CN104318099B - The mobile analogue experiment method of dynamic point on two-dimensional random road network - Google Patents

Abstract

The invention discloses a moving point movement simulation experiment method on a two-dimensional random road network. The specific steps are as follows: a random number generating module generates random numbers; a modeling module establishes a random model framework, and saves path model information to a file; Establish a random model, use the time queue algorithm to calculate and simulate the real-time state of the moving object at each moment, and save the calculation results in the form of files; the analysis module reads the data to analyze and count the characteristics of the random movement, and graphically reports the analysis results displayed in the interface. The invention solves the problem that the existing mobile model cannot simulate the state information of random moving objects at each moment, is an inspiration platform for multi-cluster Markov chains, can be flexibly configured, and provides an experimental environment for various problems.

Description

Experimental method for moving point simulation on two-dimensional random road network

technical field

The invention belongs to the technical field of moving point movement simulation experiment methods, and in particular relates to a moving point movement simulation experiment method on a two-dimensional random road network.

Background technique

The classical theory of random walks, which appears in many mathematical and physical models, mainly considers random walks on simple but unrestricted graphs. Taking the lattice diagram as an example, if the particle is allowed to swim indefinitely, will the particle return to the starting point with probability 1? Will it return to the starting point infinitely many times? In 1921, Pólya proved that when n=1,2, the particle returns to the starting point infinitely many times with probability 1, but when n>3, the particle will only return to the starting point finitely many times.

The random walk on the Unicom undirected graph, that is, the reversible Markov chain, the internal connection with the electrical network, and the successful application of matrix analysis and harmonic analysis methods make it the most researched and most fruitful in the field of combinatorial graph theory in recent years. One of the rich subjects. Reversible Markov chains have applications in various fields. Research on the movement of random moving points mainly focuses on the establishment of position index models. Assuming that the object moves arbitrarily in two-dimensional space, according to different needs, the following index structures have emerged one after another: for the current and future position information of the moving object, a type of model for information position management has been generated; as people pay attention to past phenomena With the improvement of the accuracy, the model that can process the historical position information of the moving object has developed to a certain extent; as a development trend in recent years, the model that can simultaneously process the past, current and future position information of the moving object has also emerged, which greatly enriches the The application layer of Modo Mobile.

In the study of mobile models, the spatio-temporal data model of moving objects in 2D network started relatively late. Existing spatio-temporal data models mainly focus on recording the motion state of moving objects, such as adding time-indexed record sets to road network data models. The research field of moving objects in spatio-temporal networks is of great significance to the classic analysis of networks. In practical applications, the motion patterns of moving objects can be divided into unrestricted motion (such as a ship driving in the sea), restricted motion (such as the motion of pedestrians), and motion in a fixed network (such as a train, a car moving along a fixed line mobile), of which fixed network movement is the most prevalent mode in application. When the motion pattern of a moving object is defined as unlimited motion on a fixed network, its motion trajectory can be understood as a Markov chain that preserves past, current, and future information, and its motion development has nothing to do with the past.

At present, most of the moving point movement simulation experiments on a fixed network set the two-dimensional path network to be fixed, and there are few studies on environmental changes and portability. The simulation experiment of moving point movement is mostly researched on random walk, more is from the index point of view, and the research is oriented to the positioning of moving point. There are few platform designs to provide a good simulation experiment environment, and it cannot be simulated when the environmental conditions are changeable. The state information of the random moving object at each moment.

Contents of the invention

The purpose of the present invention is to provide a moving point movement simulation experiment method on a two-dimensional random road network, which solves the problem that the existing movement model cannot simulate the state information of a random moving object at each moment.

The technical solution adopted in the present invention is that the moving point moving simulation experiment method on the two-dimensional random road network is based on the moving point moving simulation experiment platform on the two-dimensional random road network, and the specific steps are as follows:

Step 1: The random number generation module generates a random number after receiving the command, and provides a random data source for the modeling module and the operation module;

Step 2: The modeling module obtains the data source of the random number generation module, establishes a random model framework, encapsulates the random model framework in a class, saves it in memory, and saves the information of the path model to a file;

Step 3: The calculation module is responsible for the data calculation at runtime. According to the random model framework established in the second step, a random motion model is established, and the time queue algorithm is used to calculate and simulate the real-time state of the moving object at each moment. At the same time, the real-time random calculation results It is encapsulated in the form of a class, stored in memory, and the operation result is saved in the form of a file through the data output interface;

Step 4: Output the file saved in step 2 and the file saved in step 3 to the analysis module, the analysis module reads the data, can reproduce the entire random motion process, and analyze and count the characteristics of random motion, through the file The analysis results are saved in a graphical way, and the real-time random motion model, the state of the moving point at each moment and the analysis results are displayed graphically.

The present invention is also characterized in that,

The random number generating module in the first step includes a command receiving interface, a random number generator and a data sending interface, and the random number generator generates a robust random number by calling the CryptGenRandom function.

Step 2 The process of building a random model framework in the modeling module is as follows:

Step 2.1: First set the modeling parameters, then read the modeling parameters, and create random node positions according to the modeling range;

Step 2.2: Use the Waxman modeling method to create random paths between random nodes, and the paths between nodes satisfy the Poisson distribution;

Step 2.3: Test the connectivity of the random path created in step 2.2 through the breadth-first algorithm. If there is no isolated node, perform step 2.4; if there is an isolated node, return to step 2.2 and recreate the random path; If there are still isolated nodes, return to step 2.1 and reset the modeling parameters;

Step 2.4: Create moving points, set the parameters of each moving point according to the simulation requirements, save all model data to external files, and the modeling is completed.

Waxman modeling method, as shown in formula (1):

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where P(u, v) is the direct connection probability between node u and node v, modeling parameters α>0, β<=1, d is the distance between vertex u and vertex v, L is all vertices in the plane The farthest distance among them; the larger the α value, the more edges in the graph; the larger the β value, the larger the ratio of the long side to the short side in the graph. Waxman believes that the connection probability between nodes is related to its distance, and the out-degree The frequency follows a Poisson distribution, and the closer the distance, the greater the probability.

The specific operation process of the operation module in step 3 is as follows:

Step 3.1: The operation module obtains the random motion model,

Step 3.2: Create a time queue according to the random motion model, add all dynamic nodes to the time queue, and initialize their running time to 0;

Step 3.3: Determine whether the movement time of the moving point exceeds the total time limit set when initially creating the model. If the movement time exceeds the limit, end the calculation and perform step 3.7; if the movement time does not exceed the limit, proceed to step 3.4;

Step 3.4: Calculate the upcoming state of the moving point at the head of the time queue, that is, whether the moving point will move at the next moment and its direction of movement, and calculate the time when the next state of the moving point changes according to the state of the moving point at the next moment, and update the moving point state of the point;

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{{\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the formula, l _i represents the current path of the moving point; and Indicates the two ends of the l _i path; (x _ii (t), y _ii (t)) indicates the coordinates of the moving point on the l _i path; t' is the interval sampling time; v _ci is the rate randomly assigned to the moving point; Δt _m is the subdivision function within the interval sampling time t'; v _i represents the speed of the moving point, Δt _m-1 is a reference, which refers to the equal division of t'; m is the division of t' interval number; among them, the discrete random variable ζ _l ={l ₁ ,…,l _i ,…,l _k } represents the length of the path l _i , among which, k represents the number of paths; Δt _p represents the pth path The time; p represents the number of times through the path;

The position of the moving point at the next moment is obtained by formula (2) and formula (3); the path length l _i can be obtained according to the current position and the position of the next moment; the next moment is updated by formula (4) and formula (5) Δt _m ;

Step 3.5: According to the state of the updated moving point, update the time queue, that is, the updated moving point is reinserted into the time queue in ascending order according to the size of its Δt _m value, so that the next updated moving point is arranged at the end of the time queue ahead;

Step 3.6: return to step 3.3;

Step 3.7: Finally, encapsulate the real-time random operation result in a class, save it in the memory, and save the operation result in the form of a file through the data output interface.

The analysis of the characteristics of random motion in the fourth step includes the graphical reproduction of the running process of the random moving point, the analysis of the running track of the moving point, the probability statistics of the occurrence of the moving point in the entire model platform, and the tracking between multiple moving points Relationship analysis, movement analysis of moving points in the state of dynamic and static transition.

The moving point movement simulation experiment platform on the two-dimensional random road network includes a random number generation module, a modeling module and an operation module respectively connected with the random number generation module, and both the modeling module and the operation module are connected with the analysis module.

The beneficial effects of the present invention are: the moving point movement simulation experiment method on the two-dimensional random road network of the present invention adopts random number drive to create a random path model, and simulates the state of the random moving point at each moment through the time queue algorithm, solving the problem of To solve the problem that the existing mobile model cannot simulate the state information of random moving objects at each moment, adopt the object-oriented idea, encapsulate the path model and the moving point object, increase the reusability of the code, and save the path model and moving point in the form of files. Point state data, analysis and statistical data, and finally graphically display the analysis results. It is an inspiration platform for multi-cluster Markov chains, which can be flexibly configured to provide an experimental environment for various problems.

Description of drawings

Fig. 1 is a frame diagram of a moving point moving simulation experiment platform on a two-dimensional random road network;

Fig. 2 is the flow chart of the modeling module of the moving point moving simulation experiment method on the two-dimensional random road network of the present invention;

Fig. 3 is the operation flowchart of the moving point mobile simulation experiment method operation module on the two-dimensional random road network of the present invention;

Fig. 4 is the logical hierarchical diagram of the moving point moving simulation experiment method on the two-dimensional random road network of the present invention;

Fig. 5 is the relationship diagram of the data-driven layer and the operation layer of the moving point moving simulation experiment method on the two-dimensional random road network of the present invention;

Fig. 6 is the random model frame file structure diagram of the moving point moving simulation experiment method on the two-dimensional random road network of the present invention;

Fig. 7 is a structure diagram of a random model statistical file of the moving point moving simulation experiment method on a two-dimensional random road network of the present invention.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The moving point movement simulation experiment method on the two-dimensional random road network of the present invention is based on the moving point movement simulation experiment platform on the two-dimensional random road network, as shown in Figure 1, including a random number generation module and building blocks connected to the random number generation module The modeling module and the calculation module, the modeling module and the calculation module are all connected with the analysis module, and the specific steps are as follows:

Step 1: The random number generation module generates a random number after receiving the command, and provides a random data source for the modeling module and the operation module; the random number generation module includes a command receiving interface, a random number generator and a data sending interface, and the random number generator uses The CryptographicServiceProvider (CSP) technology generates a robust random number by calling the CryptGenRandom function to provide a random data source for the modeling module and the operation module; Randomness of motion model;

Step 2: The modeling module obtains the data source of the random number generation module, and establishes a random model framework, including model node parameters, moving point parameters and path models, as shown in Figure 2, the specific process of the modeling module establishing a random model framework for:

Step 2.1: Set the modeling parameters through the parameter setting interface, and set the key parameters during modeling, including the size of the model, the number of nodes in the model, the α and β parameters of the Waxman modeling method used for the generation path, etc.; read Modeling parameters to create random node positions according to the modeling scope;

Step 2.2: Use the Waxman modeling method to create random paths between random nodes, but not all nodes have paths. According to the Waxman modeling method, the paths between nodes will satisfy the Poisson distribution, that is, the closer the distance between nodes The more likely there is a path connection, the curve of the distribution is controlled by the parameters α and β;

Step 2.3: Since the entire model must be guaranteed to start from any node and reach any other node, the path generated by using the Waxman modeling method is only guaranteed to satisfy the Poisson distribution, and every node cannot be guaranteed to be connected, so after generating the path, Use the breadth-first algorithm to test the connectivity of the random path created in step 2.2: if there is no isolated node, perform step 2.4; if there is an isolated node, return to step 2.2 and use the Waxman modeling method to recreate the random path; If there are still isolated nodes after three times, return to step 2.1, change the probability distribution by modifying the α and β parameters, and reset the modeling parameters;

The Waxman modeling method is a stochastic model. As a basic common algorithm for network topology generation, it is usually used to generate random networks, which can ensure that the path generation of the two-dimensional random road network satisfies the Poisson distribution. The Waxman modeling method, such as formula (1 ) as shown:

$\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where P(u, v) is the direct connection probability between node u and node v, modeling parameters α>0, β<=1, d is the distance between vertex u and vertex v, L is all vertices in the plane The farthest distance among them; the larger the α value, the more edges in the graph; the larger the β value, the larger the ratio of the long side to the short side in the graph. Waxman believes that the connection probability between nodes is related to its distance, and the out-degree The frequency obeys the Poisson distribution, the closer the distance, the greater the probability;

Step 2.4: After the path model is created, create the moving point. It is necessary to set the starting position of each moving point (that is, the moving object), the moving speed of the moving point and other parameters. The design of the model parameters is flexible, and the specific movement simulated according to the needs Object settings, for example, if you need to simulate dynamic vehicle routing problems, you can set requirements for moving points, set loads for vehicles, and finally save all model data to external files, and the modeling is over;

Encapsulate the random model framework in the form of a class and save it in the memory, and save the information of the path model to a file in XML format to make the model reproducible, and random motion experiments can be performed multiple times in the same model, and Provide model data for experimental analysis;

Step 3: The calculation module is responsible for the data calculation at runtime. According to the random model framework established by the Waxman modeling method in the second step, a random motion model is established, and the time queue algorithm is used to calculate and simulate the real-time state of the moving object at each moment, as shown in the figure 3, the specific operation process is as follows:

Step 3.1: The operation module obtains a random motion model;

Step 3.2: Create a time queue according to the random motion model, add all dynamic nodes to the time queue, and initialize their running time to 0;

Step 3.3: Determine whether the movement time of the moving point exceeds the total time limit set when initially creating the model. If the movement time exceeds the limit, end the calculation and perform step 3.7; if the movement time does not exceed the limit, proceed to step 3.4;

Step 3.4: Calculate the upcoming state of the moving point at the head of the time queue, that is, whether the moving point will move at the next moment and its direction of movement, and calculate the time when the next state of the moving point changes according to the state of the moving point at the next moment, and update the moving point state of the point;

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{{\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the formula, l _i represents the current path of the moving point; and Indicates the two ends of the l _i path; (x _ii (t), y _ii (t)) indicates the coordinates of the moving point on the l _i path; t' is the interval sampling time; v _ci is the rate randomly assigned to the moving point; Δt _m is the subdivision function within the interval sampling time t'; v _i represents the speed of the moving point, Δt _m-1 is a reference, which refers to the equal division of t'; m is the division of t' interval number; among them, the discrete random variable ζ _l ={l ₁ ,…,l _i ,…,l _k } represents the length of the path l _i , among which, k represents the number of paths; Δt _p represents the pth path The time; p represents the number of times through the path;

The movement time of the moving point is polled by t', and the movement situation in each t' time is judged by Δt _m . The specific judgment method is: the next moment of the moving point is obtained by formula (2) and formula (3) The moving position; the path length l _i can be obtained according to the current position and the position at the next moment; Δt _m at the next moment is updated by formula (4) and formula (5);

Step 3.5: According to the state of the updated moving point, update the time queue, that is, the updated moving point is reinserted into the time queue in ascending order according to the size of its Δt _m value, so that the next updated moving point is arranged at the end of the time queue ahead;

Step 3.6: return to step 3.3;

Step 3.7: Finally, encapsulate the real-time random operation result in a class, save it in the memory, and save the operation result in the form of XML and TXT files through the data output interface;

The time queue is the core of the entire experimental method. Its advancement represents the movement of all moving points in the entire model space. The time queue requires that all objects in the queue must implement the time interface, and all moving points can be added to the time queue. The time queue is an ordered queue. All objects are sorted according to the moment when the state changes. The moving point that is closest to the current time at the state change time is at the front of the queue and becomes the next moving point to be processed. When the moving point is processed Finally, calculate the moment of the next state change, and insert it into the time queue again in order; according to the experimental requirements, you can add sampling time points to the time queue. The insertion frequency of the sampling point represents the sampling interval and is also the sampling frequency. Can be set when inputting experimental parameters;

Step 4: Output the XML file obtained in step 2, the XML and TXT files obtained in step 3 to the analysis module, because when generating a random motion instance, data analysis is not necessarily required, or it is not known how to do it data analysis, so in the present invention, the simulation of the random motion instance is separated from the data analysis, that is, the data analysis is not performed while simulating the random motion, but the data is saved through the file output interface, and the saved data The file is in XML format or TXT format, and the content of the file can be read. By reading the data file, the entire random motion process can be reproduced. At the same time, it can also be used as the data source of the analysis module to analyze the operation results from different angles, including random motion. Graphical reproduction of the running process of the moving point, analysis of the running track of the moving point, probability statistics of the appearance of the moving point in the entire model platform, analysis of the tracking relationship between multiple moving points, and the dynamic and static conversion state of the moving point The analysis results are saved in the form of files, and the real-time random motion model, the state of the moving point at each moment and the analysis results are displayed on the interface in the form of graphics.

The logical structure of the moving point movement simulation experiment platform on the two-dimensional random road network:

As shown in Figure 4, the simulation experiment platform is divided into three levels from the logical level: data-driven layer (corresponding to the random number generation module), computing layer (corresponding to the modeling module and computing module) and analysis layer (corresponding to the analysis module).

The data-driven layer provides a data-driven interface, through which the operation layer obtains random number drive and performs random operations; the operation layer is mainly responsible for establishing a random model, performing real-time operation of moving points, and saving real-time random data through the output interface, providing analysis layer Data source; the analysis layer obtains data from real-time random data sources, analyzes it, and finally displays the analysis results in the interface in a graphical manner.

The data-driven layer is the foundation, and the operation layer is the core. The relationship between them is mainly reflected in the creation of real-time random motion models and the simulation of the implementation state. As shown in Figure 5, the data-driven layer and the computing layer are connected through a command interface and a data interface. The interface is composed of a set of methods, and data reading and command transmission are executed through the interface. The use of interfaces can reduce the coupling between each module and increase the reusability of code. The data-driven layer adopts an event synchronization mechanism, and only one request is executed at the same time, which controls the singleness of data reading and writing, and ensures the quality of generated random numbers.

The model uses object-oriented thinking, abstracts the characteristics of the model, and increases the reusability of the code through class inheritance. The inheritance relationship of classes in the model structure is:

a. Node base class

The node base class is the basis of the whole model, and the fixed node and dynamic node classes can be derived from the node base class. The node base class contains private attributes: index, the index is the globally unique identifier of each node, used when retrieving, saving or reading the model;

b. Fixed node class

The fixed node class inherits from the node base class, and represents the two endpoints of a path in the model, and is also the connection point between multiple paths. This class contains properties such as the position of fixed nodes, adjacent paths, and adjacent nodes. Since the model involved is in 2D Euclidean space, the position is a 2D coordinate value. Adjacent paths refer to paths starting or ending at the current node. Each fixed node must have at least one adjacent path to ensure that the fixed node will not become an isolated node. The adjacent node refers to another fixed node owned by the adjacent path of the current node. Since each fixed node has at least one adjacent path, it also has at least one adjacent node.

The fixed node class contains methods for adding paths, deleting paths, and saving node information. When modeling, create the entire model by adding paths and deleting paths; after modeling, save node information to the hard disk by saving node information.

c. Time interface

The time interface defines the time methods of dynamic nodes, including methods for calculating the next moment and methods for updating the current time. All dynamic nodes must implement this interface.

d. Dynamic node class

The dynamic node class inherits from the node base class, and realizes the time interface at the same time. In the model, it represents the moving object swimming on the path model. According to different experiments, different moving objects can be derived. This class contains properties such as the speed of the dynamic node, the starting node, the target node, and the path. Speed refers to the movement speed of dynamic nodes. This property is randomly generated during modeling, and the lower limit and upper limit of the speed are specified when setting the modeling parameters. The starting node refers to which fixed node the dynamic node starts from during the current movement process. The target node refers to which fixed node the dynamic node moves to during the current movement process. The current path refers to which path the current node is moving on.

The dynamic node class contains the method of saving node information, and implements the method of calculating the next moment and the method of updating the current time in the time interface.

e. Path class

The Path class represents a connection path between two fixed nodes in the model. This class contains attributes such as the length, endpoint, and index of the path. Length, which refers to the Euclidean distance between the two endpoints of the path. Endpoints refer to two fixed nodes that a path connects. Index refers to the globally unique identifier of the path, which is used when retrieving, saving or reading the model.

The path class contains methods for setting path endpoints, calculating path length, and saving path information. Create paths by setting path endpoints during modeling; use the method of saving path information after modeling to save node information to the hard disk. The method to calculate the path length will be used when the experiment is run.

f. Path model class

The path model class saves all static objects in the model, that is, objects that will not change after being created during modeling. This class contains a collection of fixed nodes and paths.

The path model class contains public methods such as clearing and creating. All static objects can be created for the model through the creation method; all static objects in the model can be cleared through the cleanup method.

When creating model static objects, there may be unconnected isolated points. This type of private method traverses all fixed nodes and paths through breadth-first traversal. When isolated points are found, all static objects are cleared and remodeled. .

g. Instance interface

A real-time random motion model experiment platform instance must have two methods: the method of initializing the instance and the method of running the instance, which are defined in the instance interface. All real-time random motion model experiment platform instances must implement this interface.

h.Instance class

The instance class contains the static data and dynamic data of a real-time random motion model experiment, including path model objects, moving points, current time nodes, and time queues. The path model object is modeled by the instance initialization method and provides static data support for the entire instance. Motion points are created and initialized at modeling time, and the real-time state of each motion point is calculated as the time queue progresses while the instance is running. The current time node, when the instance is running, indicates the current point in time. Time queue, the core of the real-time random motion model experiment platform, all moving points move according to the time queue.

After the path model is created by the modeling module, the information of the path model will be saved in the XML file to provide static object data support for the analysis module. When the calculation module calculates the state of each moving point, the state of the current moving point will be saved in real time Into the XML file, the file format is shown in Figure 6; while calculating the status of each moving point, statistics are made on all moving points, and also statistics on the visits of all stationary moving points, such as paths and fixed nodes are visited After all calculations are completed, save the statistical information to a text file, and the file format is shown in Figure 7.

Inheritance relationship of the file output interface: the file output class implements the file output interface, which contains two methods for saving files, and these two methods are rewritten in various file output classes derived thereafter; the file output class Derived classes include: parameter output class, time output class, path model output class and motion point output class; each derived class stores files for different objects, and can store files in XML format or TXT format.

The present invention is designed for the random motion on the random connected graph in the two-dimensional Euclidean space, so for different random motion models, different data analysis methods may be adopted, and data analysis from different angles for the same set of data or the same instance . Aiming at the uncertainty of the data analysis module, the invention provides an interface for the data analysis module. By reading the data file in the interface, the state information of the entire random motion instance can be obtained, and then the analysis method in the interface is called to analyze the data. The interface uses the form of a dynamic link library, which separates the data analysis module from the entire moving point movement simulation experiment platform, reduces the coupling degree between modules, and enables the analysis module to be written in different languages.

The moving point movement simulation experiment method on the two-dimensional random road network of the present invention uses an object-oriented method to encapsulate the routes, nodes and moving objects in the model into classes, and through the characteristics of class abstraction, encapsulation, inheritance, and polymorphism, Perform data calculations, provide external standard interfaces for the model, increase the scalability of the model, save the data in the model in XML format and text format, and provide data sources for data analysis. It is an inspiration platform for multi-cluster Markov chains. It can be flexibly configured to provide an experimental environment for a variety of problems.

Claims (1)

1. The moving point moving simulation experiment method on the two-dimensional random road network is characterized in that, based on the moving point moving simulation experiment platform on the two-dimensional random road network, the concrete steps are as follows: Step 1: The random number generation module generates a random number after receiving the command, and provides a random data source for the modeling module and the operation module; Step 2: The modeling module obtains the data source of the random number generation module, establishes a random model framework, encapsulates the random model framework in a class, saves it in memory, and saves the information of the path model to a file; Step 3: The calculation module is responsible for the data calculation at runtime. According to the random model framework established in the second step, a random motion model is established, and the time queue algorithm is used to calculate and simulate the real-time state of the moving object at each moment. At the same time, the real-time random calculation results It is encapsulated in the form of a class, stored in memory, and the operation result is saved in the form of a file through the data output interface; Step 4: Output the file saved in step 2 and the file saved in step 3 to the analysis module, the analysis module reads the data, can reproduce the entire random motion process, and analyze and count the characteristics of random motion, through the file Save the analysis results in a graphical way, and display the real-time random motion model, the state of the moving point at each moment and the analysis results in a graphical way; The dynamic point mobile simulation experiment platform on the two-dimensional random road network includes a random number generation module and a modeling module and an operation module that are respectively connected with the random number generation module, and the modeling module and the operation module are all connected with the analysis module; The number generating module includes a command receiving interface, a random number generator and a data sending interface, and the random number generator generates a robust random number by calling the CryptGenRandom function; The process of setting up the random model framework in the 2nd step modeling module is: Step 2.1: First set the modeling parameters, then read the modeling parameters, and create random node positions according to the modeling range; Step 2.2: Use the Waxman modeling method to create random paths between random nodes, and the paths between nodes satisfy the Poisson distribution; Step 2.3: Perform a connectivity test on the random path created in step 2.2 through the breadth-first algorithm. If there is no isolated node, perform step 2.4; if there is an isolated node, return to step 2.2 and recreate the random path; if step 2.2 repeats Orphaned nodes still appear after times, then return to step 2.1 and reset the modeling parameters; Step 2.4: Create moving points, set the parameters of each moving point according to the simulation requirements, save all model data to external files, and the modeling is completed; Described Waxman modeling method, as shown in formula (1): $\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ Where P(u, v) is the direct connection probability between node u and node v, modeling parameters α>0, β<=1, d is the distance between vertex u and vertex v, L is all vertices in the plane The farthest distance among them; the larger the α value, the more edges in the graph; the larger the β value, the larger the ratio of the long side to the short side in the graph. Waxman believes that the connection probability between nodes is related to its distance, and the out-degree The frequency obeys the Poisson distribution, the closer the distance, the greater the probability; The specific operation process of the 3rd step operation module is: Step 3.1: The operation module obtains the random motion model, Step 3.2: Create a time queue according to the random motion model, add all dynamic nodes to the time queue, and initialize their running time to 0; Step 3.3: Determine whether the movement time of the moving point exceeds the total time limit set when initially creating the model. If the movement time exceeds the limit, end the calculation and perform step 3.7; if the movement time does not exceed the limit, proceed to step 3.4; Step 3.4: Calculate the upcoming state of the moving point at the head of the time queue, that is, whether the moving point will move at the next moment and its direction of movement, and calculate the time when the next state of the moving point changes according to the state of the moving point at the next moment, and update the moving point state of the point; ${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; bl</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; al</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{{\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}\\ {\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ In the formula, l _i represents the current path of the moving point; and Indicates the two ends of the l _i path; (x _ii (t), y _ii (t)) indicates the coordinates of the moving point on the l _i path; t′ is the interval sampling time; v _ci is the rate randomly assigned to the moving point; Δt _m is the subdivision function within the interval sampling time t′; v _i represents the moving speed of the moving point, Δt _m-1 is a reference, which refers to the equal division of t′; m is the division of t′ interval number; among them, the discrete random variable ζ _l ={l ₁ ,…,l _i ,…,l _k } represents the length of the path l _i , among which, k represents the number of paths; Δt _p represents the pth path The time; p represents the number of times through the path; The position of the moving point at the next moment is obtained by formula (2) and formula (3); the path length l _i can be obtained according to the current position and the position of the next moment; the next moment is updated by formula (4) and formula (5) Δt _m ; Step 3.5: According to the state of the updated moving point, update the time queue, that is, the updated moving point is reinserted into the time queue in ascending order according to the size of its Δt _m value, so that the next updated moving point is arranged at the end of the time queue ahead; Step 3.6: return to step 3.3; Step 3.7: Finally, encapsulate the real-time random operation result in a class, save it in the memory, and save the operation result in the form of a file through the data output interface; The analysis of the characteristics of the random movement in the fourth step includes the graphic reproduction of the running process of the random moving point, the analysis of the moving track of the moving point, the probability statistics of the occurrence of the moving point in the entire model platform, and the relationship between multiple moving points. The tracking relationship analysis, the movement analysis of the moving point in the state of dynamic and static conversion.