years, with the development of science and technology, the level of public security governance has been constantly improved, and regional security incident governance has also become one of the research hotspots. However, factors like personnel congestion, open environment, rapid information transmission and others in regional security incidents also bring certain difficulties to public security event processing. As a result, once an aggressive public security event occurs, how to improve the emergency efficiency and to quickly and effectively allocate the rescue personnel and materials to the site is a key approach to reduce the loss [3, 4]. Currently, some relevant studies have been carried out centering on the site selection of public safety emergency facilities, among which the traditional site selection research studies of emergency facilities mostly focus on natural disasters, such as flood, hurricane and earthquake, and realise the layout of emergency facilities and the distribution of emergency supplies by virtue of the derived site selection-distribution model [5] and site selection-path model [6] besides solving by branch-bound, column generation, various heuristics or biological evolution algorithms [7]. In recent years, the site selection of public safety emergency facilities has gradually attracted more attention. Unlike natural disasters, an attacker's attack strategy is adjusted according to the defender's defence deployment. Therefore, to characterise the game relationship between defenders and attackers, Berman and Gavious [8] constructed the emergency facility location problem as a Stackelberg game model, where after Berman et al. [9] took a further step to explore the Nash game location model under the not disclosed defender location selection information. Han et al. [10] supplemented the genetic algorithm for solving large-scale network problems. Chai et al. [11] considered the site selection of emergency facilities under the continuous attack. Xiang Yin and Wei Hang [12] studied the situation of realistic situation security resource allocation for attackers that is not completely rational and led to a new game model suitable for general scenarios. Meng et al. [13] studied the risk of interruption of emergency facilities. Xiang Yin [14] studied the optimal strategy for defenders’ location information in 2019.

All of the above studies provide effective countermeasures for defenders, which, nonetheless, leave room for improvement. Firstly, existing studies consider less about that the diffusion of the consequences of regional public safety event, the panic generated in groups and loss in the process of controlling public opinion that will produce joint losses. Therefore, the regional road network security resource facilities layout problem considering the diffusion of the loss needs to be solved urgently. Secondly, in the planning process, existing studies propose the assumption of unlimited facility capacity. The handling is in place at a time. However, materials often cannot be carried in place at once in reality. Accordingly, this paper considers the situation of multiple material handling into the material planning model. In contrast to the previous studies, in view of the layout of regional road network security resource facilities, this paper fully considers the diffusion of safety incidents and the limited material planning and handling and proposes a class of problems covering the safety resource facility allocation and planning optimisation, which enriches the site selection theory and algorithm of emergency facilities.

Problem hypothesis
Problem description

Site location of security resource emergency facilities can be described as below. In a given regional traffic network M(V, E), V (v1,v2,…,vn) is a set of vertices representing a collection of important facilities or sites in the region. It is a collection of potential attack targets and an alternative collection of selected points for security resource facilities. When E(e1,e2,…,en) is the edge set, it represents the set of sections in the regional traffic network. We set d(i, j) as the shortest path distance between the vertex vi and the top point vj, and set wi as the security resource required after each vertex vi which suffers an attack. It is directly proportional to the importance of the vertex vi and also represents the weight of the vertex vi. There are two types of participants in attack and defence now. Attackers are divided into three types based on the degree of rationality, attacking respectively the vertices in the vertex set V with different attack strategies. We assume that the attack must succeed. In order to reduce the loss of the attack, the defenders need to select several vertices in the vertex set V to build the security resource placement points for the security resource rescue for the attack points so as to improve the emergency efficiency after the attack. Because the attack strategies of different types of attackers vary, we need to consider the classification and construct the corresponding site selection model in turn. In this paper, we first define the specific types of attackers. In the current research studies on security resource allocation, Hao et al. [15] and Xiang Yin and Wei Hang [12] have roughly divided the attackers into three categories: (1) completely rational attacker, (2) irrational attacker and (3) incompletely rational attacker. We will discuss this content in Section 3. the higher the degree of rationality of the attacker, the higher the information level and computing power, with the goal of maximising the attack revenue. Among the above three types of attackers, completely rational and irrational attack decision and responses are partial to two extremes, which are rare in reality. The incompletely rational attacker has the characteristics of both completely rational and irrational attackers, which is more in line with the real scene. Therefore, in this paper, we assume that the attacker is incompletely rational.

The hypothesis on security resources path planning can be described as follows. On the basis of security resource emergency facilities site problem, we assume that the attack point vi is attack and needs certain security emergency resources rescue. Meanwhile, as there are multiple security resources emergency facilities to meet the conditions, we need to select a point for the vertex vi to have emergency rescue and plan the path. Among them, if the road situation is known, there is an effective connection between any two nodes, and each emergency facility is subject to the deployment of the system.

Problem research objectives

As it can be seen from the above description of the location of security resource emergency facilities, the defender's decision goal is to minimise the loss, while the attacker's is to maximise the perceived defender loss. The ultimate goal of path planning is to solve a point to rescue the vertex vi from multiple security resource emergency facility points and plan the path.

Model construction
Site selection model of attack and defence game in a completely rational situation

Berman [8, 9] and Han et al. [10] discussed the facility site location model, where security information is that the attacker is completely rational, and abstracted the site selection problem into a Stackelberg game model. The defenders first set up k facility points and form the strategy space s = {s1,s2,…,sk}. After observing the pioneer's strategy, the attackers make mixed strategies, attacking the vertex in the vertex set and forming the strategy space set π = {π1,π2,…,πk}. πk represents the probability of attacking point k, which considers only a single attack, meaning that the sum of all attack probabilities is equal to 1.

In the relevant literature of Berman [8, 9] and Han et al. [10], the sum of defender disutility is defined as the sum of attack loss and facility construction costs, and attacker utility is defined as attack loss. Xiang Yin and Wei Hang [12] improved the utility function and obtained the defensive negative utility function in the general attack case. Based on the above research, considering the loss caused by the event diffusion of a road network in a public safety area, the paper sets the improved defensive negative utility function of τ as follows: UGR(s,π)=i=1nπi[αd(s,i)+βlnwiγ]wi+cm+τ {U_{GR}}\left( {s,\pi } \right) = \sum\limits_{i = 1}^n {\pi _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + {cm} + \tau

UGR represents the defender's disutility function and πi [α ·d (s,i) + β ln wiγ]wi the loss of the individual vertices after suffering an attack. When i is not attacked, that is, when the attack loss at the πi = 0, α · d (s,i) · wi represents the loss arising during transport and α represents the loss caused by the time delay of the unit of materials during the transportation of rescue materials while c represents the cost of setting each vertex security resource point, m indicates the number of emergency facilities, τ represents the sum of losses resulting from the diffusion of individual vertex events, β is the loss caused by the time delay of unit material unit and γ is the pioneer's ability to manage unit materials.

The utility formula of the attacker Eq. (2) lacks the item cm when compared with Eq. (1). As shown by Eq. (2), the utility obtained by the attacker is also directly affected by the spread of the event and the defender's strategy s as well as the attacker's attack strategy. UTR(s,π)=i=1nπi[αd(s,i)+βlnwiγ]wi+τ {U_{TR}}\left( {s,\pi } \right) = \sum\limits_{i = 1}^n {\pi _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + \tau

Therefore, in the face of completely rational attackers, the integrated model formula of Eqs (1) and (2), Eq. (3) is written as follows: minsUGR(s,π*)=i=1nπi*[αd(s,i)+βlnwiγ]wi+cm+τ \mathop {\min }\limits_s {U_{GR}}\left( {s,{\pi ^*}} \right) = \sum\limits_{i = 1}^n \pi _i^*\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + cm + \tau s.t.{i=1nπi*=1π*(s)argmaxiUGR(s,π)=i=1nπi[αd(s,i)+βlnwiγ]wi+τπi0 s.t.\left\{ {\matrix{ {\sum\nolimits_{i = 1}^n {\pi _i^* = 1} } \hfill \cr {{\pi ^*}(s) \in argma{x_i}{U_{GR}}\left( {s,\pi } \right) = \sum\nolimits_{i = 1}^n {{\pi _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + \tau } } \hfill \cr {{\pi _i} \ge 0} \hfill \cr } } \right.

In Eq. (3), there are three constraints. First, there is only one attack. Second, each vertex has an attack probability ≥ 0. And third, the attacker responds optimally to the defender's location strategy to maximise its utility function.

In allusion to the completely rational situation, the game problem becomes a single constraint linear planning problem. Assuming that k(i) is the node nearest to the attack point vi in the site selection strategy s, then the optimal attack solution of the perfectly rational attacker and the unique equilibrium solution s*, πz*(s*) is obtained: z*(s)=argmaxii=1nπi*[αd(s,i)+βlnwiγ]wi {z^*}\left( s \right) = \mathop {\arg \max }\limits_i \sum\limits_{i = 1}^n \pi _i^*\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i}

And the optimal solution of the defence's location strategy is written as follows: s*=argmins[αd(s,z*(s))+βlnwz*(s)γ]wz*(s)+cm+τ {s^*} = \mathop {arg \min }\limits_s \left[ {\alpha \cdot d\left( {s,{z^*}\left( s \right)} \right) + \beta \ln {w_{{z^*}\left( s \right)}} - \gamma } \right]{w_{{z^*}\left( s \right)}} + cm + \tau

Site selection model of attack and defence game in the irrational case

Since this situation will hardly happen in reality, there is no literature focussing specifically on irrational attack game models. By the definition of irrationality through game theory, Xiang Yin and Wei Hang [12] described the location selection problem when the attacker is irrational as follows: in a regional traffic extension network M(V, E), V (v1,v2,…,vn) is the vertex set and E(e1,e2,…,en) is the edge set; there exists only a main body, defenders, who have known that attackers will attack each vertex with a fixed probability σ = (σ1,σ2,…,σn), where σi=wi/i=1nwi {\sigma _i} = {w_i}/\sum\nolimits_{i = 1}^n {w_i} , and the attack probability of each vertex is directly proportional to the vertex weight. Consequently, in this game case, the defence side only needs to reasonably select m vertices to build safety resource emergency facilities to reduce the loss, and the attackers will not react according to the defence's strategy. It can be concluded that the game model in irrational cases is as in Eq. (6). The strategy has two constraints. On the one hand, the total attack probability of all vertices is 1, and on the other hand, the attack probability of each vertex is ≥ 0. minsUGNR(s,σ)=i=1nσi[αd(s,i)+βlnwiγ]wi+cm+τ \mathop {\min }\limits_s \;{U_{GNR}}\left( {s,\sigma } \right) = \sum\limits_{i = 1}^n {\sigma _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + cm + \tau s.t.{σi=wi/i=1nwiσi0 s.t.\left\{ {\matrix{ {{\sigma _i} = {w_i}/\sum\nolimits_{i = 1}^n {{w_i}} } \hfill \cr {{\sigma _i} \ge 0} \hfill \cr } } \right.

The site selection model in the irrational attack mode Eq. (6) is equivalent to the p-median model, where the attacker is completely irrational, and the attack probability is also given externally. Thus, the defensive location problem can be transformed into a 0–1 planning problem, namely a vertex placed facility point j or no facility point, j rescue attack point i or no rescue. Let the dij be the shortest distance between i and j. The most optimal solution obtained is s**: s**=argminsi=1nσi[αd(s,i)+βlnwiγ]wi+cm+τ {s^{**}} = \mathop {arg \min }\limits_s \sum\limits_{i = 1}^n {\sigma _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + cm + \tau

Site selection model of attack and defence game in incomplete rational situation

Many real attackers are not completely rational; therefore, Hao et al. [15] and Xiang Yin [7,14] all considered the allocation model of incomplete rational attackers in the process of studying the security resource allocation problem. This paper learns from the introduction of a rational degree factor of modelling literature in the analysis of incomplete rational game situation from the documents of Xiang Yin and Wei Hang [12].

Let p ∈ [0,1], the obtained corresponding model is Eq. (8). When p = 1, the attacker is completely rational. Simplifying Eq. (8) to be equivalent to Eq. (3), σi's constraint on Eq. (8) won’t be effective or affect the decision result. When p = 0, that is, when the attacker is irrational, formula simplifying Eq. (8) to be equivalent to Eq. (6), πi's constraint on Eq. (8) will neither work nor affect the decision result. minsUGLR(s,π*,σ)=pi=1nπi*[αd(s,i)+βlnwiγ]wi+(1p)i=1nσi[αd(s,i)+βlnwiγ]wi+cm+τ \mathop {\min }\limits_s \;{U_{GLR}}\left( {s,{\pi ^*},\sigma } \right) = p \cdot \sum\limits_{i = 1}^n \pi _i^*\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + (1 - p)\sum\limits_{i = 1}^n {\sigma _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + cm + \tau s.t.{i=1nπi*=1π*(s)argmaxiUGR(s,π)=i=1nπi[αd(s,i)+βlnwiγ]wi+τπi0,σi0σi=wi/i=1nwi s.t.\left\{ {\matrix{ {\sum\nolimits_{i = 1}^n {\pi _i^* = 1} } \hfill \cr {{\pi ^*}(s) \in \arg {{\max }_i}{U_{GR}}\left( {s,\pi } \right) = \sum\nolimits_{i = 1}^n {{\pi _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + \tau } } \hfill \cr {{\pi _i} \ge 0,{\sigma _i} \ge 0} \hfill \cr {{\sigma _i} = {w_i}/\sum\nolimits_{i = 1}^n {{w_i}} } \hfill \cr } } \right.

In the above two parts, the irrational attacker's attack probability is determined by exogenous factors, while the completely rational attacker's is completely determined by endogenous factors. Bringing the above reaction function into the Eq. (8), we can then work out the optimum solution of the only equilibrium solution s′,πz*(s,) of the defender location selection strategy in the incompletely rational case: s'=argminsp[αd(s,z*(s))+βlnwz*(s)γ]wz*(s)+(1p)i=1nσi[αd(s,i)+βlnwiγ]wi+cm+τ \matrix{ {{s^'} = \mathop {arg \min }\limits_s p \cdot \left[ {\alpha \cdot d\left( {s,{z^*}\left( s \right)} \right) + \beta \ln {w_{{z^*}\left( s \right)}} - \gamma } \right]{w_{{z^*}\left( s \right)}}} \hfill \cr {\;\;\; + \left( {1 - p} \right) \cdot \sum\limits_{i = 1}^n {\sigma _i}\left[ {\alpha \cdot d\left( {s,i} \right) + \beta \ln {w_i} - \gamma } \right]{w_i} + cm + \tau } \hfill \cr }

Path planning problem model construction

In existing research studies, the shortest path refers to the shortest path from the starting point and the end point and the smallest sum of the path weights. However, after the occurrence of the emergency, besides the shortest path to the demand point, the effective time of delivery materials and other restrictive condition are added. Comprehensively analysing, the so-called ‘optimal path of security resource scheduling path’ refers to the shortest one, ensuring the supplies to be delivered in order to reduce the more unnecessary losses incurred during the transportation process and arrived within the scope of time requirements when a security event occurs at a certain point in the road network of the park. Since there are more than one site in the campus for storing materials, it involves multiple material point, that is, the ‘optimal path’ of the campus security material scheduling. Therefore, it is necessary to propose the u-Dijkstra algorithm as shown in the following Eqs (10)–(12) on the basis of the existing improved Dijkstra algorithm proposed by Zhang Yajing et al. [16]. d1=0 {d_1} = 0 dj=minij,(vi,vj)E{dj+lijwij}=minij,(vi,vj)E{dj+ntijkijwij}(j=2,3,,n) {d_j} = \mathop {\min }\limits_{i \ne j,({v_i},{v_j}) \in E} \left\{ {{d_j} + {l_{ij}}{w_{ij}}} \right\} = \mathop {\min }\limits_{i \ne j,\left( {{v_i},{v_j}} \right) \in E} \left\{ {{d_j} + {{n{t_{ij}}} \over {{k_{ij}}}}{w_{ij}}} \right\}(j = 2,3, \ldots ,n) dj<dmax {d_j} < {d_{max }} where vi is the node in the map network, E is the edge set of vi to vj, lijwij is the effective path length, lij is the equivalent weight factor of the roadway from node vi to vj laneway, dj is the optimal path, dmax is the longest path, tij is the impact factor of length, kij is the traffic efficiency and n is the number of trips required for transporting materials. Among the many storage points on the map, one is selected to mobilise supplies for the attack point.

Algorithm design

Through the illustration in the third section, completely rational security resource location model and irrational security resource location model are two extreme special cases when the incompletely rational model is in the attacker rational degree of 0 and 1, respectively. In the site selection algorithm design process, the Floyd (exhaustive attack method) algorithm can be employed to simulate. The Floyd algorithm refers to the method of enumerating all the elements in a set composed of finite elements one by one and studying. Its efficiency is not high and applicable to the cases with no obvious rules to follow. However, because the Floyd method will increase exponentially with the number of fixed points, the complexity of the calculation is too high and does not apply for strategic site selection. For instance, if there are 22 vertices and 3 points are selected as security resource points, we need to list C223 C_{22}^3 strategies. This paper first uses the Floyd algorithm to calculate the shortest path, as a reference for the genetic algorithm data set and to verify the correctness of the path planning.

Genetic algorithm can greatly reduce the workload. First, the initial population composed of a certain number of site selection scheme is randomly generated. Then the biological genetic process is simulated to iterate and update the site selection scheme. The genetic algorithm adopts the parallel search method of multiple clues, and the calculation speed is fast.

The algorithm used in this article is shown in the following figure:

Step 1: Initialise the population pop, input the relevant parameters of the model and select some points of the n points to build the security resource facility, as expressed by 0/1. Each of these chromosomes represents a site selection strategy.

Step 2: In allusion to each chromosome (with no one vertex), calculate the defence loss function of each rescue point under attack and find the best rescue point. For each chromosome, the sum of defensive sector losses and facility costs and dispersal impact losses completes the population evaluation.

Step 3: Hybridize and recombine pop (t) and generate newpop (t).

Step 4: Evaluate the newly generated newpop and make chromosome selection in step 2; finally, select pop (t + 1), judge the number of reproductive generations and proceed to the next step; otherwise, the cycle starts from step 3.

Step 5: Get the optimal chromosome, that is, the most advantage and return to the corresponding results.

Case analysis

Based on the simulation planning and analysis of the traffic topology network in a university campus, we mainly study the corresponding facility layout strategy, the applicable situation and practical value of path planning under the condition that the attacker is not fully rational.

Scene description and data source

In this paper, Xinjiang Normal University is treated as an example. The campus map is shown in Figure 1a. Campus network number map and important campus places are abstract as random numbers, and roads between important sites are edges. The park network map is shown in Figure 1b. The map is composed of 44 nodes and 64 edges.

Fig. 1

Campus map and campus network

In this paper, considering the real data and importance data on the campus security, data demensitisation processing, select the vertex 1–22 importance value as shown in Table 1, the actual test distance between vertices, exhaustive calculation, and then according to a certain proportion, get the shortest path distance of each vertex to other vertices, as shown in Figure 2 below:

Fig. 2

Shortest path distance d from each vertex to other vertices unit (per unit distance)

Campus node importance assignment

VertexImportanceVertexImportanceVertexImportance

1318922017228
2302109918371
359119119138
41281214420253
51051340421287
63031410022312
73051538
827016127
Simulation results and analysis

First, in order to intuitively observe the impact of the number of parameter security resource facility points m on the loss of defenders, this paper uses mathematical modelling software MATLAB to experiment. The results are shown in Figure 3, and the number of security facility points increases after the end of the second genetic algorithm.

Fig. 3

The relationship map between defender loss and attacker rationality p of 0.5 and site selection facilities

When m=3, α = 2, β = 0.5 and γ = 0.2, the obtained p-value is 0, 0.3, 0.6, and 0.9, respectively. In Figure 4, as the degree of rationality of the attacking party increases, the loss of the attacker also increases significantly.

Fig. 4

Relationship map between defender loss and attacker degree of rationality change, site selection facilities of m=3

The results shown in Figure 5 show that in the fixed number of fixed emergency facilities, α = 2, β = 0.5, γ = 0.2, as the degree of rationality of the attacker decreases, the completely rational attacker causes the most loss to the defence, while in Figure 3, the irrational attacker causes the least loss to the defender. This is because irrational attackers always fail to adopt optimal solutions after observing defensive actions and maximise their utility. A perfectly rational attacker is quite the opposite. Therefore, the attack consequences of a completely rational attacker are the worst case, while the attack consequences of an irrational attacker are the best case. This point can be used in daily management: (1) In the case of funds allowed, increasing the number of security resource facilities points can effectively reduce the loss. (2) The judgement of the attacker can be affected by releasing interference information so as to reduce the rationality of the attacker. (3) Due to the relevant value of public opinion management introduced in the loss item, the resulting loss will also increase; so, the hidden loss can be reduced by controlling the spread influence of preventive events.

Fig. 5

Relationship map between defender loss and rational degree change of attacker and site selection facilities of m=3–8

Secondly, in Figure 5, when the degree of rationality is fixed, the defensive loss gradually decreases as the number of facilities increases, but obviously, when the number of facilities increases to a certain extent, increasing the number of facilities has little impact on the defensive loss. And by changing the rationality of the attacker, the relationship between the number of facilities and the defensive utility remains.

In this paper, the simulation is conducted at p=0.5, p = 0.5, m=3 and m=5. According to the results of the site selection strategy, the blue route planning is shown in Figures 6 and 7. After calculating the verification of the weights of the path and the shortest path in the table, the results prove that the planning path is accurate.

Fig. 6

When m = 3, the shortest path planning is shown as blue line

Fig. 7

When m = 5, the shortest path planning is shown as blue line

Conclusion

The real-world regional public security management problems with the attackers are not completely rational attackers. If the existing classic site selection model and game model for emergency facilities site selection decision are used, it is easy to obtain the inefficient site selection scheme and make the security event spread persistent negative effects, thus increasing the loss caused by the attack. Considering the degree of incomplete rationality, the number of security resources and facilities, the diffusion characteristics of security events and other realistic situations, this paper fuses a game idea, putting forward a new hybrid site selection model, conducting path planning for the attack point of security resources scheduling and combining with a university case to analyse the impact of the damage point relief loss, thus providing scientific decision support for regional road network public security event management.

In the subsequent work, there is still a lot of research space for regional public safety management. In view of the proliferation of security incidents in the regional road network and the incomplete rational characteristics of the attackers, further research in the future can involve the following content:

First, conduct the related study of the dynamic game security resource site selection model. In reality, many security events also have continuity characteristics, and the multi-round game is more suitable for this scenario. Therefore, in the future research work, it can be more efficient to build multi-party game, multi-round game and multi-layer game models.

Second, generalise the regional road network security resource site selection model. We can further optimise the results of larger data and make the effect of the algorithm model more suitable for more scenarios.

Third, use the attacker's not completely rational characteristics to solve practical problems. From the fifth summary conclusion, it can be concluded that the incomplete rational characteristics can be used in the governance process of the public security events. On the one hand, the rational degree of the defence can be strengthened by further studying the algorithm. On the other hand, the rational degree of the attacker can be reduced by changing strategies and hiding information.

Fourth, for other research content, the model scenario assumption can be used in the field of public safety and can be employed in disaster governance, public opinion control, disease control and other fields as an attempt.

Fig. 1

Campus map and campus network
Campus map and campus network

Fig. 2

Shortest path distance d from each vertex to other vertices unit (per unit distance)
Shortest path distance d from each vertex to other vertices unit (per unit distance)

Fig. 3

The relationship map between defender loss and attacker rationality p of 0.5 and site selection facilities
The relationship map between defender loss and attacker rationality p of 0.5 and site selection facilities

Fig. 4

Relationship map between defender loss and attacker degree of rationality change, site selection facilities of m=3
Relationship map between defender loss and attacker degree of rationality change, site selection facilities of m=3

Fig. 5

Relationship map between defender loss and rational degree change of attacker and site selection facilities of m=3-8
Relationship map between defender loss and rational degree change of attacker and site selection facilities of m=3-8

Fig. 6

When m = 3, the shortest path planning is shown as blue line
When m = 3, the shortest path planning is shown as blue line

Fig. 7

When m = 5, the shortest path planning is shown as blue line
When m = 5, the shortest path planning is shown as blue line

Campus node importance assignment

Vertex Importance Vertex Importance Vertex Importance

1 318 9 220 17 228
2 302 10 99 18 371
3 59 11 91 19 138
4 128 12 144 20 253
5 105 13 404 21 287
6 303 14 100 22 312
7 305 15 38
8 270 16 127

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