Dynamic energy balancing method for mobile crowdsensing based on Lyapunov optimization

Abstract

The present invention belongs to the field of mobile crowd sensing and discloses a dynamic energy balancing method for mobile crowd sensing based on Lyapunov optimization. The method comprises the following steps: constructing the energy balancing problem as a time-discrete model; determining a dynamic load balancing strategy using the Lyapunov optimization algorithm, taking system utility as the objective function, and measuring the degree of load balancing using the variance of the residual energy of participants; solving the problem based on linear programming and genetic algorithms to obtain long-term dynamic energy balance for online tasks and assigning tasks to sensing participants. The present invention minimizes energy consumption and achieves relative energy balance among participants without sacrificing system efficiency, thereby maintaining the number of participants, extending the life of the mobile crowd sensing system, and promoting the completion of sensing tasks. This method achieves long-term online dynamic control of task admission strategies and task allocation schemes.

Description

Technical Field

[0001] The present invention belongs to the field of mobile crowd sensing technology, and in particular relates to a mobile crowd sensing dynamic energy balancing method based on Lyapunov optimization. Background Art

[0002] In mobile crowd sensing, the battery capacity of mobile sensing devices is limited. When some participants consume too much energy and run out of battery capacity, they exit the system and are unable to continue their sensing tasks. A sharp drop in the number of participants can severely impact the lifespan of the mobile crowd sensing system and the quality of the sensing data. Therefore, selecting a reasonable task allocation scheme that minimizes participant energy consumption and maintains energy load balance among participants is crucial for extending the lifespan of mobile crowd sensing systems and facilitating the completion of sensing tasks. In existing research, achieving energy balance often comes at the expense of system efficiency.

[0003] In recent years, with the development of wireless communication technology and rising incomes, the number of mobile device users has exploded. Advances in computer hardware technology and the miniaturization of sensor devices have led to an increasing number of sensor devices being embedded in mobile devices, such as cameras, microphones, accelerometers, and electronic compasses. Mobile crowd sensing technology is increasingly applying these sensor devices to areas such as traffic management, health monitoring, and environmental protection, making environmental perception and information collection more flexible, convenient, and efficient. Mobile crowd sensing (MCS), first proposed by Raghu K. Ganti et al. in 2011, represents widespread community sensing. Mobile crowd sensing provides a paradigm for collecting sensor data and extracting valuable information. This paradigm involves a large number of mobile devices, each capable of sensing, computing, and communicating. These devices, recruited and coordinated by a server, sense the surrounding environment, for example, monitoring air quality, noise levels, and traffic congestion. After acquiring sensor data, mobile devices upload it to a data collection server via cellular networks, Wi-Fi, or Bluetooth, providing data support for various applications. Mobile crowd sensing has garnered widespread attention in recent years.

[0004] The typical mobile crowd sensing system consists of two parts: the sensing platform and the sensing participants. Figure 1As shown in the figure, the perception platform is responsible for collecting perception data requests from various external applications, recruiting and selecting appropriate perception participants, assigning perception tasks, receiving perception data from participants, and providing it to various applications. Perception participants, namely the various mobile devices mentioned above, are primarily responsible for executing perception tasks, acquiring, storing, and uploading perception data to the perception platform. When the perception platform receives a perception information request, it assigns the perception task to the appropriate participant through a specific incentive mechanism and selection decision. The participant perceives, collects, and processes the raw data, and then transmits it to the perception platform via wireless communication. The perception platform then stores and processes the data, ultimately serving various external applications.

[0005] The mobile crowdsensing process can be broadly summarized as four stages: task allocation, data perception, data processing, and data upload. Existing research on mobile crowdsensing primarily focuses on these four stages, including the design of incentive mechanisms, task allocation strategies and resource scheduling mechanisms, improved data processing methods, and innovative data transmission methods. The main research objectives are to recruit a sufficient number of participants, save costs, reduce overall energy consumption, shorten task completion time, improve data quality, and protect participant privacy and security.

[0006] In mobile crowd sensing, most mobile sensing devices, such as smartphones and smart wristbands, are small, lightweight, and easy to carry. However, their battery capacity is limited, and energy consumption cannot be quickly replenished through rewards and feedback from the sensing platform. The energy consumed by participants while performing sensing tasks is primarily due to sensor data acquisition, local data processing, and data transmission, which directly affects the remaining battery capacity of the sensing devices. When some participants perform too many tasks, consume too much energy, and have insufficient battery capacity, they will exit the system and be unable to continue sensing tasks. A sharp drop in the number of participants will seriously affect the lifespan of the mobile crowd sensing system and the quality of the sensing data. Therefore, maintaining energy balance among participants is crucial to maintaining the number of participants and completing sensing tasks.

[0007] Currently, there are numerous research projects on energy-saving technologies for mobile crowdsensing. For example, in the task allocation phase, optimizing task allocation methods and reducing the amount of data collected and uploaded can reduce overall energy consumption in mobile crowdsensing. In the data perception phase, low-energy sensors are used to replace traditional sensors to reduce perception energy consumption. In the data transmission phase, low-power wireless networks are used instead of cellular networks, and data can be uploaded when mobile users are making calls or using apps, reducing data transmission energy consumption. These technologies aim to reduce overall energy consumption but do not address the energy imbalance between participants. Summary of the Invention

[0008] To achieve relative energy balance among participants while ensuring system efficiency, this paper proposes a mobile crowdsensing energy balancing method (OEBS) based on the Lyapunov optimization algorithm. First, the energy balancing problem is formulated as a time-discrete model. Then, the method uses the Lyapunov optimization algorithm, takes system utility as the objective function, and measures the degree of load balancing using the variance of the participants' residual energy. Finally, the problem is solved using linear programming and genetic algorithms, ultimately achieving long-term dynamic energy balancing for online tasks.

[0009] The present invention discloses a mobile crowd-sensing dynamic energy balancing method based on Lyapunov optimization, comprising the following steps:

[0010] The energy balance problem is formulated as a time-discrete model;

[0011] The dynamic load balancing strategy is determined by Lyapunov optimization algorithm, the system utility is used as the objective function, and the variance of the residual energy of participants is used to measure the load balancing degree.

[0012] Solve the problem based on linear programming and genetic algorithm to obtain the long-term dynamic energy balance for online tasks and assign tasks to perception participants;

[0013] Wherein, the time discrete model is:

[0014] N perception participants register to the perception platform, participate in and complete perception tasks. There are M types of perception tasks, j represents different perception task types, j∈{1,…,M}, and divides time into discrete time slots of equal length t, O j (t) represents the number of sensing tasks of type j that arrive at the sensing platform at time slot t. The sensing platform assigns different types of tasks to sensing participants in each time slot;

[0015] If Q j (t) Satisfy:

[0016]

[0017] Then Q j (t) is the average rate stable, that is, all the sensing tasks entering the sensing platform will be executed; when {Q j (t)},j∈{1,…,M} all satisfy the above formula, then the mobile crowd sensing system is stable.

[0018] Furthermore, in the time discrete model, at each time slot, the perception platform assigns different types of tasks to the perception participants, i.e., the allocation decision, x(t) represents the task allocation at time slot t, x ij(t) indicates whether task j is assigned to perception participant i in time slot t, i∈{1,…,N}, that is, whether perception participant i performs task j. ij When (t) = 1, the perceptual participant i performs task j; when x ij When (t) = 0, the perceptual participant i does not perform task j. In each time slot, the same perceptual participant can simultaneously perform multiple types of unit-number tasks. After task allocation, the number of tasks j that can be performed in time slot t is expressed as r. j (t):

[0019] r j (t)=∑ i∈N x ij (t) (2)

[0020] where 0≤r j (t)≤N;

[0021] Q(t)=(Q1(t),Q1(t),…,Q M (t)) represents the backlog vector of different types of perception request queues in the perception platform at time slot t, and its dynamic change obeys the following formula:

[0022] Q j (t+1)=max[Q j (t)-r j (t),0]+o j (t) (3)

[0023] Among them, j (t) represents the number of sensing tasks of type j that enter the sensing platform after the sensing platform selection decision at time slot t, 0≤o j (t)≤O j (t).

[0024] Furthermore, when a perception participant performs a perception task, sensor data collection, local data processing, and data transmission will all lead to device energy consumption. Moreover, different participants will experience different energy consumption when performing the same type of perception task. In order to reflect the difference in residual energy among different perception participants, the residual energy variance is used to measure it, V c (t) represents the remaining energy after all participants have completed their tasks in time slot t The variance of , that is:

[0025]

[0026] in, represents the mean residual energy of all participants,

[0027] It represents the remaining energy after participant i completes the assigned task in time slot t, and its variation over time obeys the following formula:

[0028]

[0029] Among them, c ij It represents the energy consumption of participant i when performing unit number task j.

[0030] Furthermore, to ensure load balancing among participants, the remaining energy variance is limited:

[0031]

[0032] Among them, V max The maximum variance value specified for the mobile crowdsensing system.

[0033] Furthermore, U(t) represents the benefit of the sensing platform in time slot t, and its size depends on the number of sensing tasks entering the platform.

[0034]

[0035] Where β represents the benefit that the perception platform can obtain by executing a unit number of tasks, which is a positive constant.

[0036] Furthermore, the problem to be solved by the time discrete model is to ensure the energy load balance of each participant while maximizing the average benefit of the system by selecting control and task allocation under the condition of satisfying the stability of the perceived task queue. The objective function of the problem is:

[0037]

[0038] stconstraints(1)(3) (8)

[0039] Wherein formula (8) is:

[0040]

[0041] Then the virtual queue z(t) is said to be stable.

[0042] Furthermore, the virtual queue z(t) is defined as follows:

[0043] z(t+1)=max[z(t)-V max ,0]+V c (t) (9)

[0044] Here, z(0)=0, and for all t, there exists a virtual queue z(t)≥0.

[0045] Furthermore, the dynamic load balancing strategy includes:

[0046] At each time slot t, the sensing platform takes turns selecting each of the M tasks and selects o j (t), so that the following formula is minimized:

[0047] Perception platform selection x(t) = {x ij (t),i∈{1,…,N},j∈{1,…,M}}, so that the following formula is minimized:

[0048]

[0049] The perception platform updates Q according to formula (2) j (t), j∈{1,…,M},

[0050] The perception platform is updated according to formula (5) i∈{1,…,N},

[0051] The perception platform updates z(t) according to formula (9).

[0052] Furthermore, the optimization function of the Lyapunov optimization algorithm is:

[0053]

[0054] Furthermore, the problem solving based on linear programming and genetic algorithm includes:

[0055] Randomly initialize the population P, for each individual P in the population k , crossover and mutation are performed according to the crossover probability and mutation probability, and the offspring with low fitness are eliminated according to the fitness function, and the offspring with high fitness are retained and continue to perform inheritance, crossover, mutation and selection operations as the parent generation. After iterating G generations, the individual chromosome with the highest fitness is the optimal task allocation solution;

[0056] The fitness function is as follows:

[0057] F k =-(g k -max{g k |k=0,…,K})

[0058] Among them, K is the number of individuals in the population, g k is a function of individual chromosomes:

[0059]

[0060] Unlike previous technologies, the energy balance problem studied in this invention is closer to reality. The beneficial effects of this invention are as follows:

[0061] The realization of energy balance should not be at the expense of system benefits. Therefore, the present invention can, by designing a reasonable task allocation strategy, reduce energy consumption as much as possible and achieve relative energy balance among participants while ensuring system benefits, thereby maintaining the number of participants, extending the life of the mobile crowd intelligence perception system, and promoting the completion of perception tasks.

[0062] In practice, online task allocation is more common than offline task allocation, and multi-type tasks are more common than single-type tasks. Therefore, this paper studies the energy balance problem in online multi-type task allocation. Based on the Lyapunov optimization algorithm, we use system utility as the objective function and solve the problem using linear programming and genetic algorithms. We achieve long-term online dynamic control of task admission strategies and task allocation schemes.

[0063] For the first time, the variance of participants' residual energy was proposed as a criterion for measuring the degree of load balancing.

[0064] In order to evaluate the algorithm performance fairly and effectively, in addition to comparing with existing algorithms in the experimental simulation part, the present invention also designs a utility optimal algorithm (UOA) based on Lyapunov optimization.

[0065] Experiments show that the present invention significantly improves the energy balance level. No participants exit the system due to insufficient remaining energy, effectively maintaining the number of participants, extending the system life by 129.3%, and increasing the total benefit by 130.5%. Moreover, by adjusting the V value, the system can achieve the maximum average benefit. In addition, the energy balance capability of the present invention is long-term and effective, and will not be attenuated due to different V values.

[0066] Experiments have shown that the present invention can effectively balance participant energy, extend system lifespan, and maximize system benefits, even when there are fewer participants and more tasks. Compared with the benefit-optimizing algorithm and the LP-relaxation algorithm, no participants in the present invention exited the system due to insufficient remaining energy in the comparative experiment. The present invention effectively maintains the number of participants. Compared with the UOA and LP-relaxation algorithms, the system lifespan of the present invention is extended by 129.3% and 130.4%, respectively. Compared with the UOA, the total system benefit of the present invention increases by 130.5%, and the average system benefit is maximized by adjusting the value of V. In addition, the energy balancing capability of the present invention is continuously effective and does not decay with changes in the V value. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Schematic diagram of a typical mobile crowdsensing system;

[0068] Figure 2Comparison chart of the residual energy variance of participants between the present invention and different algorithms;

[0069] Figure 3 A comparison chart of the system benefits of the present invention and different algorithms;

[0070] Figure 4 Average length when V value is different Different change curves of

[0071] Figure 5 The residual energy variance V when V value is different c The change curve diagram of

[0072] Figure 6 The curve of average benefit U_avg changing with V value. DETAILED DESCRIPTION

[0073] The present invention will be further described below with reference to the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention fall within the scope of protection of the present invention.

[0074] The system time discrete model of the present invention is as follows:

[0075] In actual situations, different applications request different sensing data. Therefore, the MCS system studied in this paper has multiple types of sensing tasks. Assume that there are M types of sensing tasks, let j represent different sensing task types, j∈{1,…,M}. Divide time into discrete time slots of equal length t, t∈{0,1,2,…}. The type and number of sensing tasks arriving at the platform in each time slot are different. Let O j (t) represents the number of sensing tasks of type j arriving at the sensing platform at time slot t, and is an independent and identically distributed random variable (O j (t)is iidover slots with E{O j (t)}=λ i for j∈{1,…,M}), It is worth noting that not all arriving perception tasks can enter the perception platform to be executed. The platform decides which tasks can enter the system and be executed based on the execution status of the tasks in the previous time slot, that is, the selection decision. j (t) represents the number of sensing tasks of type j that enter the sensing platform after the platform selection decision at time slot t, 0≤o j (t)≤O j (t).

[0076] Assume that there are N perception participants registered in the perception platform, participating in and completing perception tasks. Let i represent different perception participants, i∈{1,…,N}. In each time slot, the platform needs to assign different types of tasks to the perception participants, that is, the allocation decision. x(t) represents the task allocation in time slot t, x ij (t) indicates whether task j is assigned to participant i in time slot t, that is, whether participant i executes task j. ij When (t) = 1, participant i performs task j; when x ij When (t) = 0, participant i does not perform task j. In each time slot, the same participant can perform multiple types of unit-number tasks at the same time. After task allocation, the number of tasks j that can be performed in time slot t is expressed as r j (t):

[0077]

[0078] where 0≤r j (t)≤N.

[0079] Let Q(t)=(Q1(t),Q1(t),…,Q M (t)) represents the backlog vector of different types of perception request queues in the time slot t platform, and its dynamic change obeys the following formula:

[0080] Q j (t+1)=max[Q j (t)-r j (t),0]+o j (t) (2)

[0081] Among them, Q j (0)=0, j∈{1,…,M}. For all j and t, Q j (t)≥0.

[0082] If Q j (t) Satisfy:

[0083]

[0084] Then Q j (t) is the mean rate stable, that is, all the sensing tasks entering the sensing platform will be executed; when {Q j When {(t)},j∈{1,…,M} all satisfy the above formula, the MCS system is said to be stable.

[0085] Perceive the remaining energy of participants and their variance:

[0086] When a perception participant performs a perception task, sensor data collection, local data processing, and data transmission will all lead to device energy consumption, and the energy consumption caused by different participants performing the same type of perception task will also vary greatly. ij represents the energy consumption of participant i when performing unit number task j, It represents the remaining energy after participant i completes the assigned task in time slot t, and its variation over time obeys the following formula:

[0087]

[0088] In order to reflect the difference in residual energy between different perception participants, the present invention uses the residual energy variance to measure it, and let V c (t) represents the remaining energy after all participants have completed their tasks in time slot t The variance of , that is:

[0089]

[0090] in, represents the mean residual energy of all participants,

[0091] The necessity of load balancing in mobile crowdsensing has been explained above. To ensure load balancing among participants, the present invention imposes a limit on the residual energy variance:

[0092]

[0093] Among them, V max is the maximum variance value specified by the MCS system. V max The values ​​are different.

[0094] 3. System benefits

[0095] Let U(t) represent the benefit of the sensing platform in time slot t, whose size depends on the number of sensing tasks entering the platform,

[0096]

[0097] Where β represents the benefit that the perception platform can obtain by executing a unit number of tasks, which is a positive constant.

[0098] 4. Problem Formulation

[0099] The problem to be solved by the present invention is to ensure the energy load balance of each participant while maximizing the average benefit of the system by selecting control and task allocation under the condition of satisfying the stability of the perceived task queue. Therefore, the objective function of this problem is designed as follows:

[0100]

[0101] stconstraints(2)(3)(6)(9)

[0102] In order to solve the above optimization problem, the present invention adopts Lyapunov optimization theory as a dynamic load balancing strategy, which greatly reduces the complexity of problem solving.

[0103] In order to satisfy the inequality constraint (6), the present invention introduces a virtual queue. First, define the virtual queue z(t):

[0104] z(t+1)=max[z(t)-V max ,0]+V c (t) (10)

[0105] Here, z(0)=0, and for all t, z(t)≥0.

[0106] like:

[0107]

[0108] Then z(t) is said to be stable.

[0109] It can be seen intuitively from the above formula that when the residual energy variance V in a certain time slot c (t) is greater than the maximum variance V specified by the system max When the load is uneven due to task distribution, the virtual queue z(t) will increase. In order to maintain long-term queue stability, V should be reduced. c (t). Therefore, the above formula transforms the long-term inequality constraint into a virtual queue stability problem, which is proved as follows.

[0110] Theorem 1: When z(t) is stable, the constraint inequality (6) holds.

[0111] Proof: According to equation (10), there exists:

[0112] z(τ+1)=max[z(τ)-V max ,0]+V c (τ) (12)

[0113] Assume τ∈{0,1,…,t-1}, for t>0:

[0114]

[0115] Considering t→∞, we get the following:

[0116]

[0117] Therefore, if z(t) is average rate stable:

[0118]

[0119] therefore

[0120]

[0121] Right now:

[0122]

[0123] Therefore, the constraint inequality (6) is satisfied. Theorem 1 is proved.

[0124] At this point, the objective function is transformed into:

[0125]

[0126] stconstraints(2)(3)(11) (19)

[0127] 3.2 Dynamic Load Balancing Strategy

[0128] In order to satisfy the stability of the MCS system and the constraint inequality (6), the platform’s internal sensing request queue Q j (t) is combined with the virtual queue z(t), and the Lyapunov optimization function of time slot t is defined as:

[0129]

[0130] Define the Lyapunov drift function (penalty drift) as:

[0131]

[0132] Adding the utility function as a penalty function to the above drift function yields the drift-plus-penalty function:

[0133]

[0134] Here, V is a nonnegative constant. By adjusting the value of V, we can control the proportional relationship between stability and utility function. The role of V will be described in detail in subsequent simulation experiments.

[0135] Theorem 2: At each time slot t, any feasible solution of the objective function (8) or the objective function (18) satisfies the following inequality:

[0136]

[0137] in is a positive constant.

[0138] Proof: By 0≤o j (t)≤O j (t) It can be seen that:

[0139]

[0140] in addition:

[0141] (max[Q j (t)-r j (t),0]) 2 ≤(Q j (t)-r j (t)) 2 (25)

[0142] Squaring both sides of equation (2), we can obtain the following inequality:

[0143]

[0144] therefore:

[0145]

[0146] in is a positive constant.

[0147] Similarly, square both sides of equation (10), according to (max[z(t)-V max ,0]) 2 ≤(z(t)-V max ) 2 And equations (4) and (5), we can get:

[0148]

[0149] therefore:

[0150]

[0151] in is a positive constant.

[0152]

[0153] Considering Equation (27) and Equation (29), for j∈{1,…,M}, adding the right side of Equation (30) to both sides yields:

[0154]

[0155] Theorem 2 is proved.

[0156] Theorem 2 provides an upper bound for the drift-plus-penalty function. This invention minimizes this upper bound in each time slot by designing a dynamic load balancing strategy, thereby achieving queue stability, utility maximization, and load balancing. Let F(t) represent the right side of Equation (31), then:

[0157]

[0158] make

[0159]

[0160]

[0161] therefore

[0162] F(t)=B1+B2+f(o j (t))+g(x(t),o j (t))-z(t)V max (35)

[0163] Where B1 and B2 can be regarded as constants that do not change with the selection control and task allocation in the current time slot. The value of z(t) is determined by the length of the virtual queue in the previous time slot and the variance of the remaining energy. Therefore, -z(t)V max The term can also be considered a constant within the current time slot. Therefore, minimizing the upper bound of the drift-plus-penalty function is simplified to minimizing f(t) + g(t). Based on this, the present invention designs a dynamic load balancing strategy, as shown in Table 1.

[0164] Table 1 Dynamic load balancing strategy

[0165]

[0166] The above algorithm steps are: in each time slot t, the sensing platform takes turns to select each task of M tasks, and selects o j (t), so that the following formula is minimized: Perception platform selection x(t)={x ij (t),i∈{1,…,N},j∈{1,…,M}}, so that the following formula is minimized:

[0167]

[0168] The perception platform updates Q according to formula (2) j (t), j∈{1,…,M},

[0169] The perception platform is updated according to formula (4) i∈{1,…,N},

[0170] The perception platform updates z(t) according to formula (10).

[0171] 2. Strategy implementation based on linear programming and genetic algorithm

[0172] In order to implement the above dynamic load balancing strategy, it is necessary to solve the minimization problems in the selection control and task allocation processes respectively.

[0173] f(o j (t)) with o j (t) changes linearly, so the minimization problem of equation (33) is actually a linear programming problem, and its optimal solution is:

[0174]

[0175] For the minimization problem of equation (34), there are many unknown variables, and the solution space expands rapidly with the increase of the number of perception participants and the type of tasks. If an accurate algorithm is used to solve it, the amount of calculation will increase greatly. However, considering the characteristics of the task allocation process, the unknown variable x ij (t) takes a value range of 0 or 1, so the genetic algorithm is used to solve it.

[0176] Genetic algorithm is a heuristic algorithm that draws on the theory of biological evolution. First, the initial population is set, that is, the possible solution to the problem. Then, the next generation population is generated through inheritance, crossover, mutation and selection, and individuals with low fitness are gradually eliminated and individuals with high fitness are added. After many generations of evolution, an approximate optimal solution is found. Let P represent the initial population, which contains K individuals, P = {P k |k=0,…,K},the task allocation scheme of the present invention {x ij (t), i∈{1,…,N}, j∈{1,…,M}} as the binary encoding of the individual chromosome, equation (34) becomes a function of the individual chromosome:

[0177]

[0178] Set the fitness function to:

[0179] F k =-(g k -max{g k |k=0,…,K}) (38)

[0180] Different chromosomes have different fitness, F = {F k |k=0,…,K}.

[0181] After the offspring chromosomes are inherited from the parent chromosomes, they undergo crossover and mutation with the crossover probability crossover_rate and mutation probability mutation_rate respectively. The offspring with low fitness are eliminated, and the offspring with high fitness are retained and continue to perform inheritance, crossover, mutation and selection operations as the parent generation. After G generations of iterations, the individual chromosome with the highest fitness is the optimal task allocation solution.

[0182] Table 2 Minimization problem of Equation (37) solved by genetic algorithm

[0183]

[0184] The steps of the above algorithm are: randomly initialize the population P, for each individual P in the population k , crossover and mutation are performed according to the crossover probability and mutation probability, and the offspring with low fitness are eliminated according to the fitness function, and the offspring with high fitness are retained and continue to perform inheritance, crossover, mutation and selection operations as the parent generation. After iterating G generations, the individual chromosome with the highest fitness is the optimal task allocation plan.

[0185] Performance Analysis

[0186] This section analyzes and proves the stability and bounded performance of the queue Q(t) and the virtual queue z(t).

[0187] Stability analysis

[0188] Theorem 3: For problems (18)-(19), the queue Q(t) and the virtual queue z(t) are mean rate stable.

[0189] Proof: If problems (18)-(19) are feasible, then for any δ>0 there exists a dynamic load balancing strategy that satisfies: for all t,

[0190] E{U(t)}≥U opt -δ (39)

[0191] E{V c (t)}≤V max +δ (40)

[0192] E{o j (τ)}≤E{r j (t)}+δ (41)

[0193] U opt represents all feasible strategies that satisfy problems (18)-(19).

[0194] make have From equation (22), we can get:

[0195]

[0196] When δ = 0, equations (39), (40), (41) yield:

[0197] Δ v (Q(t),z(t))≤B-VU opt (43)

[0198] Where B is a positive constant that satisfies all the following t:

[0199]

[0200] According to Theorem 4.2 in the non-patent literature “J. Neely, Stochastic Network Optimization With Application to Communication and Queueing Systems [M]. San Rafael, CA, USA: Morgan and Claypool Publishers, 2010”, the queue Q(t) and the virtual queue z(t) are average rate stable, and the proposition is proved.

[0201] bounded performance:

[0202] Theorem 4: The average optimization strategy obtained by the dynamic load balancing strategy is determined by the following formula:

[0203]

[0204] in

[0205] prove:

[0206] For τ∈{0,1,…,t-1}, summing equation (43), we get: for all t>0,

[0207]

[0208]

[0209]

[0210] The proposition is proved.

[0211] In order to verify the superiority of the present invention, we selected two algorithms for comparison: the benefit optimization algorithm based on Lyapunov optimization and the LP-relaxation algorithm.

[0212] 1. Benefit Optimization Algorithm Based on Lyapunov Optimization

[0213] To effectively compare with the algorithm proposed in this paper, we also designed a benefit optimization algorithm based on Lyapunov optimization. This algorithm uses the Lyapunov optimization method and takes system benefit as the objective function to maximize benefit. It is an online dynamic task allocation algorithm that does not consider the energy load balance of participants. To maintain consistency, the system model, energy consumption, and system utility function settings in this algorithm are the same as those in the algorithm proposed in this paper, but no constraints are imposed on the residual energy variance of participants. Therefore, the objective function of this algorithm can be expressed as follows:

[0214]

[0215] stconstraints(2)(3) (50)

[0216] The specific parameter symbols are the same as above and will not be repeated here. The following solves this problem.

[0217] The Lyapunov optimization function for time slot t is defined as:

[0218]

[0219] Define the Lyapunov drift function (penalty drift) as:

[0220]

[0221] Adding the utility function as a penalty function to the above drift function yields the drift-plus-penalty function:

[0222]

[0223] Where V is a non-negative constant.

[0224] Theorem 5: At each time slot t, any feasible solution of problem (49) (50) satisfies the following inequality:

[0225]

[0226] in

[0227] The proof is the same as Theorem 2 and is omitted here.

[0228] Theorem 5 provides an upper bound for the drift-plus-penalty function. To achieve queue stability and maximize utility, this upper bound needs to be minimized in each time slot. By transforming the right side of equation (54), we can obtain:

[0229]

[0230] The design of the benefit-optimal algorithm based on Lyapunov optimization is shown in Table 3.

[0231] Table 3 Benefit-optimal algorithm based on Lyapunov optimization

[0232]

[0233] Among them, changes linearly with o j (t), so its optimal solution is:

[0234]

[0235] To minimize the upper bound, should be maximized:

[0236] ① When Q j (t)+o j (t)≥N, x ij (t)=1, i∈{1,…,N}, j∈{1,…,M}, that is, in order to achieve maximum benefit, all participants execute tasks;

[0237] ② When Q j (t)+o j (t)<N, select (Q j (t)+o j (t)) participants to execute the tasks in the queue.

[0238] 2. LP-relaxation algorithm

[0239] The LP-relaxation algorithm is proposed by the non-patent literature "Load Balanced Mobile User Recruitment for Mobile Crowdsensing Systems. IEEE Communications Letters, 2017", and achieves load balancing by controlling the maximum value of the energy consumed by executing tasks among different participants. It should be noted that this algorithm is not an online task allocation algorithm, so in the experiment, this algorithm only considers the number of tasks arriving at the platform in the current time slot, and the number of tasks does not have time correlation. Let U_maxmin(t) represent the utility of the sensing platform in time slot t, and its magnitude depends on the actual task execution situation of the participants,

[0240]

[0241] where β represents the utility that the sensing platform can obtain for executing a unit number of tasks, and is a positive constant.

[0242] The evaluation indicators are as follows:

[0243] 1. Variance of the remaining energy of the participants V c

[0244] From equation (5):

[0245]

[0246] The dynamic load balancing strategy proposed in this invention aims to prolong the system life by balancing the residual energy of each participant. Therefore, the residual energy variance is an important indicator reflecting the load balancing ability of different algorithms.

[0247] 2. System life T

[0248] Balancing energy loads among participants effectively maintains the number of participants, extending the lifespan of the mobile crowdsensing system and facilitating the completion of sensing tasks. To measure the impact of different algorithms on system lifespan, we assume that the system ceases operation and its lifespan ends when a device stops serving or the number of devices decreases. This paper represents the system lifespan T as the number of time slots during which all participants can function normally, i.e., the duration of normal MCS system operation.

[0249] 3. System benefits

[0250] The ultimate goal of improving the algorithm's load balancing ability is to improve system efficiency by extending system life. Therefore, system efficiency is an important indicator for measuring the pros and cons of task allocation strategies. System efficiency indicators are divided into average efficiency U_avg and total efficiency U_sum. different.

[0251] The calculation methods of system benefits vary for different algorithms. The dynamic load balancing algorithm based on Lyapunov optimization and the benefit optimization algorithm based on Lyapunov optimization are both long-term online task allocation algorithms. Therefore, the size of the system benefit depends on the number of sensing tasks entering the platform in the current time slot, that is, equation (7):

[0252]

[0253] Where β represents the benefit that the perception platform can obtain by executing a unit number of tasks and is a positive constant. However, the LP-relaxation algorithm is an offline task allocation algorithm, and the system benefit is determined by the actual task execution of the participants in the current time slot, that is, equation (57):

[0254]

[0255] Where β is the same as the above formula β.

[0256] Average benefit U_avg:

[0257] Total benefit U_sum:

[0258] 4. Average Captain

[0259] In order to verify the stability of the queue Q(t) and study the impact of V value on the performance of the MCS system, the present invention also proposes the average length index:

[0260] The present invention mainly conducts an experimental evaluation on the algorithm performance of OEBS when there are few participants and many tasks. The present invention sets 5 types of perception tasks. The number of different types of tasks arriving at the perception platform in each time slot is generated by Poisson distribution with different parameters λ, where λ1=10, λ2=5, λ3=15, λ4=25, and λ5=15. In the experiment, it is assumed that there are 5 participants performing perception tasks. In order to test the load balancing ability of the algorithm, different initial energies are set for each participant, namely C1=2500mAh, C2=2900mAh, C3=3000mAh, C4=1500mAh, and C5=2100mAh. As can be seen from the above, different participants consume different amounts of energy when performing the same type of perception tasks, and the same participant consumes different amounts of energy when performing different types of perception tasks. Therefore, the energy consumption when different participants perform a unit number of different types of perception tasks is set as follows:

[0261] Table 4 Energy consumption (mAh) of different participants when performing different types of perceptual tasks

[0262]

[0263] In practical applications, it is necessary to ensure that participants maintain the basic power of the sensing device. Therefore, the present invention also sets a minimum energy value C R =200mAh, that is, when the device energy is lower than 20mAh, which is 10% of the total power, the device stops serving.

[0264] The experiment runs for 500 time slots, t∈{0,1,…,499}. In order to maximize the benefits of both OEBS and UOS and make the experimental comparison more fair, we set V=15000 in OEBS and V=6000 in UOA, set β=1, and the maximum variance value V max = 10000. Since the present invention adopts a genetic algorithm to solve the minimization problem of equation (34), the genetic algorithm parameters are set as follows based on experience: the binary chromosome length is 5, the population size is 2000, the crossover rate is 0.8, the mutation rate is 0.005, and the number of evolutionary iterations is 100.

[0265] Firstly, a comparative experiment was conducted on the dynamic load balancing algorithm based on Lyapunov optimization, the benefit optimization algorithm based on Lyapunov optimization and the LP-relaxation algorithm. The results are as follows: Figure 2-Figure 3 shown.

[0266] Figure 2 Represents the variance of the remaining energy V of participants under different algorithms c Changes over time. As the perception task continues to execute, the variance of the remaining energy of the participants in the Lyapunov-optimized benefit-optimal algorithm and the LP-relaxation algorithm increases dramatically. c The increase and growth rate are both the largest, and the V of the dynamic load balancing algorithm based on Lyapunov optimization proposed in this invention is c Gradually decrease to V max , and eventually tends to 0. The system lifetime of the Lyapunov-optimized benefit-optimization algorithm was 218, with participant 4 exiting the system due to insufficient energy. The system lifetime of the LP-relaxation algorithm was 217, with participant 4 exiting the system due to insufficient energy. The system lifetime of the Lyapunov-optimized dynamic load balancing algorithm was 500, indicating that no participants exited, and the system continued to operate. Compared with the UOA and LP-relaxation algorithms, the OEBS system lifetime was extended by 129.3% and 130.4%, respectively. The main reason for this phenomenon is that while the LP-relaxation algorithm balances the energy consumed by task execution, it does not significantly balance the remaining energy or extend the system lifetime. The UOA algorithm, which primarily aims to maximize system benefits, does not balance the remaining energy or extend the system lifetime. Therefore, the remaining energy variance and system lifetime of the two algorithms are relatively similar. However, the Lyapunov-optimized dynamic load balancing algorithm fully considers the differences in the initial energy of participants. By controlling the remaining energy variance, it significantly improves load balancing, maintains the number of participants, and extends the system lifetime.

[0267] Figure 3It shows the variation of the system benefit U with time under different algorithms. The total system benefit of UOA is 15153, the total system benefit of the LP-relaxation algorithm is 4259, and the total system benefit of OEBS is 34930. For the LP-relaxation algorithm, the method of calculating the system benefit is different, so the total benefit is significantly lower than the other two algorithms. This invention mainly compares the total benefits of UOA and OEBS. The total benefit of OEBS is 130.5% higher than that of UOA. This is because the system life of OEBS is significantly higher than that of UOA, so the system benefit is significantly higher than other algorithms. To measure the impact of different algorithms on the system benefit more fairly and objectively, this invention also examines the average benefits of different algorithms: the average benefit of UOA is U_avg = 69.83, the average benefit of the LP-relaxation algorithm is U_avg = 19.63, and the average benefit of OEBS of this invention is U_avg = 69.86. By reasonably setting the value of V, not only is the total benefit of OEBS significantly higher than the other two algorithms, but its average benefit is also almost equal to that of UOA and can nearly reach the maximum value of 70. The reason for the maximum value of 70 will be described in detail below

[0268] In summary, UOA only considers the system benefit, so the average benefit is relatively high. However, this algorithm is at the cost of a huge difference in the remaining energy of participants, so the system life is limited. The LP-relaxation algorithm balances the energy consumed in executing tasks, but does not consider the difference in the initial energy of participants. Therefore, this algorithm cannot effectively balance energy and extend the system life. OEBS significantly improves the load balancing level, maintains the number of participants, significantly extends the system life, and at the same time the average benefit can reach the maximum value, and the total benefit is much higher than the other two algorithms.

[0269] To study the impact of the value of V on the queue backlog, we respectively set V = 1, V = 201, V = 401, V = 601, V = 801, V = 1001, V = 1201, V = 1401, V = 1601, V = 1801, V = 2001, and conducted experimental simulations on the dynamic load balancing algorithm based on Lyapunov optimization. The results are as Figure 4-Figure 5 shown.

[0270] From Figure 4 it can be seen that as the value of V continues to increase, the convergence value of the average queue length continues to increase, and the larger the value of V, the closer the convergence value is to the value of V. This is determined by Equation (36). When Q j (t) < Vβ, o j (t) = O j (t), and the average queue length continues to increase. When the queue backlog Q j (t) increases to Vβ, oj (t) = 0, average queue length tends to be stable and finally converges near the value of V. Therefore, the larger the value of V, the slower the convergence rate of the average queue length, that is the longer the time required for convergence and the larger the convergence value. The stability of the queue Q(t) is verified. It should be noted that the abnormality at the end of the curve when V = 801 is due to the system having a shorter lifespan than at other V values and exiting the service in advance.

[0271] Figure 5 represents the curve of the variance of the remaining energy V with different values of V c Obviously, the value of V has no effect on the change of V c That is, the load balancing ability of the algorithm proposed in this invention is continuously effective and will not decay due to different values of V.

[0272] To study the influence of the value of V on the system benefit, let V = 1, V = 2001, V = 4001, V = 6001, V = 8001, V = 10001, V = 12001, V = 1400, V =, V = 16001, V = 18001, V = 20001 respectively. From Figure 6 it can be seen that as the value of V continuously increases, the average benefit U_avg also gradually increases and finally reaches the maximum value when U_avg = 70. It can be seen from the figure that when V = 12001, U_avg is already close to the maximum value and tends to be stable. After that, increasing the value of V will not improve the average benefit. The reason for the above phenomenon is that: when Q j (t) < Vβ, o j (t) = O j (t), the larger the value of V, the j slower the convergence rate of Q j (t), so the more time slots of o j (t) = O (t); and

[0273] The beneficial effects of this invention are as follows:

[0274] The realization of energy balance should not be at the expense of system benefits. Therefore, the present invention can, by designing a reasonable task allocation strategy, reduce energy consumption as much as possible and achieve relative energy balance among participants while ensuring system benefits, thereby maintaining the number of participants, extending the life of the mobile crowd intelligence perception system, and promoting the completion of perception tasks.

[0275] In practice, online task allocation is more common than offline task allocation, and multi-type tasks are more common than single-type tasks. Therefore, this paper studies the energy balance problem in online multi-type task allocation. Based on the Lyapunov optimization algorithm, we use system utility as the objective function and solve the problem using linear programming and genetic algorithms. We achieve long-term online dynamic control of task admission strategies and task allocation schemes.

[0276] For the first time, the variance of participants' residual energy was proposed as a criterion for measuring the degree of load balancing.

[0277] In order to evaluate the algorithm performance fairly and effectively, in addition to comparing with existing algorithms in the experimental simulation part, the present invention also designs a utility optimal algorithm (UOA) based on Lyapunov optimization.

[0278] Experiments show that the present invention significantly improves the energy balance level. No participants exit the system due to insufficient remaining energy, effectively maintaining the number of participants, extending the system life by 129.3%, and increasing the total benefit by 130.5%. Moreover, by adjusting the V value, the system can achieve the maximum average benefit. In addition, the energy balance capability of the present invention is long-term and effective, and will not be attenuated due to different V values.

[0279] Experiments have shown that the present invention can effectively balance participant energy, extend system lifespan, and maximize system benefits, even when there are fewer participants and more tasks. Compared with the benefit-optimizing algorithm and the LP-relaxation algorithm, no participants in the present invention exited the system due to insufficient remaining energy in the comparative experiment. The present invention effectively maintains the number of participants. Compared with the UOA and LP-relaxation algorithms, the system lifespan of the present invention is extended by 129.3% and 130.4%, respectively. Compared with the UOA, the total system benefit of the present invention increases by 130.5%, and the average system benefit is maximized by adjusting the value of V. In addition, the energy balancing capability of the present invention is continuously effective and does not decay with changes in the V value.

[0280] As used herein, the word "preferred" is intended to serve as an example, instance, or illustration. Any aspect or design of the present invention described as "preferred" is not necessarily to be construed as being more advantageous than other aspects or designs. Rather, the use of the word "preferred" is intended to present concepts in a specific manner. As used herein, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise specified or clear from the context, "X employs A or B" is intended to mean any of the naturally inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied in any of the aforementioned examples.

[0281] In summary, the above embodiment is one implementation method of the present invention, but the implementation method of the present invention is not limited to the described embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A dynamic energy balancing method for mobile crowd sensing based on Lyapunov optimization, characterized by: The following steps are involved: The energy balance problem is formulated as a time-discrete model; The dynamic load balancing strategy is determined by Lyapunov optimization algorithm, the system utility is used as the objective function, and the variance of the residual energy of participants is used to measure the load balancing degree. Solve the problem based on linear programming and genetic algorithm to obtain the long-term dynamic energy balance for online tasks and assign tasks to perception participants; Wherein, the time discrete model is: N perception participants register to the perception platform, participate in and complete perception tasks. There are M types of perception tasks, j represents different perception task types, j∈{1,…,M}, and divides time into discrete time slots of equal length t, O j (t) represents the number of sensing tasks of type j that arrive at the sensing platform at time slot t. The sensing platform assigns different types of tasks to sensing participants in each time slot; If Q j (t) Satisfy: Then Q j (t) is the average rate stable, that is, all the sensing tasks entering the sensing platform will be executed; when {Q j (t)}, j∈{1,…,M} all satisfy the above formula, the mobile crowd sensing system is stable. When the sensing participants perform the sensing task, sensor data collection, local data processing and data transmission will all lead to device energy consumption, and the energy consumption caused by different participants performing the same type of sensing task will vary. In order to reflect the difference in residual energy of different sensing participants, the residual energy variance is used to measure it, V c (t) represents the remaining energy after all participants have completed their tasks in time slot t The variance of , that is: in, represents the mean residual energy of all participants, It represents the remaining energy after participant i completes the assigned task in time slot t, and its variation over time obeys the following formula: Among them, c ij It represents the energy consumption of participant i when performing unit number task j.

2. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 1, characterized in that: In the time discrete model, at each time slot, the perception platform assigns different types of tasks to the perception participants, i.e., the allocation decision, x(t) represents the task allocation at time slot t, x ij (t) indicates whether task j is assigned to perception participant i in time slot t, i∈{1,…,N}, that is, whether perception participant i performs task j. ij When (t) = 1, the perceptual participant i performs task j; when x ij When (t) = 0, the perceptual participant i does not perform task j. In each time slot, the same perceptual participant can simultaneously perform multiple types of unit-number tasks. After task allocation, the number of tasks j that can be performed in time slot t is expressed as r. j (t): r j (t)=Σ i∈N x ij (t) (2) where 0≤r j (t)≤N; Q(t)=(Q1(t),Q1(t),…,Q M (t)) represents the backlog vector of different types of perception request queues in the perception platform at time slot t, and its dynamic change obeys the following formula: Q j (t+1)=max[Q j (t)-r j (t),0]+o j (t) (3) Among them, j (t) represents the number of sensing tasks of type j that enter the sensing platform after the sensing platform selection decision at time slot t, 0≤o j (t)≤O j (t).

3. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 1, characterized in that: To ensure load balancing among participants, a limit is imposed on the variance of the remaining energy: Among them, V max The maximum variance value specified for the mobile crowdsensing system.

4. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 1, characterized in that: U(t) represents the benefit of the perception platform in time slot t, and its size depends on the number of perception tasks entering the platform. Where β represents the benefit that the perception platform can obtain by executing a unit number of tasks, which is a positive constant.

5. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 4, characterized in that: The problem that the time discrete model needs to solve is to ensure the energy load balance of each participant while maximizing the average benefit of the system by selecting control and task allocation under the condition of satisfying the stability of the perceived task queue. The objective function of the problem is: stconstraints(1)(3)(8) Wherein formula (8) is: Then the virtual queue z(t) is said to be stable.

6. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 5, characterized in that: The virtual queue z(t) is defined as follows: z(t+1)=max[z(t)-V max ,0]+V c (t) (9) Here, z(0)=0, and for all t, there exists a virtual queue z(t)≥0.

7. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 1, characterized in that: The dynamic load balancing strategy includes: At each time slot t, the sensing platform takes turns selecting each of the M tasks and selects o j (t), so that the following formula is minimized: Perception platform selection x(t)={x ij (t),i∈{1,…,N},j∈{1,…,M}}, so that the following formula is minimized: The perception platform updates Q according to formula (2) j (t), j∈{1,…,M}, The perception platform is updated according to formula (5) The perception platform updates z(t) according to formula (9).

8. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 7, characterized in that: The optimization function of the Lyapunov optimization algorithm is:

9. The method for dynamic energy balancing of mobile crowd intelligence perception based on Lyapunov optimization according to claim 7, characterized in that: The problem solving based on linear programming and genetic algorithm includes: Randomly initialize the population P, for each individual P in the population k , crossover and mutation are performed according to the crossover probability and mutation probability, and the offspring with low fitness are eliminated according to the fitness function, and the offspring with high fitness are retained and continue to perform inheritance, crossover, mutation and selection operations as the parent generation. After iterating G generations, the individual chromosome with the highest fitness is the optimal task allocation solution; The fitness function is as follows: F k =-(g k -max{g k |k=0,…,K}) Among them, K is the number of individuals in the population, g k is a function of individual chromosomes:

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