Task list scheduling method based on vehicle cooperation cluster

By designing task models and communication models in vehicle cooperation clusters, predicting task priority and considering communication link occupation, and using PPTS_CC algorithm for task scheduling, the problem of low task scheduling efficiency in vehicle networking is solved, and more efficient task completion is achieved .

CN119212099AActive Publication Date: 2024-12-27NANJING UNIV OF POSTS & TELECOMM
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Patent Information

Application Number
CN202411723586.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-28
Publication Date
2024-12-27
Estimated Expiration
2044-11-28

AI Technical Summary

Technical Problem

The existing technology fails to effectively consider the occupation of the Internet of Vehicles communication link, resulting in low task scheduling efficiency in vehicle cooperation clusters and long completion time.

Method used

A task list scheduling method based on vehicle cooperative cluster was designed. Through the task model and communication model, task priority is predicted, task data is selected, and task data is transmitted. Considering the occupancy of communication links, and task scheduling is used using the PPTS_CC algorithm.

Benefits of technology

It improves the utilization rate of computing resources in vehicle cooperative clusters, reduces task completion time, and improves the acceleration of task completion.

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Abstract

The invention provides a task list scheduling method based on a vehicle cooperation cluster, and the method comprises the steps: firstly, designing a vehicle task model and an Internet of Vehicles communication model, and considering the link occupation condition of V2V communication; then, a task list scheduling algorithm based on communication occupation and task priority prediction is designed, the algorithm can predict the calculation priority of each task, executed tasks and vehicle calculation equipment are selected according to priority values, and then the optimal path is selected to transmit data of the tasks. Finally, through experimental comparison between the algorithm and other algorithm schemes, simulation results show that the algorithm reduces the average task completion time by about 27% and improves the efficiency of vehicle computing equipment by about 18%.
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Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication networks, and in particular to a task list scheduling method based on vehicle cooperation clusters. Background Art

[0002] With the rapid development of intelligent transportation systems, the Internet of Vehicles is gradually maturing. Idle vehicles on the road can form a vehicle cooperation cluster. Many tasks use the computing resources of the vehicle cooperation cluster to schedule tasks. Since vehicle-to-vehicle network (V2V) communication is direct communication, the scheduling of dependent tasks needs to consider the link occupancy of the Internet of Vehicles communication.

[0003] However, many current studies on the Internet of Vehicles do not consider the communication occupancy, so this paper proposes a task list scheduling method based on vehicle cooperative clusters. First, the vehicle task model and the Internet of Vehicles communication model are designed, considering the link occupancy of V2V communication. Then, the calculation priority of each task is predicted, and the tasks and vehicle computing devices to be executed are selected according to the priority value, and then the optimal path is selected to transmit the task data. Summary of the invention

[0004] To solve the above problems, the present invention discloses a task list scheduling method based on vehicle cooperative clustering, a scheduling algorithm for completing dependent tasks in a vehicle cooperative clustering scenario, which takes into account the occupancy of V2V communication links and improves the performance in heterogeneous computing systems. It is superior to the proposed algorithms in terms of completion time, acceleration and efficiency.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a task scheduling method based on vehicle cooperative cluster, comprising the following specific steps: Step 1: The user requests the vehicle cooperation cluster to schedule the task flow to be executed; Step 2: Design the user's task flow model, which is represented by a directed acyclic graph. The nodes of the graph are tasks, and the edges of the graph are the dependency relationships between the execution of two tasks. Step 3: Design the communication environment model of the vehicle cooperation cluster and provide the execution cost model of the task in the vehicle's computing device; Step 4: Under the condition that there is link occupancy in the communication environment model, define the scheduling problem of the task flow and give the objective function of minimizing the time; Step 5: Design a task scheduling algorithm based on communication link occupancy and predicted priority, calculate task priority, determine the execution order of tasks, and schedule tasks to the computing devices of the vehicle cooperation cluster for execution.

[0006] Furthermore, in step 1, the task flow that the user requests to schedule to be executed from the vehicle cooperation cluster is composed of multiple tasks with dependencies, and the tasks need to be executed on each vehicle computing device in the vehicle cooperation cluster according to the dependencies.

[0007] Furthermore, the task flow model of the user in step 2 is composed of a set of tasks with dependencies, which is represented by a directed acyclic graph (DAG), G=(T,E,D), where T represents a set of |T| tasks with dependencies requested by the user; E is a set of edges between the predecessor task and the successor task, representing the dependency between the tasks; D is a set of the transmission data size of the predecessor task and the successor task, , task i is the predecessor task of task j, Indicates the size of data that needs to be transferred to task j after task i is executed.

[0008] Furthermore, the communication environment model of the vehicle cooperation cluster designed in step 3 is as follows: Define an undirected graph represents the heterogeneous vehicle communication environment, is the set of vehicle computing devices, where k is the number of vehicles in the vehicle cooperation cluster; is the set of communication links, where q is the number of communication links between vehicles, is the set of transmission speeds of the communication link; Indicates the communication link After the predecessor task is completed on the source vehicle computing device, a communication link is selected to transmit the data required for the successor task to the target vehicle computing device for execution.

[0009] Furthermore, in step 3, it is assumed that the data From the task Transfer tasks , Is processing task The source vehicle computing device, Is processing task The target vehicle computing device, Representative source vehicle computing device and target vehicle computing device between A collection of communication routes, each route passing through multiple vehicle computing devices and composed of multiple communication links with different transmission rates Composition, searched by depth-first search algorithm or breadth-first search algorithm; definition Source vehicle computing device and target vehicle computing device Average communication speed; ,in Representative path communication speed; Since the vehicle adopts the direct communication scheme for message forwarding, the source vehicle computing device and target vehicle computing device The communication speed is determined by the minimum speed of the link, so the path The communication speed is: ;in Indicates the communication link The transmission speed on the source vehicle computing device is defined The average communication speed with other vehicle computing devices is: ,in Represents the number of available vehicle computing devices in the vehicle cooperation cluster.

[0010] Furthermore, the execution cost model of the task in the computing device of the vehicle in step 3 includes four parts: the first part is the data size of the task, and the data of task i is defined as The second part is the computing device equipped in each vehicle. Assuming that each vehicle is equipped with only one computing device, define the vehicle computing device set , the computing power of the device is composed of the collection express, represents the computing power of the vehicle computing device k; the third part is the definition It's a task In-vehicle computing equipment The calculation time on is given by: ;Task The average execution time is defined as follows: , the fourth part is the task In-vehicle computing equipment The estimated communication time at the location, that is, the size of the data transmitted from the predecessor task to the successor task and the vehicle computing device The ratio of the average transmission rate is calculated by the following formula: ,in Represents vehicle computing device The average transmission rate, Represents the predecessor task To the successor task The amount of data transmitted.

[0011] Furthermore, in step 4, since the earliest start time of the task depends on the task start transmission time, and the task transmission time is limited by the actual link completion time LFT, it is necessary to obtain the link start time LST in advance. Through the above analysis, it is necessary to obtain the value of the actual link completion time LFT, and define the link start time as LST. The definition of LST is as follows: ;in Indicates the amount of data transferred From the source vehicle computing device To the target vehicle computing device The start time of link x on communication path z, represents the available time of link x on path z, Representation Task In-source vehicle computing equipment The actual end time at the location; the start time of the first link on path z should take the maximum value between the link available time and the completion time of the predecessor task, and the start time of the subsequent links is the start time of the previous path; similarly, the value of LFT is as follows: ,in Indicates the amount of data transferred From the source vehicle computing device To the target vehicle computing device The end time of link x on communication path z; each task is implemented on a different vehicle computing device There are different communication times. The start time of the task is determined by the availability of the vehicle computing equipment and the availability of the transmission link; the start task The start time of other tasks is 0. The start time is given by the following formula: ;in It's a task The set of predecessor tasks, Is to perform the predecessor task Vehicle computing devices, Is the target vehicle computing device The earliest available time, Indicates the amount of data transferred From the table source vehicle computing equipment To the target vehicle computing device The end time of the last link on the communication path z. The above formula shows that EST and LFT are closely related. When the vehicle equipment wants to send task data, it may not transmit immediately. Because the communication link to be transmitted may be occupied by other messages until it is free. From this, the end time of task i can be obtained ;in Representation Task In the target vehicle computing device The estimated start time of Representation Task In the target vehicle computing device Finally, define makespan as the completion time of the task flow. Makespan is determined by the completion time of the end task. The objective function of the problem is to minimize the completion time, which is defined by the following formula: ,in Indicates the end of the task In the target vehicle computing device The completion time of the place.

[0012] Further, in step 5, the task scheduling algorithm based on communication link occupancy and prediction priority is the PPTS_CC algorithm, which uses the concept of predictability to determine the task priority stage and the vehicle computing device selection stage. First, based on the prediction cost matrix Calculate the priority of each task, then select a vehicle with an unoccupied communication link to perform the task, and select the vehicle computing device with the shortest completion time among all available vehicles for the task; define PCM as a A matrix where each element Representation Task In each vehicle computing device The maximum value of the upper priority; Each task is recursively calculated by traversing the given vehicle task flow model from the end task to the start task; It is determined recursively by the following equation: ,in express The subsequent task, Representation Task With the task In-vehicle computing equipment The average transfer time on .

[0013] Furthermore, the first stage of task scheduling is to prioritize tasks. First, each task is calculated The priority value is Indicates, indicates tasks The average PCM value is given by: .

[0014] Furthermore, in step 5, during the vehicle computing device selection phase, first, the forward prediction value of each task on the arriving vehicle computing device is calculated. ; Then, select The smallest vehicle computing device performs the task and establishes a path between the source vehicle computing device and the target vehicle computing device. Mark as occupied until the task data transmission is completed; the goal of this stage is to ensure that the successor tasks of the current task can be completed in advance without increasing the complexity of the algorithm; forward prediction value The calculation method is as follows: .

[0015] Beneficial effects of the present invention: Compared with the prior art, the present invention adopts a scheduling algorithm (PPTS_CC) that considers the occupancy of the communication link and predicts the priority of the task to solve the problem of scheduling dependent task flows in an environment where the V2V communication link is occupied in the vehicle cooperation cluster, thereby improving the utilization rate of computing resources in the vehicle cooperation cluster, reducing the task completion time, and improving the acceleration of task completion. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a diagram of the vehicle cooperative cluster task scheduling model of the present invention.

[0017] Figure 2 This is a diagram of the task flow model of a user of the present invention.

[0018] Figure 3 This is a flow chart of the PPTS_CC algorithm of the present invention. DETAILED DESCRIPTION

[0019] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0020] like Figure 1-3 As shown, this embodiment provides a task list scheduling method based on vehicle cooperation cluster, including the following steps: In step 1, the task flow requested by the user is composed of multiple tasks with dependencies, and the tasks need to be executed on each vehicle computing device in the vehicle cooperation cluster according to the dependencies.

[0021] In step 2, the user's task flow model is composed of a set of dependent tasks, represented by a directed acyclic graph (DAG) G=(T,E,D), where T represents the set of |T| dependent tasks requested by the user; E is the set of edges between the predecessor task and the successor task, representing the dependency relationship between tasks; D is the set of transmission data sizes between the predecessor task and the successor task. , task i is the predecessor task of task j, Indicates the size of data that needs to be transferred to task j after task i is executed.

[0022] In step 3, the communication environment model of the vehicle cooperation cluster is given as follows: Define the undirected graph represents the heterogeneous vehicle communication environment, is the set of vehicle computing devices, where k is the number of vehicles in the vehicle cooperation cluster; is the set of communication links, where q is the number of communication links between vehicles, is the set of transmission speeds of the communication link; Indicates the communication link Transmission speed on Source vehicle computing device and target vehicle computing device Average communication speed; ;according to Figure 2 The vehicle cooperative cluster communication model diagram example can obtain the path transmission rate value between each vehicle computing device of UG, { V 1 -V 2 : 1, V 2 -V 3 : 1, V 2 -V 4 : 2}, V 3 -V 4 : 4, V 4 -V 5 : 4}. For example There are two paths in total, ;in Representative path The communication speed is faster than that of the source vehicle computing device. and target vehicle computing device The communication speed is determined by the minimum speed of the link, so the path The communication speed is: ;in represents the communication speed of link q, defining the source vehicle computing device The average communication speed with other vehicle computing devices is: ,in Represents the number of available vehicle computing devices in the vehicle cooperation cluster.

[0023] For example, the above path , , because the link The transmission rate is minimum.

[0024] according to Figure 2 The vehicle cooperative cluster communication model diagram example, the above steps can be used to obtain the average transmission rate value of each vehicle computing device in the cooperative cluster as shown in Table 1: Table 1: Average transmission rate values ​​of various vehicle computing devices

[0025] The execution cost model of a task in the vehicle’s computing device consists of four parts: The first part is the data size of the task, where the data of task i is defined as The second part is the computing device equipped in each vehicle. Assuming that each vehicle is equipped with only one computing device, define the vehicle computing device set , the computing power of the device is composed of the collection express, represents the computing power of the vehicle computing device k; the third part is the definition It's a task In-vehicle computing equipment The calculation time on is given by: ; Each task Vehicle computing equipment The estimated computation time on Indicates that the task The average execution time is defined as follows: , the fourth part is the task In-vehicle computing equipment The estimated communication time at is calculated as follows:

[0026] That is, the size of the data transferred from the predecessor task to the successor task With computing devices The ratio of the average transmission rate is calculated by the following formula: ,in Represents vehicle computing device The average transmission rate, Represents the predecessor task To the successor task The amount of data transmitted.

[0027] In step 4, since the earliest start time of the task depends on the task start transmission time, and the task transmission time is limited by the actual link completion time LFT, it is necessary to obtain the link start time LST in advance. Through the above analysis, it is necessary to obtain the value of the actual link completion time LFT, and define the link start time as LST. The definition of LST is as follows: In step 4, since the earliest start time of the task depends on the task start transmission time, and the task transmission time is limited by the actual link completion time LFT, it is necessary to obtain the link start time LST in advance. Through the above analysis, it is necessary to obtain the value of the actual link completion time LFT, and define the link start time as LST. The definition of LST is as follows: ;in Indicates the amount of data transferred From the source vehicle computing device To the target vehicle computing device The start time of link x on communication path z, represents the available time of link x on path z, Representation Task In-source vehicle computing equipment The actual end time at the location; the start time of the first link on path z should take the maximum value between the link available time and the completion time of the predecessor task, and the start time of the subsequent links is the start time of the previous path; similarly, the value of LFT is as follows: ,in Indicates the amount of data transferred From the source vehicle computing device To the target vehicle computing device The end time of link x on communication path z; each task is implemented on a different vehicle computing device There are different communication times. The start time of the task is determined by the availability of the vehicle computing equipment and the availability of the transmission link; the start task The start time of other tasks is 0. The start time is given by the following formula: ;in It's a task The set of predecessor tasks, Is to perform the predecessor task Vehicle computing devices, Is the target vehicle computing device The earliest available time, Indicates the amount of data transferred From the table source vehicle computing equipment To the target vehicle computing device The end time of the last link on the communication path z. The above formula shows that EST and LFT are closely related; thus, the end time of task i is obtained as: ;in Representation Task In the target vehicle computing device The estimated start time of Representation Task In the target vehicle computing device Finally, define makespan as the completion time of the task flow. Makespan is determined by the completion time of the end task. The objective function of the problem is to minimize the completion time, which is defined by the following formula: ,in Indicates the end of the task In the target vehicle computing device The completion time of the place.

[0028] In step 5, the task scheduling algorithm based on communication link occupancy and prediction priority is the PPTS_CC algorithm, which uses the concept of predictability to determine the task priority stage and the vehicle computing device selection stage. First, based on the prediction cost matrix Calculate the priority of each task, then select a vehicle with an unoccupied communication link to perform the task, and select the vehicle computing device with the shortest completion time among all available vehicles for the task; define PCM as a A matrix where each element Representation Task In each vehicle computing device The maximum value of the upper priority; Each task is recursively calculated by traversing the given vehicle task flow model from the end task to the start task; It is determined recursively by the following equation: ,in express The subsequent task, Representation Task With the task In-vehicle computing equipment The average transfer time on .

[0029] The first stage of task scheduling is to prioritize tasks. First, calculate each task The priority value is Indicates, indicates tasks The average PCM value is given by: .

[0030] In step 5, during the vehicle computing device selection phase, first, the forward prediction value of each task on the arriving vehicle computing device is calculated. ; Then, select The smallest vehicle computing device performs the task and establishes a path between the source vehicle computing device and the target vehicle computing device. Mark as occupied until the task data transmission is completed; the goal of this stage is to ensure that the successor tasks of the current task can be completed in advance without increasing the complexity of the algorithm; forward prediction value The calculation method is as follows: .

[0031] according to Figure 2 In the case of the user's task flow model diagram, the above steps can be used to obtain the predicted cost PCM value of DAG as shown in Table 2: Table 2: Computational cost of each task on different vehicle computing devices

[0032] The priority of each task is shown in Table 3: Table 3: Final priority values ​​of each task

[0033] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above technical features.

Claims

1. A task list scheduling method based on vehicle cooperative clusters, characterized in that: The specific steps include: Step 1: The user requests the vehicle cooperation cluster to schedule the task flow to be executed; Step 2: Design the user's task flow model, which is represented by a directed acyclic graph. The nodes of the graph are tasks, and the edges of the graph are the dependency relationships between the execution of two tasks. Step 3: Design the communication environment model of the vehicle cooperation cluster and provide the execution cost model of the task in the vehicle's computing device; Step 4: Under the condition that there is link occupancy in the communication environment model, define the scheduling problem of the task flow and give the objective function of minimizing the time; Step 5: Design a task scheduling algorithm based on communication link occupancy and predicted priority, calculate task priority, determine the execution order of tasks, and schedule tasks to the computing devices of the vehicle cooperation cluster for execution.

2. The task list scheduling method based on vehicle cooperative cluster according to claim 1 is characterized by: In step 1, the task flow that the user requests the vehicle cooperation cluster to schedule to be executed is composed of multiple tasks with dependencies, and the tasks need to be executed on each vehicle computing device in the vehicle cooperation cluster according to the dependencies.

3. The task list scheduling method based on vehicle cooperative cluster according to claim 1 is characterized in that: The user's task flow model in step 2 is composed of a set of tasks with dependencies, which is defined as a directed acyclic graph G=(T,E,D), where T represents a set of |T| tasks with dependencies requested by the user; E is a set of edges between the predecessor task and the successor task, representing the dependency between the tasks; D is a set of transmission data sizes between the predecessor task and the successor task, , task i is the predecessor task of task j, Indicates the size of data that needs to be transferred to task j after task i is executed.

4. The task list scheduling method based on vehicle cooperative cluster according to claim 1 is characterized in that: The communication environment model of the vehicle cooperation cluster designed in step 3 is as follows: Define the undirected graph represents the heterogeneous vehicle communication environment, is the set of vehicle computing devices, where k is the number of vehicles in the vehicle cooperation cluster; is the set of communication links, where q is the number of communication links between vehicles, is the set of transmission speeds of the communication link; Indicates the communication link After the predecessor task is completed on the source vehicle computing device, a communication link is selected to transmit the data required for the successor task to the target vehicle computing device for execution.

5. The task list scheduling method based on vehicle cooperative cluster according to claim 4 is characterized in that: In step 3, it is assumed that the data needs to be From the task Transfer tasks , Is processing task The source vehicle computing device, Is processing task The target vehicle computing device, Representative source vehicle computing device and target vehicle computing device between A collection of communication routes, each route passing through multiple vehicle computing devices and composed of multiple communication links with different transmission rates Composition, searched by depth-first search algorithm or breadth-first search algorithm; definition The source vehicle computing device and target vehicle computing device Average communication speed; ,in Representative path communication speed; Since the vehicle adopts the direct communication scheme for message forwarding, the source vehicle computing device and target vehicle computing device The communication speed is determined by the minimum speed of the link, so the path The communication speed is: ;in Indicates the communication link The transmission speed on the source vehicle computing device is defined The average communication speed with other vehicle computing devices is: ,in Represents the number of available vehicle computing devices in the vehicle cooperation cluster.

6. The task list scheduling method based on vehicle cooperative cluster according to claim 1 is characterized by: The execution cost model of the task in the computing device of the vehicle in step 3 includes four parts: the first part is the data size of the task, and the data of task i is defined as The second part is the computing device equipped in each vehicle. Assuming that each vehicle is equipped with only one computing device, define the vehicle computing device set , the computing power of the device is composed of the collection express, represents the computing power of the vehicle computing device k; the third part is the definition It's a task In-vehicle computing equipment The calculation time on is given by: ;Task The average execution time is defined as follows: , the fourth part is the task In-vehicle computing equipment The estimated communication time at the location, that is, the size of the data transmitted from the predecessor task to the successor task and the vehicle computing device The ratio of the average transmission rate is calculated by the following formula: ,in Represents vehicle computing device The average transmission rate of Represents the predecessor task To the successor task The amount of data transmitted.

7. The task list scheduling method based on vehicle cooperative cluster according to claim 1 is characterized by: In step 4, since the earliest start time of the task depends on the task start transmission time, and the task transmission time is limited by the actual link completion time LFT, it is necessary to obtain the link start time LST in advance, obtain the value of the actual link completion time LFT, and define the link start time as LST. The definition of LST is as follows: ;in Indicates the amount of data transferred From the source vehicle computing device To the target vehicle computing device The start time of link x on communication path z, represents the available time of link x on path z, Indicates the task In-source vehicle computing equipment The actual end time at the location; the start time of the first link on path z should take the maximum value between the link available time and the completion time of the predecessor task, and the start time of the subsequent links is the start time of the previous path; similarly, the value of LFT is as follows: ,in Indicates the amount of data transferred From the source vehicle computing device To the target vehicle computing device The end time of link x on communication path z; each task is implemented on a different vehicle computing device There are different communication times. The start time of the task is determined by the availability of the vehicle computing equipment and the availability of the transmission link; the start task The start time of other tasks is 0. The start time is given by the following formula: ;in It's a task The set of predecessor tasks, Is to perform the predecessor task Vehicle computing devices, Is the target vehicle computing device The earliest available time, Indicates the amount of data transferred From the table source vehicle computing equipment To the target vehicle computing device The end time of the last link on the communication path z, the above formula shows that EST and LFT are closely related; thus, the end time of task i is obtained; ;in Indicates the task In the target vehicle computing device The estimated start time of Indicates the task In the target vehicle computing device Finally, define makespan as the completion time of the task flow. Makespan is determined by the completion time of the end task. The objective function of the problem is to minimize the completion time, which is defined by the following formula: ,in Indicates the end of the task In the target vehicle computing device The completion time of the place.

8. The task list scheduling method based on vehicle cooperative cluster according to claim 1 is characterized by: In step 5, the task scheduling algorithm based on communication link occupancy and prediction priority is the PPTS_CC algorithm, which uses the concept of predictability to determine the task priority stage and the vehicle computing device selection stage. First, based on the prediction cost matrix Calculate the priority of each task, then select a vehicle with an unoccupied communication link to perform the task, and select the vehicle computing device with the shortest completion time among all available vehicles for the task; define PCM as a A matrix where each element Indicates the task In each vehicle computing device The maximum value of the upper priority; Each task is recursively calculated by traversing the given vehicle task flow model from the end task to the start task; It is determined recursively by the following equation: ,in express The subsequent task, Indicates the task With the task In-vehicle computing equipment The average transfer time on .

9. The task list scheduling method based on vehicle cooperative cluster according to claim 8, characterized in that: The first stage of task scheduling is to prioritize tasks. First, calculate each task The priority value is Indicates, indicates tasks The average PCM value is given by: .

10. The task list scheduling method based on vehicle cooperative cluster according to claim 8, characterized in that: In step 5, during the vehicle computing device selection phase, first, the forward prediction value of each task on the arriving vehicle computing device is calculated. ; Then, select The smallest vehicle computing device performs the task and establishes a path between the source vehicle computing device and the target vehicle computing device. Mark as occupied until the task data transmission is completed; the goal of this stage is to ensure that the successor tasks of the current task can be completed in advance without increasing the complexity of the algorithm; forward prediction value The calculation method is as follows: .

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