Undirected graph task scheduling method applied to edge-end collaborative network

Abstract

The embodiment of the invention provides an undirected graph task scheduling method applied to an edge-end collaborative network. The method comprises the following steps: carrying out time period modeling, edge-end collaborative service topology modeling, undirected graph task modeling, V2V and V2I communication modeling, undirected graph task completion time modeling and energy cost modeling on the edge-end collaborative network; based on the model obtained through modeling, modeling is conducted on the undirected graph task scheduling problem of the edge-end collaborative network, an undirected graph task scheduling optimization model is obtained, and the optimization target is to minimize the undirected graph task completion time under the specific energy budget; and decomposing an optimization target of the undirected graph task scheduling optimization model into a series of deterministic sub-targets by using a Lyapunov optimization framework, and on the basis, carrying out optimization solution on the undirected graph task scheduling optimization model by adopting an undirected graph task scheduling algorithm. In this way, the undirected graph task scheduling efficiency and the resource utilization rate in the edge-end collaborative network can be effectively improved, and the method is suitable for various dynamic and uncertain scenes.

Description

Technical Field

[0001] The present invention relates to the technical field of edge-cloud collaborative networks, and in particular, to an undirected graph task scheduling method applied to edge-cloud collaborative networks. Background Art

[0002] With the rapid development of the Internet of Vehicles (IoV) and edge computing, edge-cloud collaborative networks have become an important computing paradigm. In such a network, vehicles not only serve as communication nodes but also as mobile servers, providing computing resources for other vehicles or edge servers. However, the undirected graph task scheduling in edge-cloud collaborative networks faces many challenges. On the one hand, undirected graph tasks appear in the form of undirected graphs, containing multiple subtasks and complex topological structures; on the other hand, due to the mobility of vehicles and the limitations of communication ranges, the undirected graph task scheduling process needs to be dynamically adjusted and optimized. Traditional undirected graph task scheduling methods often struggle to adapt to the dynamics and uncertainties of edge-cloud collaborative networks. These methods are usually based on static network topologies and fixed task models, and cannot fully utilize the mobility and computing resources of vehicles. Therefore, there is an urgent need for a method that can adapt to the dynamic edge-cloud collaborative network environment and achieve efficient undirected graph task scheduling. Summary of the Invention

[0003] In a first aspect, an embodiment of the present invention provides an undirected graph task scheduling method applied to edge-cloud collaborative networks, the method comprising:

[0004] Performing time period modeling, edge-cloud collaborative service topology modeling, undirected graph task modeling, V2V and V2I communication modeling, undirected graph task completion time modeling, and energy cost modeling for the edge-cloud collaborative network to obtain a time period model, an edge-cloud collaborative service topology model, an undirected graph task model, a V2V and V2I communication model, an undirected graph task completion time model, and an energy cost model;

[0005] Based on the time period model, the edge-cloud collaborative service topology model, the undirected graph task model, the V2V and V2I communication model, the undirected graph task completion time model, and the energy cost model, modeling the undirected graph task scheduling problem of the edge-cloud collaborative network to obtain an undirected graph task scheduling optimization model, the optimization objective of which is to minimize the undirected graph task completion time under a specific energy budget;

[0006] Using the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-goals, and on this basis, using an undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model.

[0007] In some realizable ways of the first aspect, the time period modeling includes:

[0008] Using {1,..., τ,..., τ*} represents multiple time periods of different lengths; at the beginning of each time period, multiple undirected graph tasks will arrive, and the edge server will check the available computing resources and undirected graph task buffers within its coverage area, and further coordinate the undirected graph task scheduling process.

[0009] In some implementations of the first aspect, edge collaborative service topology modeling includes:

[0010] The edge collaborative service topology is modeled as an undirected graph task within a time period τ, using Represents; where the vertex set represents the server in the time period τ, further, using represents the edge server in the time period τ, and the moving vehicles As a mobile server, In addition, the server With attributes Quantify its computing power; edge set represents the available connections between different servers in the time period τ, each edge Contains attributes It represents the contact duration between servers, thus encapsulating the temporal dynamics of the interactions between servers in the edge collaboration network.

[0011] In some implementations of the first aspect, undirected graph task modeling includes:

[0012] At the beginning of each time period τ, the edge server as the coordinator checks the current undirected graph task buffer, which is expressed as Buffer Q <τ> Each element in Represents an undirected graph task, using Indicates that Represents the set of undirected graph task components and the edges between undirected graph task components; each undirected graph task component You Yuan Description, where Indicates the size of the data to be processed. Represents the tolerable time for completion; each edge between two undirected graph task components is assigned a weight Characterizes the minimum required connection time associated with it, that is, the contact time between two servers processing two connected undirected graph task components should be greater than or equal to To support the intermediate data exchange required during the execution of undirected graph tasks; since undirected graph task components are processed in parallel on different servers, Depending on the completion time of the undirected graph task component that finishes first, that is, where represents the completion time of the undirected graph task component on the server ; represents the completion time of the undirected graph task component on the server ;

[0013] In some realizable ways of the first aspect, the V2V and V2I communication modeling includes:

[0014] Using and to represent the speed and relative position of the vehicle, i.e., the mobile server, at a certain moment, where k≠1; for the edge server, let regard the speed of each vehicle at each moment as a constant speed; in addition, the communication radii of the edge server and the vehicle are represented as and respectively;

[0015] For the vehicles within the coverage range of the edge server during the time period τ, the remaining residence time for the vehicle to interact with the edge server through a one-hop V2I communication link is represented as the V2V communication duration

[0016]

[0017] When two vehicles and are within the corresponding signal coverage ranges of each other, a contact event occurs, and calculate the connection duration between the two vehicles and traveling in the same direction

[0018]

[0019] In some realizable ways of the first aspect, the undirected graph task completion time modeling includes:

[0020] Using to represent the allocation relationship between the undirected graph task component and the server during the time period τ, where represents that the undirected graph task component is processed on the server , otherwise it is 0; using to represent the undirected graph task scheduling policy during the time period τ, where i∈{1, 2, …, |Q <τ> |}; meanwhile, using to represent the scheduling decision matrix corresponding to the time period τ; in addition, using Denote the data transfer rate from the edge server to the vehicle within the time period τ; based on this, the data transfer time required to transfer the relevant data from the edge server to the undirected graph task execution server It is expressed as:

[0021]

[0022] Then, when the undirected graph task component is processed on the server the execution time is expressed as:

[0023]

[0024] where z represents the computing intensity;

[0025] The completion time of the undirected graph task component is determined by the sum of the data transfer time and the execution time, that is:

[0026]

[0027] The overall completion time of the undirected graph task depends on the last completed undirected graph task component and is defined as: where i ∈ {1, 2, …, |Q <τ> |}; meanwhile, the total execution time consumed by all undirected graph tasks within the time period τ is expressed as:

[0028]

[0029] In some realizable ways of the first aspect, the energy cost modeling includes:

[0030] Express the energy consumed to transfer the data volume of the undirected graph task component from the edge server to the vehicle as:

[0031]

[0032] where p <τ> represents the transmission power of the edge server; in addition, the server processing the undirected graph task component the energy consumed is expressed as:

[0033]

[0034] where γ represents the energy cost coefficient;

[0035] The energy cost generated by executing the undirected graph task component on the server is expressed as:

[0036]

[0037] Total energy cost for processing undirected graph tasks Expressed as:

[0038]

[0039] Using Represents the total energy cost consumed by all undirected graph tasks within the time period τ.

[0040] In some realizable ways of the first aspect, the optimization objective of the undirected graph task scheduling optimization model is expressed as:

[0041]

[0042] Subject to the following constraint conditions:

[0043] Constraint condition C1:

[0044] Constraint condition C2:

[0045] Constraint condition C3:

[0046] Constraint condition C4:

[0048] Constraint condition C5:

[0049] Wherein, Represents the average energy budget.

[0050] In some realizable ways of the first aspect, the Lyapunov optimization framework is used to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-objectives, including:

[0051] First, using Represents the buffer for newly arrived undirected graph tasks within the time period τ, and assuming the average arrival rate is λ, denoted as Using Represents the undirected graph tasks that have been successfully scheduled within the time period τ. Based on this, there is:

[0052]

[0053] Here, Q <τ+1> Is regarded as the real queue within the time period τ + 1, and Q <τ> Is regarded as the real queue within the time period τ;

[0054] Introduce a virtual buffer, that is, a virtual queue To capture the deviation of the total energy cost, specifically, the update of the virtual queue is expressed as:

[0055]

[0056] Here will As a virtual queue in the time period τ+1, is regarded as a virtual queue within the time period τ; and represent the energy consumption and energy budget in the time period τ, respectively;

[0057] The average energy budget Expressed as:

[0058]

[0059] Average energy budget Represents until the time period τ * The cumulative energy allocated so far is used as a comparison basis for total energy consumption;

[0060] Then, the Lyapunov function is introduced and Lyapunov drift It is expressed as follows:

[0061]

[0062] Adopt drift plus penalty function to minimize undirected graph task completion time and stabilize Q <τ> and The details are as follows:

[0063]

[0064] in, represents the Lyapunov drift, which is used to measure the expected backlog of different queues over time, represents the expected task completion delay given the current different queue states; parameter V is a non-negative control coefficient used to balance the trade-off between queue stability and time efficiency;

[0065] To derive the upper bound of the drift plus penalty function, first, express the squared value of the queue update as:

[0066]

[0067] By summing both sides, we get:

[0068]

[0069] Then, based on this, the Lyapunov drift is derived as:

[0070]

[0071]

[0072] where the constants B1 and B2 are as follows:

[0073]

[0074] Let It can be obtained that The upper bound of is:

[0075]

[0076] Based on this, the drift-plus-penalty function is expressed as:

[0077]

[0078] On this basis, the optimization objective is decomposed into deterministic sub-objectives for each time period τ, expressed as follows:

[0079]

[0080] According to the upper bound of, the optimization objective is converted to:

[0081]

[0082] Subject to the following constraints:

[0083] Constraint C1 to Constraint C4;

[0084] Constraint C6:

[0085] Constraint C7:

[0086] In some realizable ways of the first aspect, an undirected graph task scheduling algorithm is used to optimize and solve the undirected graph task scheduling optimization model, including:

[0087] Converting the converted optimization objective (also known as the optimization objective for a fixed time period) into an optimization objective based on logical time periods, so as to adapt to the dynamically changing undirected graph task scheduling requirements; performing priority sorting on the undirected graph task queue, and preferentially scheduling undirected graph tasks with higher urgency; using the merge pruning strategy - backtracking greedy scheduling strategy to find a feasible near-optimal solution to achieve the final optimization objective.

[0088] In the second aspect, an embodiment of the present invention provides an undirected graph task scheduling device applied to an edge-end collaborative network. The device includes:

[0089] A modeling module, configured to perform time period modeling, edge-cloud collaborative service topology modeling, undirected graph task modeling, V2V and V2I communication modeling, undirected graph task completion time modeling, and energy cost modeling for the edge-cloud collaborative network, so as to obtain a time period model, an edge-cloud collaborative service topology model, an undirected graph task model, a V2V and V2I communication model, an undirected graph task completion time model, and an energy cost model;

[0090] The modeling module is further configured to, based on the time period model, the edge-cloud collaborative service topology model, the undirected graph task model, the V2V and V2I communication model, the undirected graph task completion time model, and the energy cost model, model the undirected graph task scheduling problem of the edge-cloud collaborative network, so as to obtain an undirected graph task scheduling optimization model, whose optimization objective is to minimize the undirected graph task completion time under a specific energy budget;

[0091] A solving module, configured to use the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-objectives, and on this basis, use an undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model.

[0092] In a third aspect, an embodiment of the present invention provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor, so that the at least one processor can execute the method as described above.

[0093] In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium storing computer instructions, and the computer instructions are used to cause a computer to execute the method as described above.

[0094] Compared with the prior art, the present invention has at least the following technical effects:

[0095] In view of the dynamics and uncertainties of the edge-cloud collaborative network, the present invention constructs an undirected graph task scheduling optimization model with the optimization objective of minimizing the undirected graph task completion time under a specific energy budget, then uses the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-objectives, and on this basis, uses an undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model, realizing the optimization of the undirected graph task scheduling. In this way, the undirected graph task scheduling efficiency and resource utilization rate in the edge-cloud collaborative network can be effectively improved, and it is applicable to various dynamic and uncertain scenarios.

[0096] It should be understood that the content described in the Summary of the Invention section is not intended to limit the key or important features of the embodiments of the present invention, nor to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In conjunction with the accompanying drawings and with reference to the following detailed description, the above and other features, advantages, and aspects of the embodiments of the present invention will become more apparent. The drawings are used to better understand the present invention and do not constitute a limitation to the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements, where:

[0098] Figure 1 is a flowchart of an undirected graph task scheduling method applied to an edge-cloud collaborative network provided by an embodiment of the present invention;

[0099] Figure 2 is a structural diagram of an undirected graph task scheduling device applied to an edge-cloud collaborative network provided by an embodiment of the present invention;

[0100] Figure 3 is a structural diagram of an exemplary electronic device capable of implementing the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0101] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0102] In addition, the term "and / or" in the present invention is merely a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in the present invention generally represents an "or" relationship between the associated objects before and after.

[0103] To solve the technical problems presented in the background art, embodiments of the present invention provide an undirected graph task scheduling method, device, equipment, and storage medium applied to an edge-cloud collaborative network. Below, with reference to the accompanying drawings, a detailed description of an undirected graph task scheduling method, device, equipment, and storage medium applied to an edge-cloud collaborative network provided by embodiments of the present invention will be given through specific embodiments.

[0104] Figure 1 is a flowchart of an undirected graph task scheduling method applied to an edge-cloud collaborative network provided by an embodiment of the present invention, asFigure 1 As shown in Figure 1 , the undirected graph task scheduling method 100 may include:

[0105] S110, perform time period modeling, edge-cloud collaborative service topology modeling, undirected graph task modeling, V2V and V2I communication modeling, undirected graph task completion time modeling, and energy cost modeling for the edge-cloud collaborative network to obtain a time period model, an edge-cloud collaborative service topology model, an undirected graph task model, a V2V and V2I communication model, an undirected graph task completion time model, and an energy cost model.

[0106] S120, based on the time period model, the edge-cloud collaborative service topology model, the undirected graph task model, the V2V and V2I communication model, the undirected graph task completion time model, and the energy cost model, model the undirected graph task scheduling problem of the edge-cloud collaborative network to obtain an undirected graph task scheduling optimization model, whose optimization objective is to minimize the undirected graph task completion time under a specific energy budget.

[0107] S130, use the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-goals, and on this basis, use an undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model.

[0108] For the convenience of further understanding, the above steps will be described in detail below in combination with specific embodiments:

[0109] (1) Edge-cloud collaborative network modeling

[0110] (1.1) Time period modeling

[0111] To facilitate the analysis while describing the dynamic and uncertain characteristics of the edge-cloud collaborative network (VECN), use {1,..., τ,..., τ *} to represent multiple time periods with different durations. At the beginning of each time period, multiple undirected graph tasks will arrive. At the same time, the edge server (ES) will check the available computing resources and the undirected graph task buffer within its coverage area, and further coordinate the undirected graph task scheduling process.

[0112] (1.2) Edge-cloud collaborative service topology modeling

[0113] Model the edge-cloud collaborative service topology (VECC) as an undirected graph task (UWG) within the time period τ, using to represent. Among them, the vertex set represents the servers (edge servers and vehicles with available resources within their coverage areas) within the time period τ. Further, use to represent the edge server within the time period τ, and the moving vehicle As a mobile server, at this time In addition, the server has an attribute to quantify its computing power. The edge set represents the available connections between different servers within the time period τ. For example,[[]] and (k≠k′) are within each other's communication range. Each edge contains an attribute representing the contact duration between servers, thus encapsulating the time dynamics of the interaction between servers within the edge-side collaborative network.[[]]

[0114] (1.3) Undirected graph task modeling

[0115] At the beginning of each time period τ, the edge server acting as the coordinator checks the current undirected graph task buffer, denoted as buffer Q <τ> Each element in represents an undirected graph task, using to represent, where respectively represent the set of undirected graph task components and the edges between undirected graph task components. Each undirected graph task component is described by the tuple( where represents the size of the data to be processed, represents the tolerable time to complete. Each edge between two undirected graph task components is assigned a weight characterizing the minimum required connection time associated with it, that is, the contact duration between the two servers processing the two connected undirected graph task components should be greater than or equal to to support the intermediate data exchange required during the execution of the undirected graph task. Since the undirected graph task components can be processed in parallel on different servers, depends on the completion time of the undirected graph task component that is completed first, that is, where represents the completion time of the undirected graph task component on the server and represents the completion time of the undirected graph task component on the server .

[0116] (1.4) V2V and V2I communication modeling

[0117] Using and respectively represent the vehicle, that is, the mobile server The speed and relative position at a certain moment, where k≠1. For the edge server, let Since the duration of the time period is relatively short, the speed of each vehicle at each moment can be regarded as a constant speed. In addition, the communication radii of the edge server and the vehicle are represented as and respectively.

[0118] For the vehicles within the coverage range of the edge server during the time period τ, the remaining residence time for the vehicles to interact with the edge server through a one-hop V2I communication link is represented as the V2V communication duration

[0119]

[0120] When two vehicles and are within the corresponding signal coverage ranges of each other, a contact event occurs, and the connection duration between the two vehicles and traveling in the same direction is calculated

[0121]

[0122] (1.5) Modeling of the undirected graph task completion time

[0123] Use To represent the allocation relationship between the undirected graph task component And the server Among them, Represents the undirected graph task component Is processed on the server , otherwise it is 0. Use To represent the undirected graph task scheduling strategy during the time period τ, where i∈{1, 2, …, |Q <τ> |}. At the same time, use To represent the scheduling decision matrix corresponding to the time period τ. In addition, use To represent the data transmission rate from the edge server to the vehicle during the time period τ. Based on this, the data transmission time Required to transmit the relevant data from the edge server to the undirected graph task execution server is expressed as:

[0124]

[0125] Then, when the undirected graph task component Is processed on the server , the execution time Is expressed as:

[0126]

[0127] Among them, z represents the computing intensity.

[0128] Since the amount of data transmitted is small, the delay of result feedback is ignored here. Therefore, the completion time of the undirected graph task component is determined by the sum of the data transmission time and the execution time, that is:

[0129]

[0130] It can be seen that the overall completion time of the undirected graph task depends on the last completed undirected graph task component, which is defined as: where \(i\in\{1, 2, \ldots, |Q|\}\). At the same time, the total execution time consumed by all undirected graph tasks within the time period \(\tau\) <τ> is expressed as:

[0131]

[0132] (1.6) Energy cost modeling

[0133] The energy required to transfer the data volume of the undirected graph task component from the edge server to the vehicle is expressed as:

[0134]

[0135] where \(p\) <τ> represents the transmission power of the edge server; in addition, the server processing the undirected graph task component the energy consumed is expressed as:

[0136]

[0137] where \(\gamma\) represents the energy cost coefficient.

[0138] Since the amount of data shared by the two servers processing the connected undirected graph task components during parallel computing is uncertain, the energy generated by data exchange is ignored here. Therefore, the energy cost generated by executing the undirected graph task component on the server is expressed as:

[0139]

[0140] Furthermore, the total energy cost of processing the undirected graph task is expressed as:

[0141]

[0142] Using to represent the total energy cost consumed by all undirected graph tasks within the time period \(\tau\).

[0143] (2) Modeling of the undirected graph task scheduling problem

[0144] Considering the structure of the graph task and the edge-side collaborative service topology, the key to undirected graph task scheduling is to minimize the task completion time under a specific energy budget from a long-term perspective. Therefore, the optimization objective of the undirected graph task scheduling optimization model can be expressed as:

[0145]

[0146] Subject to the following constraints:

[0147] Constraint C1:

[0148] Constraint C2:

[0149] Constraint C3:

[0150] Constraint C4:

[0152] Constraint C5:

[0153] Among them, Constraint C1 is used to ensure that each undirected graph task can only be assigned to one server; Constraint C2 is used to ensure that each undirected graph task component is completed on time; and Constraint C3 is used to support data exchange between two servers processing connected undirected graph task components; Constraint C4 is used to ensure that in each VECC, each vehicle is within the communication range of the edge server during time period t; Constraint C5 is an energy cost constraint from a long-term perspective, aiming to maintain the stability of energy throughout the scheduling process, where is the average energy consumption of task scheduling from a long-term perspective, that is, the average energy budget.

[0154] (3) Solving the undirected graph task scheduling optimization model

[0155] (3.1) Lyapunov optimization framework

[0156] Using the Lyapunov optimization framework, the optimization objective of the undirected graph task scheduling optimization model is decomposed into a series of deterministic sub-goals, as follows:

[0157] First, use to represent the buffer of newly arrived undirected graph tasks during time period τ, and assume that the average arrival rate is λ, denoted as Meanwhile, use to represent the undirected graph tasks that have been successfully scheduled during time period τ. Based on this, we have:

[0158]

[0159] Here, \(Q\) <τ+1> is regarded as the true queue within time period \(\tau + 1\), and \(Q\) <τ> is regarded as the true queue within time period \(\tau\).

[0160] To solve the average energy constraint, that is, constraint C5, a virtual buffer, namely a virtual queue is introduced here to capture the deviation of the total energy cost. By monitoring this virtual queue, it aims to ensure that the energy constraint is satisfied in the long term while allowing a certain degree of flexibility within a single time period. Specifically, the update of the virtual queue is expressed as:

[0161]

[0162] Here, is regarded as the virtual queue (queue of energy consumption) within time period \(\tau + 1\), and is regarded as the virtual queue within time period \(\tau\); and represent the energy consumption and energy budget within time period \(\tau\) respectively.

[0163] The average energy budget is expressed as:

[0164]

[0165] The average energy budget represents the cumulative energy allocated until time period \(\tau\) * and is used as a comparison benchmark for the total energy consumption. Based on this formula, it is possible to strictly evaluate whether the energy consumption remains within an acceptable range over time, thus ensuring the stability and feasibility of the proposed network. Intuitively, when the virtual queue is stable, the total energy consumption does not exceed guaranteeing that constraint C5 is satisfied and maintaining compliance with long-term energy conservation.

[0166] Then, the Lyapunov function and the Lyapunov drift are expressed as follows:

[0167]

[0168] The drift-plus-penalty function is adopted to minimize the undirected graph task completion time and stabilize \(Q\) <τ> and as shown specifically below:

[0169]

[0170] where, Denotes the Lyapunov drift, which is used to measure the expected backlog of different queues over time. Denotes the expected task completion delay given the current states of different queues; the parameter V is a non - negative control coefficient used to balance the trade - off between queue stability and time efficiency.

[0171] Derive the upper bound of the drift - plus - penalty function. First, represent the squared value of the queue update as:

[0172]

[0173] By summing both sides, we get:

[0174]

[0175] Then, based on this, derive the Lyapunov drift as:

[0176]

[0177] where the constants B1 and B2 are as follows:

[0178]

[0179] Let We can obtain that The upper bound of is:

[0180]

[0181] Based on this, the drift - plus - penalty function is expressed as:

[0182]

[0183] On this basis, to minimize the drift - plus - penalty function, the optimization objective is decomposed into deterministic sub - objectives for each time period τ, which are expressed as follows:

[0184]

[0185] According to The upper bound of, transform the optimization objective into:

[0186]

[0187] Subject to the following constraints:

[0188] Constraint C1 to Constraint C4;

[0189] Constraint C6:

[0190] Constraint C7:

[0191] Constraint C6 is used to ensure that the number of tasks processed within a time period does not exceed the total number of tasks; Constraint C7 is used to ensure that the energy consumption within time period τ is non - negative.

[0192] (3.2) Undirected Graph Task Scheduling Algorithm

[0193] The present invention proposes a lightweight algorithm - Lightweight algorithm. This algorithm provides an approximately optimal offloading decision for the edge server within each time period, and can optimize the long - term average system benefit while ensuring that the constraints are met. In addition, the Lightweight algorithm can effectively balance between benefit and service, and the energy double - queue. During this process, the algorithm not only tries to shorten the task completion time, but also maintains reasonable control of the queue length. In the long - term operation, the Lightweight algorithm not only effectively reduces the task completion delay, but also ensures that the constraints are met and maintains the stability of the service queue.

[0194] Specifically, the Lightweight algorithm optimizes and solves the undirected graph task scheduling optimization model through the following steps:

[0195] First, the transformed optimization objective, also known as the optimization objective for a fixed time period, is converted into an optimization objective based on logical time periods to adapt to the dynamic undirected graph task scheduling requirements.

[0196] Second, the undirected graph task queue is sorted by priority, and the undirected graph tasks with a higher degree of urgency are scheduled first.

[0197] Finally, the merge pruning strategy - backtracking greedy scheduling strategy is used to find a feasible near - optimal solution to achieve the final optimization objective.

[0198] (3.2.1) Optimization Objective of Logical Time Period

[0199] Refer to Section (3.1). Through Lyapunov optimization, the long-term optimization goal is decoupled into a series of independent sub-problems related to fixed time periods. Since undirected graph task scheduling involves multiple sub-tasks and there is a certain topological structure among these sub-tasks, it takes a certain amount of time to find a feasible solution for each scheduling decision. Therefore, when the time period τ is fixed, there may be a situation where some tasks have not found a feasible solution by the end of the time period τ. This phenomenon indicates that the solution time of undirected graph task scheduling is closely related to the task scale and topological structure, and the determination of the time period length becomes a key challenge. To address this issue, this paper proposes a strategy for dynamically adjusting the time period length. The core idea of this strategy is to flexibly adjust the time period length according to the solution progress of the current task scheduling, thereby effectively controlling the decision-making solution process and ensuring that each undirected graph task can complete the scheduling decision within an appropriate time. Specifically, the algorithm regards each task scheduling as a "logical time period", so that the length of the time period τ can vary dynamically according to the actual situation. This transformation not only optimizes the optimization goal under a fixed time period but also converts it into a dynamic optimization model based on the logical time period.

[0200] Through this transformation, the transformed optimization goal in Section (3.1) can be rewritten as an optimization goal based on the logical time period:

[0201]

[0202] Among them, considering that within each logical time period, after the task scheduling decision is executed, the task queue only decreases by one task, that is This optimization goal is further simplified to:

[0203]

[0204] This optimization goal effectively balances the task completion time, resource consumption, and queue stability, and can achieve the optimal solution of undirected graph task scheduling in a dynamic environment.

[0205] (3.2.2) Priority sorting of the undirected graph task queue

[0206] In the undirected graph task queue, the scheduling of each undirected graph task is affected by the completion of the previous undirected graph task. Therefore, when an undirected graph task is added to the undirected graph task queue, it must wait for the scheduling decision of the previous undirected graph task to be generated (i.e., the resource status is updated) before it can make a scheduling decision. It should be after the scheduling is completed rather than after the undirected graph task is completed. Due to the tolerance completion times of different undirected graph tasks and the different waiting times in the undirected graph task queue, the urgency of the undirected graph tasks also changes accordingly. Therefore, in order to ensure that the undirected graph tasks can be executed within their specified completion times, a backup decision scheme is designed here.

[0207] Specifically, when the undirected graph task scheduling fails or the waiting time is too long, the undirected graph task is completely offloaded to the edge server for local execution to ensure that the task is completed on time. To achieve this goal, the rounds are divided according to logical time periods. Before the start of each logical time period, the edge server first updates the current VECC and evaluates the computing capabilities of different servers.

[0208] Suppose that in the logical time period τ, the computing capability that the edge server can allocate for task calculation is Then the undirected graph task The task completion time on the edge server Can be expressed as:

[0209]

[0210] Based on this, the remaining waiting time of the undirected graph task can be deduced from the task completion time of the alternative plan.

[0211]

[0212] Among them, the remaining waiting scheduling time of the undirected graph task The shorter it is, the more urgent the task is and the higher its priority. Therefore, the undirected graph task queue can be sorted according to the remaining waiting time of each undirected graph task. The remaining waiting time The smaller it is, the higher the priority of the undirected graph task. Based on this, a sorted undirected graph task queue can be obtained. In each logical time period, the undirected graph task with the shortest remaining waiting time is scheduled first to achieve the optimal undirected graph task scheduling order.

[0213] (3.2.3) Merge Pruning Strategy - Backtracking Greedy Scheduling Strategy

[0214] Merge Pruning Strategy: This strategy is used for the preprocessing of undirected graph tasks. It aims to reduce the number of subtask nodes and edges to be considered in the subsequent stage by merging and pruning, thereby reducing the dimension of the task and the complexity of the matching server decision. Through this step, the computing burden can be effectively reduced, providing simpler input data for subsequent scheduling.

[0215] Backtracking Greedy Scheduling Strategy: This strategy is used to find a feasible mapping between the undirected graph task and the VECC using the backtracking algorithm under the premise of meeting the constraint conditions and the subgraph isomorphism conditions. The backtracking process ensures the satisfaction of all constraint conditions when looking for the mapping, while minimizing the optimization goal of the logical time period through the greedy strategy. Specifically, the backtracking algorithm is responsible for exploring the feasible mapping space, and the greedy algorithm selects the local optimal solution at each step, thus effectively optimizing the overall goal.

[0216] Through these two strategies, a near-optimal feasible mapping can be found while satisfying subgraph isomorphism and constraint conditions. Next, the specific implementation process of the above strategies will be introduced in detail.

[0217] Phase 1. Merging and pruning of undirected graph task sub-nodes:

[0218] Considering that the computing power and resource supply of edge servers are usually better than those of mobile vehicles, in order to balance the completion time of subtasks and avoid waste of computing resources, it is assumed that edge servers can process multiple subtasks in parallel. Specifically, let N be the number of subtasks that the edge server can process in parallel during the time period τ. To balance the gap in subtask completion time as much as possible and avoid idle waste of computing resources, the value of N can be calculated by the following formula:

[0219]

[0220] where k > 1 represents the mobile vehicle. After determining the value of N, by merging some nodes in the undirected graph task and pruning its edges, the scale of the undirected graph task can be effectively reduced and the complexity of subsequent scheduling calculations can be lowered. This process mainly includes the following two steps:

[0221] Step 1. Subtask node merging

[0222] First, determine the value of N according to the computing power of the servers in the VECC, that is, the number of subtasks that the edge server can process simultaneously. Since the structural constraint conditions in the execution of the undirected graph task have strict requirements on the connections between computing nodes, the degree of sub-nodes in the undirected graph task plays a key role in determining the complexity of finding a feasible mapping. Therefore, here it is inclined to merge nodes with larger degrees into a virtual node and unload this virtual node to an edge server with stronger computing power for calculation. The specific steps are as follows:

[0223] 1) Collect the degree information of all nodes in the undirected graph task, and mark the node with the highest degree as

[0224] 2) Merge with the node with the highest degree among its neighbor nodes, and repeat this operation N - 1 times.

[0225] After these operations, a virtual task node containing N subtask nodes will be finally obtained This node will be unloaded to the edge server for task calculation. Through this step, the original task graph is transformed into a simplified graph whose number of nodes decreases from to

[0226] Step 2. Edge pruning

[0227] After the virtual task nodes are assigned to the edge servers, considering that there is a channel connection between each edge server and any moving vehicle in the VECC, and the mapped virtual task nodes satisfy the edge constraint conditions between subtasks. Therefore, in the subsequent task scheduling process, the connection relationship between the virtual task nodes and other nodes can be ignored. Based on this condition, all the edges connected to can be pruned, that is, these edges are removed from the undirected graph task to generate a new simplified undirected graph task The number of edges in this undirected graph task is significantly less. The pruned undirected graph task becomes a non-fully connected graph, which is actually composed of multiple smaller fully connected subgraphs. To further optimize the scheduling process, we sort the number of subtasks in each subgraph in non-increasing order and arrange all the subgraphs into a list according to the number of subtasks The logic behind this sorting is that subgraphs with more subtasks usually have a more complex topological structure and higher requirements for the stability of connections between subtasks. Especially when moving vehicles are used as computing nodes, this requirement for stability is even more stringent. Therefore, in the scheduling process, those subgraphs with more subtasks are given priority to ensure the efficiency and stability of task scheduling.

[0228] Phase 2. Backtracking greedy scheduling

[0229] In this phase, mainly rely on the backtracking algorithm to find a feasible task scheduling matching scheme. Specifically, at each level of backtracking, select those service nodes that tend to minimize the time slot optimization objective according to the greedy strategy, gradually construct possible matching relationships until a feasible matching scheme that satisfies all constraints is found. Through this process, the algorithm will finally obtain a valid mapping This mapping is used for the scheduling of graph tasks. This mapping not only satisfies the constraint conditions of task scheduling but also optimizes the system performance under a given time period.

[0230] (3.2.4) Backup scheduling scheme

[0231] Specifically, when the undirected graph task scheduling fails or the waiting time of the undirected graph task is too long, in order to ensure that the undirected graph task can be completed on time, a strategy of completely offloading the undirected graph task to the edge server for local execution is adopted. Specifically, when the remaining waiting time of the undirected graph task or no feasible solution is found, the undirected graph task It will be retained on the edge server for computing. This alternative ensures that the undirected graph task can be completed within the specified time, avoiding task loss or timeout caused by scheduling failure or excessive delay.

[0232] In summary, the present invention has at least achieved the following technical effects:

[0233] In view of the dynamics and uncertainties of the edge-cloud collaborative network, the present invention constructs an optimization model for undirected graph task scheduling with the optimization goal of minimizing the completion time of undirected graph tasks under a specific energy budget. Then, the Lyapunov optimization framework is used to decompose the optimization goal of the undirected graph task scheduling optimization model into a series of deterministic sub-goals. On this basis, an undirected graph task scheduling algorithm is adopted to optimize and solve the undirected graph task scheduling optimization model, realizing the optimization of undirected graph task scheduling. In this way, the scheduling efficiency of undirected graph tasks and resource utilization in the edge-cloud collaborative network can be effectively improved, and it is applicable to various dynamic and uncertain scenarios.

[0234] It should be noted that for the foregoing method embodiments, for the sake of simple description, they are all expressed as a series of action combinations. However, those skilled in the art should know that the present invention is not limited by the described action sequence, because according to the present invention, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0235] The above is the introduction of the method embodiments. The following further illustrates the solution of the present invention through device embodiments.

[0236] Figure 2 The following is a structural diagram of an undirected graph task scheduling device provided for an embodiment of the present invention. As Figure 2 shown, the undirected graph task scheduling device 200 may include:

[0237] A modeling module 210, configured to perform modeling on time periods, edge-cloud collaborative service topologies, undirected graph tasks, V2V and V2I communications, undirected graph task completion times, and energy costs for the edge-cloud collaborative network, to obtain a time period model, an edge-cloud collaborative service topology model, an undirected graph task model, a V2V and V2I communication model, an undirected graph task completion time model, and an energy cost model;

[0238] The modeling module 210 is further configured to model the undirected graph task scheduling problem of the edge-cloud collaborative network based on the time period model, the edge-cloud collaborative service topology model, the undirected graph task model, the V2V and V2I communication models, the undirected graph task completion time model, and the energy cost model, so as to obtain an undirected graph task scheduling optimization model, and its optimization objective is to minimize the undirected graph task completion time under a specific energy budget;

[0239] The solving module 220 is configured to use the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-goals, and on this basis, use the undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model.

[0240] It can be understood that Figure 2 each module / unit in the undirected graph task scheduling device 200 shown has the function of implementing Figure 1 each step in the undirected graph task scheduling method 100 shown, and can achieve its corresponding technical effects. For the sake of brevity, it will not be elaborated here.

[0241] Figure 3 It is a structural diagram of an exemplary electronic device capable of implementing the embodiments of the present invention. The electronic device 300 is intended to represent various forms of digital computers, such as, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device 300 can also represent various forms of mobile devices, such as, personal digital processors, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown in the present invention, their connections and relationships, and their functions are only examples and are not intended to limit the implementation of the present invention described and / or claimed in the present invention.

[0242] As Figure 3 shown, the electronic device 300 may include a computing unit 301, which can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 302 or the computer program loaded from the storage unit 308 into the random access memory (RAM) 303. In the RAM 303, various programs and data required for the operation of the electronic device 300 can also be stored. The computing unit 301, the ROM 302, and the RAM 303 are connected to each other through a bus 304. The input / output (I / O) interface 305 is also connected to the bus 304.

[0243] Multiple components in the electronic device 300 are connected to the I / O interface 305, including: an input unit 306, such as a keyboard, a mouse, etc.; an output unit 307, such as various types of displays, speakers, etc.; a storage unit 308, such as a magnetic disk, an optical disc, etc.; and a communication unit 309, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 309 allows the electronic device 300 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks.

[0244] The computing unit 301 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 301 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 301 executes the various methods and processes described above, such as method 100. For example, in some embodiments, method 100 can be implemented as a computer program product, including a computer program, which is tangibly contained in a computer-readable medium, such as the storage unit 308. In some embodiments, part or all of the computer program can be loaded and / or installed onto the electronic device 300 via the ROM 302 and / or the communication unit 309. When the computer program is loaded into the RAM 303 and executed by the computing unit 301, one or more steps of the method 100 described above can be executed. Alternatively, in other embodiments, the computing unit 301 can be configured to execute method 100 in any other suitable manner (e.g., by means of firmware).

[0245] The various embodiments described above in the present invention can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include: being implemented in one or more computer programs, which can be executed and / or interpreted on a programmable system including at least one programmable processor, and the programmable processor can be a dedicated or general-purpose programmable processor, which can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit the data and instructions to the storage system, the at least one input device, and the at least one output device.

[0246] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to the processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing devices, such that when the program codes are executed by the processor or controller, the functions / operations specified in the flowchart and / or block diagram are implemented. The program codes can be executed entirely on the machine, partially on the machine, executed partially on the machine and partially on a remote machine as an independent software package, or executed entirely on a remote machine or server.

[0247] In the context of the present invention, a computer-readable medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of a computer-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0248] It should be noted that the present invention also provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause a computer to execute method 100 and achieve the corresponding technical effects achieved by the method of the embodiments of the present invention. For the sake of brevity of description, it will not be elaborated herein.

[0249] In addition, the present invention also provides a computer program product, which includes a computer program that implements method 100 when executed by a processor.

[0250] It should be understood that various forms of the flow shown above can be used, reordering, adding, or deleting steps. For example, the steps recited in the present invention can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present invention can be achieved. The present invention is not limited herein.

[0251] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An undirected graph task scheduling method applied to an edge-cloud collaborative network, characterized in that The method includes: Performing time period modeling, edge-cloud collaborative service topology modeling, undirected graph task modeling, V2V and V2I communication modeling, undirected graph task completion time modeling, and energy cost modeling for the edge-cloud collaborative network to obtain a time period model, an edge-cloud collaborative service topology model, an undirected graph task model, a V2V and V2I communication model, an undirected graph task completion time model, and an energy cost model; Based on the time period model, the edge-cloud collaborative service topology model, the undirected graph task model, the V2V and V2I communication model, the undirected graph task completion time model, and the energy cost model, modeling the undirected graph task scheduling problem of the edge-cloud collaborative network to obtain an undirected graph task scheduling optimization model, whose optimization objective is to minimize the undirected graph task completion time under a specific energy budget; Using the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-goals, and on this basis, using an undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model.

2. The method according to claim 1, wherein The time period modeling includes: Use {1, … τ, …, τ *} to represent multiple time periods of different durations; at the beginning of each time period, multiple undirected graph tasks will arrive. Meanwhile, the edge server will check the available computing resources and the undirected graph task buffer within its coverage area, and further coordinate the undirected graph task scheduling process.

3. The method according to claim 2, characterized in that The edge-cloud collaborative service topology modeling includes: Model the edge-cloud collaborative service topology as an undirected graph task within a time period τ, using to represent; among which, the vertex set represents the servers within the time period τ. Further, use to represent the edge servers within the time period τ, and consider the moving vehicles as mobile servers. At this time In addition, the server has the attribute to quantify its computing power; the edge set represents the available connections between different servers within the time period τ. Each edge contains the attribute to represent the contact duration between servers, thus encapsulating the time dynamics of the interactions between servers in the edge-cloud collaborative network.

4. The method according to claim 3, wherein The undirected graph task modeling includes: At the beginning of each time period τ, the edge server acting as the coordinator checks the current undirected graph task buffer, denoted as buffer Q <τ> for each element in which represents an undirected graph task, using to denote, where represent the set of undirected graph task components and the edges between undirected graph task components respectively; each undirected graph task component is described by meta where represents the size of the data to be processed, represents the tolerable time to complete; each edge between two undirected graph task components is assigned a weight characterizing the minimum required connection time associated with it, that is, the contact duration between the two servers processing the two connected undirected graph task components should be greater than or equal to to support the intermediate data exchange required during the execution of the undirected graph task; since the undirected graph task components are processed in parallel on different servers, depends on the completion time of the undirected graph task component that is completed first, that is, where represents the undirected graph task component on server 's completion time, represents the undirected graph task component on server 's completion time.

5. The method according to claim 4, wherein The V2V and V2I communication modeling includes: Use and represent the speed and relative position of the vehicle, i.e., the mobile server, at a certain moment, where k≠1; for the edge server, let regard the speed of each vehicle at each moment as a constant speed; in addition, the communication radii of the edge server and the vehicle are represented as and respectively; For vehicles within the coverage area of the edge server during the time period τ, the remaining sojourn time for the vehicle to interact with the edge server through a one-hop V2I communication link is denoted as the V2V communication duration When two vehicles are within the corresponding signal coverage ranges of each other, a contact event occurs, and the connection duration between the two vehicles traveling in the same direction is calculated.

6. The method according to claim 5, characterized in that, The undirected graph task completion time modeling includes: Usage Indicates the allocation relationship between the undirected graph task component and the server during the time period τ, where Indicates the undirected graph task component is processed on the server , otherwise it is 0; Usage Indicates the undirected graph task scheduling policy during the time period τ, where i ∈ {1, 2, …, |Q <τ> |}; At the same time, Usage Indicates the scheduling decision matrix corresponding to the time period τ; In addition, Usage Indicates the data transmission rate from the edge server to the vehicle during the time period τ; Based on this, the data transmission time required to transmit the relevant data from the edge server to the undirected graph task execution server is expressed as: Then, when the undirected graph task component is processed on the server the execution time is expressed as: Among them, z represents the computing intensity; Completion time of the undirected graph task component Determined by the sum of the data transfer time and the execution time, i.e.: The overall completion time of the undirected graph task Depends on the last completed undirected graph task component and is defined as: where i ∈ {1, 2, …, |Q <τ> |}; meanwhile, the total execution time consumed by all undirected graph tasks within the time period τ Is expressed as:

7. The method according to claim 6, characterized in that, The energy cost modeling includes: The energy consumed to transfer the data volume of the undirected graph task component from the edge server to the vehicle is expressed as: Among them, p <τ> represents the transmission power of the edge server; in addition, the server processing the undirected graph task component the energy consumed is expressed as: Among them, γ represents the energy cost coefficient; The energy cost generated by executing the undirected graph task component on the server is expressed as: Total energy cost for processing undirected graph tasks Expressed as: Usage Indicates the total energy cost consumed by all undirected graph tasks within the time period τ.

8. The method according to claim 7, characterized in that, The optimization objective of the undirected graph task scheduling optimization model is expressed as: Subject to the following constraint conditions: Constraint C1: Constraint C2: Constraint C3: Constraint C4: Constraint C5: Among them, represents the average energy budget.

9. The method according to claim 8, characterized in that, Using the Lyapunov optimization framework to decompose the optimization objective of the undirected graph task scheduling optimization model into a series of deterministic sub-goals, including: First, use to represent the buffer of newly arrived undirected graph tasks within the time period τ, and assume that the average arrival rate is λ, denoted as Use to represent the successfully scheduled undirected graph tasks within the time period τ. Based on this, we have: Here, Q is regarded as the true queue within the time period τ + 1, and Q <τ+1> is regarded as the true queue within the time period τ; <τ> ​ Introduce a virtual buffer, namely a virtual queue to capture the deviation of the total energy cost. Specifically, the update of the virtual queue is expressed as: This is regarded as the virtual queue within time period τ + 1, and is regarded as the virtual queue within time period τ; and respectively represent the energy consumption and energy budget within time period τ; Express the average energy budget as: Average energy budget represents the cumulative energy allocated up to time period τ * and serves as a comparison benchmark for the total energy consumption; Then, introduce the Lyapunov function and the Lyapunov drift which are expressed as follows: Use drift plus penalty function to minimize the undirected graph task completion time and stabilize Q <τ> and Specifically as follows: Among them, represents the Lyapunov drift, which is used to measure the expected backlog of different queues over time, represents the expected task completion delay given the current states of different queues; the parameter V is a non - negative control coefficient used to balance the trade - off between queue stability and time efficiency; Deriving the upper bound of the drift-plus-penalty function. First, expressing the square value of the queue update as: By summing both sides, we get: Then, based on this, deriving the Lyapunov drift as: Where the constants B1 and B2 are as follows: Let It can be obtained that The upper bound of Based on this, the drift-plus-penalty function is expressed as: On this basis, decomposing the optimization objective into deterministic sub-goals for each time period τ, expressed as follows: According to the upper bound of, the optimization objective is converted to: Subject to the following constraint conditions: Constraint conditions C1 to constraint condition C4; Constraint C6: Constraint C7:

10. The method according to claim 9, wherein Using an undirected graph task scheduling algorithm to optimize and solve the undirected graph task scheduling optimization model, including: Converting the transformed optimization objective (also known as the optimization objective for a fixed time period) into an optimization objective based on logical time periods to adapt to the dynamically changing undirected graph task scheduling requirements; performing priority sorting on the undirected graph task queue and preferentially scheduling undirected graph tasks with a higher degree of urgency; using a merge pruning strategy - a backtracking greedy scheduling strategy to find a feasible near-optimal solution to achieve the final optimization objective.

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