A lyapunov optimization-based crowd-sensing task matching method

Abstract

The application discloses a kind of crowd-sourcing perception task matching methods based on Lyapunov optimization, including the following steps: information collection: at the beginning of each period, platform collects task information and perception device information, task publisher and perception device update own information to scheduling platform in time;Matching benefit calculation: the concept of matching benefit of task and device is introduced, then platform calculates the matching benefit between task demand and different devices;Matching scheme modeling: long-term task matching benefit objective function is established, and corresponding constraint conditions are set according to spatial position, energy constraint, perception device hardware constraint and other factors;Problem transformation: according to Lyapunov optimization theory, the optimization objective function is transformed into the problem of minimizing the upper bound of Lyapunov drift;Problem solving: the matching scheme is obtained by solving the problem based on the minimum weight maximum flow algorithm, and the perception command is sent to the corresponding perception device.

Description

Technical Field

[0001] This invention belongs to the field of task matching mechanism for crowd sensing, and specifically relates to a crowd sensing task matching method based on Lyapunov optimization. Background Technology

[0002] With the advancement of mobile devices and their powerful sensing capabilities, a promising sensing paradigm, mobile crowdsensing (MCS), has received considerable attention in recent research. Roughly speaking, an MCS refers to a group of mobile devices performing sensing tasks through sensors equipped within them. In this context, many attractive mobile applications, such as traffic prediction, environmental monitoring, healthcare, and indoor positioning, can be implemented using MCS with very high quality and low cost. Despite its enormous potential, mobile users in an MCS are often reluctant to provide services to others. Therefore, the success of MCS applications is closely related to the recruitment of appropriate mobile devices / participants within the system. Current research has two shortcomings:

[0003] 1. Existing work mainly focuses on optimizing perceived quality, social welfare, or minimizing crowd sensing / participation costs, while neglecting the urgent need to complete the task. For example, in the study of quality-aware sensing coverage in budget-constrained mobile crowd sensing networks (M. Zhang, P. Yang, C. Tian, ​​S. Tang, X. Gao, B. Wang, F. Xiao, “Quality-Aware Sensing Coverage in Budget-Constrained Mobile Crowdsensing Networks,” in IEEE Transactions on Vehicular Technology, vol. 65, no. 9, pp. 7698–7707, Sept. 2016.), a participant selection algorithm was proposed to achieve optimal quality-aware coverage within budget constraints. Furthermore, in the study of robust task assignment for mobile crowd sensing systems (L. Wang, Z. Yu, K. Wu, D. Yang, E. Wang, T. Wang, Y. Mei, B. Guo, “Towards Robust Task Assignment in Mobile Crowdsensing Systems,” in IEEE Transactions on Mobile…), a participant selection algorithm was proposed to achieve optimal quality-aware coverage within budget constraints. The work allocation in *Computing*, vol. 22, no. 7, pp. 4297–4313, Jul. 2023., achieves robustness of crowdsensing task allocation schemes while minimizing detour costs for participants; the mobile device crowdsourcing incentive mechanism (D. Yang, G. Xue, X. Fang and J. Tang, “Incentive mechanisms for crowdsensing:crowdsourcing with smartphones,” IEEE / ACM Transactions on Networking, vol. 24, no. 3, pp. 1732–1744, Jun. 2016.) designs an incentive mechanism to motivate mobile users participating in MCS; the information perception quality incentive mechanism for mobile crowd sensing systems (H. Jin, L. Su, D. Chen, K. Nahrstedt, and J.Xu, “Quality of information-aware incentive mechanisms for mobile crowdsensing systems,” in Proceedings of the 16th ACM International Symposium on Mobile AdHoc Networking and Computing (MobiHoc), pp. 167–176, Hangzhou, China, Jun. 2015, proposes a real auction mechanism under the premise of dynamic intelligent devices and random task arrival. None of the above studies have considered the urgency of task completion time.

[0004] 2. Considering that the matching effectiveness between smart devices and tasks varies due to factors such as task requirements, hardware capabilities, and environmental conditions, and these factors may change over time, it is necessary to pay attention to the matching effectiveness between tasks and devices, and to promptly reallocate tasks to the most suitable devices in each time slot. Traditional task allocation mechanisms, however, do not consider subsequent matching effects after matching a task to a smart device. For example, the demand-driven dynamic incentive mechanism (J.Hu, Z.Wang, J.Wei, R.Lv, J.Zhao, Q.Wang, H.Chen and D.Yang, “Towards Demand-Driven Dynamic Incentive for Mobile Crowdsensing Systems,” in IEEE Transactions on Wireless Communications, vol.19, no.7, pp.4907–4918, 2020.) proposes a task allocation mechanism based on on-demand task requirements. In this mechanism, the on-demand management system categorizes tasks into five levels based on their urgency and rewards tasks at different levels. Furthermore, crowdfunding costs depend on the distance between the user and the task. The goal of an on-demand management system is to maximize the overall return on a task. While this approach takes into account the urgency of task completion, it does not account for variations in the matching benefits between tasks and equipment. Summary of the Invention

[0005] To address the existing technical problems, this invention proposes a Lyapunov-optimized swarm intelligence sensing task matching method, which is mainly used to improve the matching method between sensing tasks and mobile devices. It designs an efficient Lyapunov-based task allocation scheme to optimize the matching efficiency of MCS from a long-term operation perspective.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A Lyapunov-optimized crowd sensing task matching method includes the following steps:

[0008] S1. Establish system model and describe system process: Introduce the crowd intelligence sensing system model, task model and user / device model; at the beginning of each time period, the platform collects task information and sensing device information, and the task issuer and sensing device update their information to the scheduling platform in a timely manner;

[0009] S2. Establish a service quality model: Introduce the service quality concept of tasks and devices, and then the platform calculates the matching benefits between task requirements and different devices.

[0010] S3. Establish a penalty model: Considering the urgency of task completion, introduce the concept of penalty for task delay;

[0011] S4. Establish a long-term task matching benefit objective function, and set corresponding constraints based on factors such as spatial location, energy constraints, and sensing device hardware constraints.

[0012] S5. To maintain the stability of energy on user equipment, establish an equipment energy queue model;

[0013] S6. To consider equipment load and fairness, establish an equipment fairness queue model;

[0014] S7. Based on Lyapunov theory, establish a penalty-reduction utility function model for the objective function;

[0015] S8. Solve for the upper bound of the penalty-reduction utility function. According to Lyapunov optimization theory, the optimization objective function is transformed into a problem of minimizing this upper bound.

[0016] S9. Solve the problem using the minimum weight maximum flow algorithm to obtain a matching scheme, and send a sensing command to the corresponding sensing device.

[0017] Further, step S1 includes: modeling the crowd sensing process: considering a general mobile crowd sensing system, which includes a set of task requesters initiating crowd sensing tasks and a set of mobile devices / users participating in crowd sensing, representing the set of all crowd sensing tasks as... M is the number of tasks in the current time period, and task i is represented as <

[0018] π i ,τ i ,L i ,θ i >, where π i This indicates the perceived requirements of the task; τ iIndicates the remaining deadline for the task; L i Indicates the geographical location of the task publisher, published by the task publisher at the start of each round; θ i This indicates the tolerance for data precision in a task;

[0019] use This represents the set of all mobile devices / users participating in the crowdsensing, using l j To indicate the current position of device j, use e. j ={e 1,j ,e 2,j ,…,e M,j} represents the energy consumption vector perceived by user j for different tasks in each time period. Assume... It is the set of co-sensory tasks in which user j participates. s is only considered valid if the distance between user j and task i does not exceed a threshold. j Only then can one participate in task i, using ∈ j This indicates the quality of data provided by device j, and this information is communicated to user s by the task requester. j It is obtained through historical assessments of perceptual abilities;

[0020] To recruit suitable participants, task requesters submit their requirements to the MCS platform. Assuming the system operates in a time-slot manner, the MCS workflow in each time slot is described as follows:

[0021] 1) Information Collection: The platform collects information from task requesters and mobile devices;

[0022] 2) Participant Recruitment: The platform assigns tasks to participants in this round and notifies them on their mobile devices;

[0023] 3) Task requirement update: The task requester updates their perceived requirements in the next round;

[0024] The above process continues until all tasks are completed or the tasks fail, defining the variable x. i,j (t) indicates whether task i is assigned to user j in time slot t, i.e.:

[0025]

[0026] Further, step S2 specifically involves: defining the crowd-sensing utility as U(t) in time slot t, and defining the crowd-sensing service quality proportionally to the distance between the task and the mobile device; defining the crowd-sensing service quality Q(t) for time period t as the sum of service quality and data quality, i.e.:

[0027]

[0028] in L is the distance between task publisher i and user j in time terminal t.i =(L i (x), L i (y) represents the coordinates of task i, l j =(l j (x), l j (y) represents the coordinates of user j; α is a parameter used to balance the importance of service quality and data quality. This represents the collection of all mobile devices / users participating in the collective experience. Represents the set of all cosensory tasks, ∈ j Indicates the data quality provided by device j, x i,j (t) indicates whether task i is assigned to user j in time slot t.

[0029] Further, step S3 specifically involves: imposing penalties on unfinished and delayed tasks in the current round. The penalty is directly proportional to the remaining collective needs and inversely proportional to the task's deadline. The task penalty should be minimized. The task penalty for time slot t is defined as follows:

[0030]

[0031] Where π i (t) represents the perceived requirements of the task; τ i This indicates the remaining deadline for the task.

[0032] Further, step S4 specifically involves: combining the aforementioned perceived quality and penalty, expressing the long-term task matching utility function as the average of the matching benefits over the first T time slots, which is:

[0033]

[0034] Where β is a parameter that adjusts the crowdsourcing quality and the importance of penalties; P(t) represents the task penalty item for time slot t, and Q(t) is the sum of service quality and data quality;

[0035] In MCS, mobile user s j Energy will be consumed to perform task i. Assume user j consumes e energy during time period t to perform task i. i,j (t), in order to maintain the energy balance of user j, the energy E of the user equipment must be guaranteed. j The stability of (t) is expressed as follows:

[0036] User j's mean energy is stable if and only if

[0037]

[0038] in For the defined variables, For the expected operation, E j (T) represents the device's energy; to avoid unfair task allocation, the long-term average number of tasks assigned to each user must have an upper limit, i.e.

[0039]

[0040] Among them B max This represents the upper limit of the average number of tasks a user can perform over a long period. Let x represent the set of all cosensory tasks. i,j (t) indicates whether task i is assigned to user j in time slot t. Let represent the set of all mobile devices / users participating in the crowdsourcing; considering the above issues, the long-term utility optimization problem of crowdsourcing is expressed as:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Where U is the long-term task matching utility function, in the above constraints, Equation (6) represents the crowd-sensory demand of task i, that is, the number of participants recruited; Equation (7) indicates that the energy of each user must be mean-stable; Equation (8) indicates that the long-term average number of tasks processed cannot exceed the upper bound; Equations (9) and (10) indicate that x can only be set when user j can execute task i. i,j (t) = 1, otherwise x i,j (t) = 0.

[0048] Further, step S5 specifically involves: based on Lyapunov optimization theory and considering energy constraints, establishing an energy queue for user j with an initial value of E. j (0) = 0; Assume user j collects h within time slot t. j The energy of (t), in h max The energy queue is represented as follows, with the boundary as follows:

[0049]

[0050] Where x i,j (t) indicates whether task i is assigned to user j in time slot t, E j (t) represents the energy of the user equipment, ei,j (t) represents the energy consumed by user j in performing task i during time period t.

[0051] Furthermore, step S6 specifically includes:

[0052] To ensure that the long-term average number of tasks processed by each user does not exceed its upper bound, a virtual fair queue F is established. j (t):

[0053]

[0054] Among them B max This represents the upper limit of the average number of tasks a user can perform over a long period. This refers to the set of tasks requiring multiple senses, with an initial value F. j (0) = 0, since the total number of tasks must be finite, i.e., ∑ i∈B x i,j (t) has an upper limit, therefore each user's energy consumption must have an upper limit e. max :

[0055]

[0056] When the virtual fair queue F j When the mean of (t) is stable, i.e.

[0057]

[0058] in This represents the collection of all mobile devices / users participating in the collective experience. For the expected operation, T is the number of time slots for averaging;

[0059] Fairness constraints are satisfied:

[0060]

[0061] According to equation (12), we get:

[0062]

[0063] Add up both sides of the equation from 0 to T-1 and then divide by T:

[0064]

[0065] Due to F j (0) = 0 and the queue is mean-stable. As T → ∞, we have

[0066]

[0067] Right now:

[0068]

[0069] Furthermore, step S7 specifically includes:

[0070] For convenience, the simplified notation for the two queues is as follows: To ensure the stability of the energy queue and the virtual fairness queue, the stability constraints (2) and (3) are transformed. Based on Lyapunov theory, the Lyapunov function is defined as follows:

[0071]

[0072] in It is the set of users participating in perception, and γ is a parameter. To ensure the stability of the queue, the Lyapunov drift function is defined as follows:

[0073]

[0074] According to Lyapunov's theorem, minimizing the drift function of each time slot maintains queue stability. Combining the drift function with the task allocation problem, the penalty-reduction utility problem is obtained as follows:

[0075]

[0076] Where V∈R + R + It is a set of positive real numbers, used to adjust the importance between the original optimization objective and the stability of the queue.

[0077] Furthermore, step S8 includes: the upper bound of the penalty-reduced utility (PMU) problem is:

[0078]

[0079] in, It is the base of the user set. It is the basis of the task set, and Θ(t) is a simplified representation of the two queues;

[0080] Where e max There must be an upper limit to the energy consumption of each user, h j (t) represents the amount of energy collected by the device in each round, h max B is the upper limit of the energy harvested by the equipment per cycle. max This represents the upper bound of the user's long-term average number of tasks, and U(t) is the matching benefit. The optimization objective is achieved by minimizing the upper bound of the PMU function. By rearranging the different terms and discarding constants irrelevant to the optimization problem, the PMU problem can be reduced to the following problem:

[0081]

[0082] The constraints must satisfy equations (6), (9), and (10).

[0083] Let ω represent the optimal policy in the optimal solution and matching utility problem, and let S represent the optimal value. * The arrival of all tasks and the collection of energy are independent and follow the same distribution. The optimal solution achieved matches the long-run average utility S of the utility problem. ω The difference between (t) and the optimal value S* satisfies the following inequality:

[0084]

[0085]

[0086] The gap between the two strategies decreases as V increases.

[0087] Further, step S9 specifically involves: based on the optimal algorithm of minimum weight maximum flow, assigning tasks to appropriate mobile devices, first constructing an auxiliary flow graph G({v0,v... d}∪V1∪V2,E), where v0 and v d These represent the virtual source and virtual destination points, respectively. V1 represents the set of task nodes, V2 represents the set obtained by the user device, and E represents the set of constructed edges. Other vertices and edges are added as follows:

[0088] For each task Add a virtual vertex Up to V1,

[0089] For each mobile user Add a virtual vertex Up to V2,

[0090] For each vertex in V1 Add a line from source vertex v0 to The directed edge, i.e.

[0091] For each task i∈B, if user s j Process it, i.e., i∈B j Add a directed edge to E.

[0092] For each vertex in V2 Add a line from to target vertex v d The directed edge, i.e. Assign capacity and weight to each edge of the graph, using cap min(·) and cap max (·) is used as the minimum and maximum capacity of the edge, and w(·) is used as the weight assigned to it;

[0093] For each pair of edges in E Assign values ​​separately and Assign values ​​as its minimum and maximum capacity. As the weight of this edge;

[0094] For each pair of edges Each and Specify its minimum and maximum capacity, specify As the weight of the modified edge;

[0095] For each pair of edges Each and Specify its minimum and maximum capacity from the user node. Pointing to virtual destination v d The weight of the edge is set to 0;

[0096] Suppose B = {1, 2, 3}, S = {s1, s2, s3, s4}, B j ={1,2,3} By adding minimum and maximum capacities to each edge, for graph G, the optimal solution to the PMU problem can be obtained as follows: In graph G({v0, v... d Find the path from v0 to v in}∪V1∪V2,E). d Minimum weight maximum flow;

[0097] After transforming the above problem, we solve it using the existing minimum weight maximum flow algorithm, and then assign the task to the mobile device, as shown below: If we select in the flow... Set x i,j (t) = 1.

[0098] Compared with the prior art, the present invention has the following advantages:

[0099] The task matching mechanism of this invention takes into account the dynamic nature of the matching benefits between task devices, enabling timely reallocation of tasks to the most suitable mobile devices for perception at each time period. This invention optimizes the benefits of collective intelligent perception from a long-term operational perspective, constructing a Lyapunov optimization model to optimize system stability and the utility of collective intelligent perception; it solves for the upper bound of the derived utility function, constructs an auxiliary graph based on this, and transforms the task allocation problem into finding the minimum weight and maximum flow problem in the graph, using Lyapunov optimization theory to optimize the long-term benefits of task matching. This invention considers the urgency of task completion and combines the data perception quality of the devices with the task delay penalty to obtain a matching benefit model. This model is defined as perception quality minus the loss caused by task delay. Based on this, this invention formulates a long-term task allocation problem aimed at maximizing the defined matching benefit. Attached Figure Description

[0100] Figure 1 Here is a flowchart of a crowd-sensing task matching method based on Lyapunov optimization, as an example.

[0101] Figure 2 This is a schematic diagram illustrating an example of the maximum flow algorithm in an implementation embodiment;

[0102] Figure 3 The final matching benefit simulation verification results for different V values ​​are shown in the figure.

[0103] Figure 4a Simulation results of cumulative matching benefits under different numbers of users / devices;

[0104] Figure 4b Simulation verification results of the average number of tasks to be completed in each round under different numbers of users / devices;

[0105] Figure 4c Simulation verification results of average remaining time when the task is completed under different numbers of users / devices;

[0106] Figure 5a Simulation results of cumulative matching benefits under different μ values;

[0107] Figure 5b Simulation verification results of average remaining time when the task is completed under different μ values;

[0108] Figure 5c Simulation verification results of the average number of tasks to be completed under different μ values;

[0109] Figure 6a Simulation results of cumulative matching efficiency changes for different matching algorithms;

[0110] Figure 6bSimulation results of changes in average remaining energy of equipment under different matching algorithms;

[0111] Figure 6c Simulation results of average remaining time when different matching algorithms complete the task. Detailed Implementation

[0112] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0113] This embodiment of a crowd sensing task matching method based on Lyapunov optimization includes the following steps:

[0114] S1. Modeling the Crowd Sensing Process: First, consider a general mobile crowd sensing system, consisting of a group of task requesters initiating crowd sensing tasks and a group of mobile devices / users participating in the crowd sensing. The set of all crowd sensing tasks is represented as... Specifically, each task i can be represented as <π i ,τ i ,L i ,θ i >, where π i This indicates the sensing requirements of the task, that is, the number of times the task needs to be sensed using different mobile devices; τ i Indicates the remaining deadline for the task; L i Indicates the geographical location of the task publisher, published by the task publisher at the start of each round; θ i This indicates the tolerance for data precision in the task; different types of tasks may have different requirements for data quality.

[0115] Without loss of generality, use This represents the set of all mobile devices / users that can participate in crowdsensing. Due to hardware heterogeneity, such as sensing capabilities, the crowdsensing service and quality provided by each mobile device may vary. Specifically, for each mobile device, for example... In Use l j To indicate the current position of device j, use e. j =

[0116] {e 1,j ,e 2,j ,…,e M,j}(M is the number of tasks in the current time period) represents the energy consumption vector perceived by user j for different tasks in each time period. Assume It is the set of shared-sensory tasks that user j can participate in. s is only considered valid when the distance between user j and task i does not exceed a certain threshold. j Only then can one participate in task i. Furthermore, using ∈j This indicates the quality of data provided by device j. This information can be obtained from the task requester via the user s. j It is obtained through historical assessments of perceptual abilities.

[0117] To recruit suitable participants, task requesters submit their requests to the MCS platform. Rather than simply optimizing short-term goals, such as crowdsourcing costs or the number of participants recruited within a given timeframe, this invention focuses on long-term system performance. In dynamic MCS systems, both tasks and mobile users arrive dynamically, and task requirements may change over time. Similar to previous research, this invention assumes the system operates in a time-slot manner, denoted as... The working process of MCS in each time slot can be described as follows:

[0118] 1) Information collection: The platform collects information from task requesters and mobile devices.

[0119] 2) Participant Recruitment: The platform assigns tasks to participants in this round and notifies them on their mobile devices.

[0120] 3) Task requirement update: The task requester updates its perceived requirements in the next round.

[0121] The above process continues until all tasks are completed or the tasks expire. The specific process is as follows: Figure 1 As shown. To simplify the description, we first define the variable x. i,j (t) represents whether task i is assigned to user j in time slot t, i.e.:

[0122]

[0123] S2. Matching Benefit Calculation: Introducing the concept of matching benefit between tasks and devices, the platform then calculates the matching benefit between task requirements and different devices.

[0124] Based on the variables above, the crowdsensing utility is now defined in time slot t, denoted by U(t). First, due to communication overhead and geographical influences, crowdsensing task publishers always expect participants to be nearby. Therefore, the service quality of crowdsensing is defined proportionally to the distance between the task and the mobile device. Second, the heterogeneity of device hardware also affects the data quality of crowdsensing.

[0125] Considering the two issues above, for time period t, the service quality Q(t) of the crowdsensing service is defined as the sum of service quality and data quality, that is:

[0126]

[0127] in α is the distance between task publisher i and user j in time t, and α is a parameter used to balance the importance of service quality and data quality.

[0128] Due to a lack of sufficient participants nearby, some tasks may not be completed in the current round and must be postponed to later rounds. However, these tasks typically have strict deadlines. To account for the urgency of the tasks, a penalty is imposed on unfinished and delayed tasks in the current round. The penalty should be proportional to the remaining collective need and inversely proportional to the task's deadline. Therefore, the task penalty term for time slot t can be defined as:

[0129]

[0130] It should be minimized.

[0131] S3. Matching scheme modeling: Establish a long-term task matching benefit objective function, and set corresponding constraints based on factors such as spatial location, energy constraints, and sensing device hardware constraints.

[0132] Combining the aforementioned factors of perceived quality and penalty, the long-term task matching utility function can be expressed as:

[0133]

[0134] β is a parameter that adjusts the quality of crowdsourcing and the importance of penalties.

[0135] Next, we consider the stability of task completion. In MCS, mobile user s j Energy will be consumed to perform task i. Assume user j consumes e energy during time period t to perform task i. i,j (t). To maintain the energy balance of user j, its energy E must be guaranteed. j The stability of (t). Similar to the online energy balancing strategy based on Lyapunov optimization in mobile crowdsensing (S. Chang, S. Deng, Y. Wu, W. Ma and H. Zhou, "Online Energy Balancing Strategy Based on Lyapunov Optimization in Mobile Crowdsensing," in IEEE Transactions on Industrial Informatics, pp. 1-13, 2022, DOI: 10.1109 / TII.2022.3227618.), the stability of energy is expressed as:

[0136] The energy mean of user j is stable if and only if

[0137]

[0138] Furthermore, to avoid unfair task allocation, there must be an upper limit to the long-term average number of tasks assigned to each user, i.e.

[0139]

[0140] Considering the above issues, the long-term utility optimization problem of collective perception can be expressed as:

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] In the above constraints, constraint (6) represents the collective demand for task i, i.e., the number of participants recruited. Constraint (7) indicates that the energy of each user must be mean-stable, and constraint (8) indicates that the long-term average number of tasks processed cannot exceed the upper bound. Constraints (9) and (10) indicate that x can only be set when user j can execute task i. i,j (t) = 1, otherwise x i,j (t) = 0.

[0148] S4. Problem Transformation and Solution: Based on Lyapunov optimization theory, the optimization objective function is transformed into a problem of minimizing the upper bound of Lyapunov drift, and finally a task matching scheme is obtained, and a sensing command is sent to the corresponding device.

[0149] Due to the randomness and time averaging constraints of the energy harvesting process, this problem is difficult to solve directly. As an example, this invention proposes a task allocation algorithm based on Lyapunov. According to Lyapunov optimization theory, the defined problem can be decoupled into a single-time-slot optimization problem, making it solvable based on the information of the current round. First, considering the energy constraint, an energy queue for user j is established with an initial value of E. j (0) = 0. Similar to existing work, assume that user j can collect h within time slot t. j The energy of (t), which is a random variable with a specific distribution, is given by h. max Bounded by the boundary, the energy queue can then be represented as...

[0150]

[0151] In addition, to ensure that the long-term average number of tasks processed by each user does not exceed its upper bound, a virtual fair queue F is established. j (t),

[0152]

[0153] Its initial value F j (0) = 0. Since the total number of tasks must be finite, i.e., ∑ i∈B x i,j (t) has an upper limit, therefore each user's energy consumption must have an upper limit e. max In other words,

[0154]

[0155] This virtual queue transforms the fairness constraint problem into a queue stability problem. By maintaining the stability of this queue, the fairness constraint can be guaranteed. Based on the above definitions and assumptions, we have:

[0156] When the virtual fair queue F j When the mean of (t) is stable, i.e.

[0157]

[0158] So fairness constraints

[0159]

[0160] It can be satisfied.

[0161] According to equation (12), we can obtain

[0162]

[0163] Adding the values ​​from 0 to T-1 on both sides of the equation and then dividing by T, we get the result.

[0164]

[0165] Due to F j (0) = 0 and the queue is mean-stable. As T → ∞, we have

[0166]

[0167] In other words,

[0168]

[0169] For convenience, it is indicated that Therefore, the stability constraints (2) and (3) in the equation can be transformed to guarantee the stability of the energy queue and the virtual fairness queue. According to Lyapunov theory, the Lyapunov function is defined as follows:

[0170]

[0171] It reflects the length of the queue backlog, and γ is a parameter. To ensure the stability of the queue, the Lyapunov drift function is used, which can be expressed as:

[0172]

[0173] The drift function represents the degree of fluctuation in the queue. According to Lyapunov's theorem, the stability of the queue can be maintained by minimizing the drift function for each time slot.

[0174] Combining the drift function with the task allocation problem, we obtain the penalty-reduction utility problem as follows:

[0175]

[0176] Where V∈R + It is a parameter that adjusts the importance between the original optimization objective and queue stability. The upper bound of the penalty-reducing utility (PMU) problem is...

[0177]

[0178] in

[0179] According to equations (11), (12), and (max{ab,0}+c) 2 ≤a 2 +b 2 +c 2 +2a(cb) yields

[0180]

[0181] as well as

[0182]

[0183] According to equations (14) and (15), we can obtain

[0184]

[0185]

[0186] The system matching benefit objective function is optimized by minimizing the upper bound of the PMU function (Equation (5)); by rearranging the different terms and discarding constants irrelevant to the optimization problem, the PMU problem (16) can be reduced to the following problem:

[0187]

[0188] The constraints must satisfy equations (6), (9), and (10).

[0189] It can be seen that the above formula balances maintaining queue stability with obtaining optimal co-sensory utility. Furthermore, it can be proven that the difference between the optimal solution of equation (17) and the optimal solution of the matching utility problem (equation (5)) will not exceed the upper bound. For ease of representation, the optimal strategy of equation (5) is denoted as ω, and the optimal value of equation (5) is denoted as S. * .

[0190] If the arrival of all tasks and the collection of energy are independent and follow the same distribution, then by ω, S ω (t) The long-run average utility and optimal value S of problem (5) * The difference between them satisfies the following inequality:

[0191]

[0192] Where V is the control parameter. It is the base (number of elements) of the user set. It is the base (number of elements) of the task set, and Θ(t) is a simplified representation of the two queues;

[0193] According to (MJ Neely, "Stochastic Network Optimization with Application to Communication and Queueing Systems," Williston, VT, USA: Morgan & Claypool Publishers, 2010), there exists an optimal S-only policy σ that satisfies the following conditions:

[0194]

[0195]

[0196] Since the objective function of the optimal policy ω minimization problem (Equation (17)) is based on the upper bound of the penalty-reduction utility (PMU) problem, we obtain:

[0197]

[0198] Take the average time of the first T rounds on both sides of the inequality, then divide by V. Since L(t) ≥ 0, then...

[0199]

[0200] As T→∞, we can obtain

[0201]

[0202] The above shows that the gap between the two strategies decreases as V increases.

[0203] S5. Information Update: At the end of each time period, the task issuer and the sensing device update their information to the scheduling platform in a timely manner.

[0204] The original problem is transformed into problem (17), subject to constraints (6), (9), and (10). Therefore, this invention designs an optimal algorithm based on minimum weight maximum flow to assign tasks to appropriate mobile devices. First, an auxiliary flow graph G({v0,v... d}∪V1∪V2,E), where v0 and v d These are the virtual source and virtual destination points, respectively. Then, other vertices and edges are added, such as... Figure 2 As shown, the details are as follows:

[0205] For each task i∈B, add a virtual vertex. Up to V1, that is to say,

[0206] For each mobile user j ∈S, add a virtual vertex. Up to V2, that is

[0207] For each vertex in V1 Add a line from source vertex v0 to The directed edge, i.e.

[0208] For each task i∈B, if user s j It can be handled, i.e., i∈B j Add a directed edge to E.

[0209] For each vertex in V2 Add a line from to target vertex v d The directed edge, i.e. Next, assign capacity and weight to each edge of the graph. Use cap min(·) and cap max (·) represents the minimum and maximum capacity of edge ·, and w(·) is used as the weight assigned to it.

[0210] For each pair of edges in E Assign values ​​separately and Assign values ​​as its minimum and maximum capacity. This serves as the weight of this edge.

[0211] For each pair of edges Each and Specify its minimum and maximum capacity. As the weight of the modified edge.

[0212] For each pair of edges Each and

[0213] Specify its minimum and maximum capacity. The weight of this edge is set to 0.

[0214] Let B = {1, 2, 3} and S = {s1, s2, s3, s4}, then B j ={1,2,3} And add minimum and maximum capacities to each edge. For graph G, we can obtain:

[0215] The optimal solution of equation (17) is equivalent to the solution in graph G({v0,v... d Find the path from v0 to v in}∪V1∪V2,E). d The minimum weighted maximum flow. First, we prove that the feasible flow G of the graph is one of the feasible solutions to problem (17). For simplicity, we use F to represent the flow from v0 to v using the minimum weighted maximum flow algorithm. d The collection of all selected streams. If it is Then set x i,j (t) = 1, otherwise set x i,j (t) = 0. Since the maximum capacity from v0 to v1 is π... i (t), we can know The constraints in equation (6) are satisfied. In addition, in and Add an edge between i and B if and only if i∈B j In other words, constraints (9) and (10) in the equation are also satisfied. Therefore, the feasible flow of graph G must also be one of the feasible solutions to problem (17).

[0216] Next, we prove that a feasible solution to the PMU problem (17) is also graph G({v0,v... dOne of the feasible flows in}∪V1∪V2,E). For any x i,j (t) = 1, the flow Add to F. Because It can be deduced that the maximum flow from v0 to v1 must not exceed π. i (t). Additionally, due to x i,j (t)∈{0,1}, from arrive The flow must be 0 or 1 to satisfy the flow constraints of graph G.

[0217] Finally, based on the weight allocation of graph G, any flow The weight is Therefore, the minimum weight maximum flow in graph G is the same as the objective function of the problem (Equation (17)).

[0218] After transforming the above problem, it can be solved using the existing minimum weight maximum flow algorithm. Then, the task is assigned to the mobile device as follows: If selected in the flow... Set x i,j (t) = 1.

[0219] This embodiment uses a real-world dataset, the CRAWDAD dataset. This dataset uses a large number of taxis as mobile users in Rome, Italy, where onboard sensors collect data (e.g., outdoor temperature). Furthermore, the area with the highest taxi traffic is selected as the region / location for the co-sensing task. The sensing range of the mobile devices is then set to a circular area. If a mobile device is within the task's sensing range, it can participate in the task. In addition, mobile users will randomly collect energy at each time slot. Based on existing work, the energy collected by the user in each time slot can be set to follow a uniform distribution from 0 to 80 J. Therefore, the energy consumption due to the user's perception of the task can be set to follow a uniform distribution from 5 to 15.

[0220] As one example, the initial number of mobile devices is set to 20, which can be updated over time, and the arrival of tasks follows a Poisson distribution with a mean of μ = 20. The following test uses 500 rounds of system operation as an example.

[0221] To ensure a fair comparison, the following two baseline algorithms are used.

[0222] On-demand MCS: A task allocation mechanism based on on-demand task requirements (J.Hu, Z.Wang, J.Wei, R.Lv, J.Zhao, Q.Wang, H.Chen and D.Yang, "Towards Demand-Driven Dynamic Incentive for Mobile Crowdsensing Systems," in IEEE Transactions on Wireless Communications, vol.19, no.7, pp.4907-4918, 2020.). In this mechanism, the on-demand management system categorizes tasks into five levels based on their urgency and rewards tasks at different levels. Furthermore, the crowdfunding cost depends on the distance between the user and the task. The goal of the on-demand management system is to maximize the overall reward for tasks.

[0223] Load-balancing MCS: This proposes a load-balancing task allocation scheme that takes task deadlines into account. Specifically, in each round, the task with the most pressing deadline will be assigned a higher priority to the device with the least load.

[0224] Unlike these two benchmark algorithms, the proposed scheme considers long-term task allocation and allows tasks to dynamically update their requirements. For simplicity, the long-term task allocation scheme with dynamic task requirements is called Long-term-dynamic MCS.

[0225] Assuming that all task arrivals and energy collection are independent and follow the same distribution, the trade-off between crowd-feeling utility and the stability of the optimization objective is controlled by adjusting the Lyapunov parameter V. As V increases, the optimization objective function focuses more on crowd-feeling utility. As V decreases, the allocation scheme places greater emphasis on the stability of the energy queue and the fairness queue.

[0226] The first simulation demonstrates the cumulative perceptual utility over time under different settings of parameter V.

[0227] Depend on Figure 3 It can be seen that the cumulative group perception utility increases with the increase of V, while the rate of increase decreases with the increase of V, verifying the results of the above analysis. Now, the impact of the number of users N on the system is investigated, as shown in Figures 4(b) and 4(c). The results show that the perceived utility increases with the increase of the number of mobile users N. This is reasonable because more mobile users can perform more tasks in the system. In addition, compared with the other two baseline algorithms, the scheme proposed in this invention achieves the optimal group perception utility. Figure 4(b) and Figure 4cThe average remaining time for completed tasks and the number of incomplete tasks are also shown for different numbers of mobile users. As N increases, more urgent tasks can be served. It can be observed that the long-term dynamic MCS algorithm proposed in this invention achieves a better trade-off between deadlines and the number of incomplete tasks. On-demand MCS has the longest remaining task deadlines, but it also leaves too many incomplete tasks because it does not consider the urgency of the tasks. Compared to the on-demand MCS algorithm, the load-balanced MCS algorithm prioritizes tasks with shorter deadlines, thus achieving better performance. The algorithm of this invention achieves optimal performance because it reallocates tasks for each time period and penalizes incomplete tasks.

[0228] To simulate the dynamics of the MCS, we assume that task arrival follows a Poisson distribution. Without affecting generality, we use the task arrival rate μ to represent the number of tasks arriving per unit time. We will now investigate the impact of the task arrival rate μ on system performance.

[0229] As shown in Figure 5(a), the value of μ was increased from 15 to 30. The results show that as the task arrival rate μ increases, each mobile device will bear a greater load, leading to a decrease in cumulative crowdsense utility. Furthermore, the long-term dynamic MCS proposed in this invention exhibits the best performance. Figure 5b The average remaining deadlines for tasks in the system are given. The results show that the proposed scheme, by considering task deadlines in the optimization objective, significantly alleviates the urgency of the tasks. Figure 5c The system displays the number of remaining unfinished tasks. This approach demonstrates the best performance, further validating its effectiveness.

[0230] The overall performance of the system was compared under different baseline algorithms. First, the cumulative utility achieved during task allocation was investigated. For example... Figure 6a As shown, the cumulative utility from round 0 to round 500 is presented. It can be observed that the crowd-aware utility increases over time as more tasks are served by mobile users. Furthermore, compared to on-demand MCS and load-balanced MCS algorithms, the long-term dynamic MCS algorithm proposed in this invention achieves optimal crowd-aware utility. This is reasonable because the scheme of this invention considers the matching benefits between tasks and users that change over time and dynamically reallocates the most suitable sensing users to tasks in each round.

[0231] Next, the energy queues for these three algorithms are presented. Figure 6bAs shown, On-demand MCS only considers the urgency of tasks and ignores the stability of the user energy queue, resulting in the largest fluctuations among all algorithms. Load balancing MCS distributes tasks evenly according to the device load, thus achieving better energy stability. Based on Lyapunov optimization theory, the long-term dynamic MCS proposed in this invention combines the optimization objective with the stability problem to ensure the stability of the energy queue, thereby achieving optimal stability.

[0232] at last, Figure 6c The performance comparison of these three algorithms in terms of the number of remaining tasks is shown. Because the load balancer MCS always assigns higher-priority tasks to more urgent tasks, ignoring tasks with the least perceived demand, it results in the largest number of unfinished tasks remaining in the system. Compared to the two benchmark algorithms, the solution of this invention maintains the fewest tasks, further reducing the heavy load on the task queue.

[0233] This invention studies the task allocation problem with dynamic task requirements in MCS (Multi-Channel System). Specifically, this invention first establishes a long-term co-perception utility function, which considers both the co-perception quality of task allocation and the penalty for delayed tasks. To ensure the stability of user energy, a Lyapunov optimization model is further constructed, transforming the long-term utility optimization problem into a single-period task allocation problem. Then, the upper bound of the penalty-reduction utility function is derived, and an auxiliary flow graph is constructed based on this. The minimum-weight maximum flow algorithm on the graph is then used to allocate tasks to appropriate mobile users. Finally, simulations verify the effectiveness of the proposed scheme.

[0234] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A crowd-sensing task matching method based on Lyapunov optimization, characterized in that, Includes the following steps: S1. Establish system model and describe system process: Introduce the crowd intelligence sensing system model, task model and user / device model; at the beginning of each time period, the platform collects task information and sensing device information, and the task issuer and sensing device update their information to the scheduling platform in a timely manner; S2. Establish a service quality model: Introduce the service quality concept of tasks and devices, and then the platform calculates the matching benefits between task requirements and different devices. S3. Establish a penalty model: Considering the urgency of task completion, introduce the concept of task delay penalty. Specifically, penalties are imposed on unfinished and delayed tasks in the current round. The penalty is directly proportional to the remaining demand and inversely proportional to the task deadline. The task penalty term should be minimized. The task penalty term for time slot t is defined as: Where π i (t) represents the perceived requirements of the task; τ i Indicates the remaining deadline for the task; S4. Establish a long-term task matching benefit objective function, and set corresponding constraints based on spatial location, energy constraints, and sensing device hardware constraints. Specifically, considering both the overall service quality and penalties, the long-term task matching utility function is expressed as the average of the matching benefits over the first T time slots, i.e.: Where β is a parameter that adjusts the crowdsourcing quality and the importance of penalties; P(t) represents the task penalty term in time slot t, and Q(t) is the sum of service quality and data quality; In MCS, mobile user j will consume energy to perform task i. Assume that user j consumes e energy to perform task i in time slot t. i,j (t), in order to maintain the energy balance of user j, the energy queue E of the user equipment must be guaranteed. j The stability of (t) is expressed as follows: User j's mean energy is stable if and only if in For the defined variables, For the expected operation, E j (T) represents the device's energy queue; to avoid unfair task allocation, the long-term average number of tasks allocated to each user must have an upper limit, i.e. Among them B max This represents the upper limit of the average number of tasks a user can perform over a long period. Let x represent the set of all cosensory tasks. i,j (t) indicates whether task i is assigned to user j in time slot t. Let represent the set of all mobile devices / users participating in the crowdsourcing; considering the above issues, the long-term utility optimization problem of crowdsourcing is expressed as: Where U is the long-term task matching utility function, in the above constraints, Equation (6) represents the crowd-sensory demand of task i, that is, the number of participants recruited; Equation (7) indicates that the energy of each user must be mean-stable; Equation (8) indicates that the long-term average number of tasks processed cannot exceed the upper bound; Equations (9) and (10) indicate that x can only be set when user j can execute task i. i,j (t) = 1, otherwise x i,j (t) = 0; It is the set of shared sensory tasks in which user j participates. User j can only participate in task i if the distance between user j and task i does not exceed the threshold. S5. To maintain the stability of energy on user equipment, establish an equipment energy queue model; S6. To consider equipment load and fairness, establish an equipment fairness queue model; S7. Based on Lyapunov theory, establish a penalty-reduction utility function model for the objective function; S8. Solve for the upper bound of the penalty-reduction utility function. According to Lyapunov optimization theory, the optimization objective function is transformed into a problem of minimizing this upper bound. S9. Solve the problem using the minimum weight maximum flow algorithm to obtain a matching scheme, and send a sensing command to the corresponding sensing device.

2. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S1 includes: Modeling the crowd sensing process: Considering a general mobile crowd sensing system, which includes a set of task requesters initiating crowd sensing tasks and a set of mobile devices / users participating in crowd sensing, the set of all crowd sensing tasks is represented as M is the number of tasks in the current time period, and task i is represented as <π. i ,τ i ,… i ,θ i >, where π i This indicates the perceived requirements of the task; τ i Indicates the remaining deadline for the task; L i Indicates the geographical location of the task publisher, published by the task publisher at the start of each round; θ i This indicates the tolerance for data precision in a task; use This represents the set of all mobile devices / users participating in the crowdsensing, using l j To indicate the current position of device j, use e. j ={e 1,j ,e 2,j ,…,e M,j } represents the energy consumption vector perceived by user j for different tasks in each time period. Assume... This is the set of shared sensory tasks in which user j participates. User j can only participate in task i if the distance between user j and task i does not exceed a threshold. (Using ∈) j This indicates the quality of data provided by device j, information obtained through historical assessments by the task requester of user j's perceptual capabilities; e i,j This represents the energy consumed by user j in executing task i; To recruit suitable participants, task requesters submit their requirements to the MCS platform. Assuming the system operates in a time-slot manner, the MCS workflow in each time slot is described as follows: 1) Information Collection: The platform collects information from task requesters and mobile devices; 2) Participant Recruitment: The platform assigns tasks to participants in this round and notifies them on their mobile devices; 3) Task requirement update: The task requester updates their perceived requirements in the next round; The above process continues until all tasks are completed or the tasks fail, defining the variable x. i,j (t) indicates whether task i is assigned to user j in time slot t, i.e.:

3. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S2 specifically involves: defining the crowd perception utility in time slot t as U(t), and defining the service quality of the crowd perception proportionally to the distance between the task and the mobile device; defining the sum of service quality and data quality in time slot t as Q(t): in L is the distance between task publisher i and user j in time slot t. i =(L i (x), L i (y) represents the coordinates of task i, l j =(l j (x), l j (y) represents the coordinates of user j; α is a parameter used to balance the importance of service quality and data quality. This represents the collection of all mobile devices / users participating in the collective experience. Represents the set of all cosensory tasks, ∈ j Indicates the data quality provided by device j, x i,j (t) indicates whether task i is assigned to user j in time slot t.

4. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S5 specifically involves: Based on Lyapunov optimization theory and considering energy constraints, establishing an energy queue for user j with an initial value of E. j (0) = 0; Assume user j collects h within time slot t. j The energy of (t), in h max The energy queue is represented as follows, with the boundary as follows: Where x i,j (t) indicates whether task i is assigned to user j in time slot t, E j (t) represents the energy queue of the user equipment, e i,j (t) represents the energy consumed by user j in time slot t when performing task i.

5. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S6 specifically involves: to ensure that the long-term average number of tasks processed by each user does not exceed its upper bound, establishing a virtual fair queue F. j (t): Among them B max This represents the upper limit of the average number of tasks a user can perform over a long period. This refers to the set of tasks requiring multiple senses, with an initial value F. j (0) = 0, since the total number of tasks must be finite, i.e. There is an upper limit, therefore each user's energy consumption must have an upper limit e. max : When the virtual fair queue F j When the mean of (t) is stable, i.e. in This represents the collection of all mobile devices / users participating in the collective experience. For the expected operation, T is the number of time slots for averaging; Fairness constraints are satisfied: According to equation (12): Add up both sides of the equation from 0 to T-1 and then divide by T: Due to F j (0) = 0 and the queue is mean-stable. As T → ∞, we have Right now:

6. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S7 specifically involves: For convenience, the two queues are represented by simplified symbols as follows: Equations (2) and (3) are transformed to ensure the stability of the energy queue and the virtual fairness queue. Based on Lyapunov theory, the Lyapunov function is defined as follows: Where E j (t), F j (t) represent the energy queue and the virtual fair queue, respectively, and γ is a parameter. To ensure the stability of the queue, the Lyapunov drift function is defined as: According to Lyapunov's theorem, minimizing the drift function of each time slot maintains queue stability. Combining the drift function with the task allocation problem, the penalty-reduction utility problem is obtained as follows: Where V∈R + R + It is a set of positive real numbers, a parameter used to adjust the importance between the original optimization objective and the stability of the queue, and U(t) is the matching benefit.

7. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S8 includes: The upper bound of the penalty-reducing utility (PMU) problem is: Where E j (t) represents the energy queue, F j (t) represents the virtual fair queue. It is the base of the user set. It is the basis of the task set, Θ(t) is a simplified representation of the two queues; γ is a parameter, which is used to ensure the stability of the queues, V∈R + R + It is a set of positive real numbers, used to adjust the importance between the original optimization objective and the stability of the queue; Where e max There must be an upper limit to the energy consumption of each user, h j (t) represents the amount of energy collected by the device in each round, h max B is the upper limit of the energy harvested by the equipment per cycle. max This represents the upper bound of the user's long-term average number of tasks, and U(t) is the matching benefit. The goal is to optimize by minimizing the upper bound of the PMU function. By rearranging the different terms and discarding constants irrelevant to the optimization problem, the PMU problem can be reduced to the following problem: The constraints must satisfy equations (6), (9), and (10); Let ω represent the optimal policy in the optimal solution and matching utility problem, and let S represent the optimal value. * The arrival of all tasks and the collection of energy are independent and follow the same distribution. The optimal solution achieved matches the long-run average utility S of the utility problem. ω (t) and the optimal value S * The difference between them satisfies the following inequality: The gap between the two strategies decreases as V increases.

8. The crowd sensing task matching method based on Lyapunov optimization according to claim 1, characterized in that, Step S9 specifically involves: using the optimal algorithm based on minimum weight maximum flow, assigning tasks to appropriate mobile devices, and first constructing an auxiliary flow graph G({v0,v... d }∪V1∪V2,E), where v0 and v d These represent the virtual source and virtual destination points, respectively. V1 represents the set of task nodes, V2 represents the set of user devices, and E represents the set of constructed edges. Other vertices and edges are added as follows: For each task Add a virtual vertex Up to V1, For each mobile user Add a virtual vertex Up to V2, For each vertex in V1 Add a line from source vertex v0 to The directed edge, i.e. For each task If user j processes it, that is Add a directed edge to E For each vertex in V2 Add a line from to target vertex v d The directed edge, i.e. Assign capacity and weight to each edge of the graph, using cap min (·) and cap max (·) is used as the minimum and maximum capacity of the edge, and w(·) is used as the weight assigned to it; For each pair of edges in E Assign values ​​separately and Assign values ​​as its minimum and maximum capacity. As the weight of this edge; For each pair of edges Each and Specify its minimum and maximum capacity, specify As the weight of the modified edge; e i,j E represents the energy consumed by user j in executing task i; j (t), F j (t) represents the energy queue and the virtual fair queue, respectively; γ is a parameter, which is used to ensure the stability of the queue, V∈R + R + It is a set of positive real numbers, used to adjust the importance between the original optimization objective and the stability of the queue; For each pair of edges Each and Specify its minimum and maximum capacity from the user node. Pointing to virtual destination v d The weight of the edge is set to 0; Assumption By adding minimum and maximum capacities to each edge, for graph G, the optimal solution to the PMU problem can be obtained as follows: In graph G({v0, v... d Find the path from v0 to v in}∪V1∪V2,E). d Minimum weight maximum flow; After transforming the above problem, we solve it using the existing minimum weight maximum flow algorithm, and then assign the task to the mobile device, as shown below: If we select in the flow... Set x i,j (t) = 1.

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