Task offloading method based on resource reallocation under connection time constraints in connected vehicle networks

By establishing a traffic flow model and using assimilation mutation algorithm for resource redistribution, the connection time constraints and resource allocation problems of task unloading in the Internet of Vehicles are solved, and the success rate and system efficiency of task unloading are improved.

CN114599014BActive Publication Date: 2025-03-14CHONGQING UNIV OF POSTS & TELECOMM
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Patent Information

Application Number
CN202210261412.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-03-16
Publication Date
2025-03-14
Estimated Expiration
2042-03-16

AI Technical Summary

Technical Problem

In the Internet of Vehicles, MEC-based task offloading has problems such as connection time constraints, unreasonable channel resource allocation, and edge server resource occupation, resulting in failed task offloading or unoptimized resource allocation.

Method used

By establishing a traffic flow model, using greedy ideas to match vehicles, using assimilation variation algorithm and niche improvement balance optimizer optimization algorithm to redistribute resources to ensure the connection time of task offloading and the effectiveness of resource allocation.

Benefits of technology

It improves the stability of inter-vehicle connections and task unloading success rate, reduces the timeout rate and system costs, and realizes the effectiveness of networked vehicle tasks unloading.

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Abstract

The present invention relates to a task unloading method based on resource reallocation under the connection time constraint in a vehicle network, which belongs to the field of mobile communication technology and includes the following steps: S1: establishing a traffic flow model, deducing the driving speed according to the position information of the vehicle, and calculating the connection time between vehicles based on equivalent conversion; S2: matching vehicles based on the greedy idea; S3: comprehensively representing the resource allocation of unloading decisions, channel resource allocation, newly generated tasks and tasks being calculated as a solution matrix, probabilistic mutation strategies and correction algorithms for mutation problems are proposed for different unloading decisions in the iterative process, and normalizing some unloading decisions and resource allocation to meet the constraint conditions; S4: iteratively optimizing the solution matrix based on the assimilation mutation algorithm and the microhabitat improved balance optimizer optimization algorithm. The method improves the connection stability between vehicles and the success rate of task unloading, and reduces the timeout rate and system cost.
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Description

Technical Field

[0001] The present invention belongs to the technical field of mobile communications and relates to a task unloading method based on resource reallocation under connection time constraints in a vehicle network. Background Art

[0002] With the development of deep learning, various new applications have emerged, such as augmented reality driving, image processing, vehicle / pedestrian recognition, natural language processing and other computationally intensive and delay-sensitive applications. Usually, each of these tasks requires a large amount of computing resources and storage resources. Mobile cloud computing is a feasible solution. Cloud servers have more powerful computing resources than vehicles. The disadvantage is that cloud servers are deployed far away from the road, and their inherent propagation delay is not friendly to delay-sensitive tasks. By deploying MEC servers next to the road, vehicles can easily apply for computing resources and storage resources from MEC servers without causing excessive propagation delay, thereby meeting the delay requirements of tasks. However, there are some problems with the current task offloading based on MEC in the Internet of Vehicles. First, when a vehicle offloads a task to an edge server or a nearby vehicle, it drives out of the connection range before the calculation result is returned, which will lead to the failure of offloading; then, when the offloading vehicle offloads tasks to the RSU and idle vehicles, they share the same channel resources, which need to be reasonably allocated; finally, there may be tasks being calculated on the edge server, which will affect resource allocation. Summary of the invention

[0003] In view of this, an object of the present invention is to provide a task offloading method based on resource reallocation under connection time constraints in an Internet of Vehicles.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A method for task offloading based on resource reallocation under connection time constraints in an Internet of Vehicles comprises the following steps:

[0006] S1: Establish a traffic flow model, deduce the driving speed based on the vehicle's location information, and calculate the connection time between vehicles based on equivalent conversion;

[0007] S2: Match vehicles based on the greedy idea according to the connection time between vehicles; define the priority value of the calculation task, and unload the vehicle in order of priority value to select the unmatched idle vehicle with the longest connection time;

[0008] S3: Based on the assimilation mutation algorithm of offloading scheme encoding, the offloading decision, channel resource allocation, resource allocation of newly generated tasks and tasks being calculated are comprehensively represented as a scheme matrix. A probabilistic mutation strategy and a correction algorithm for the mutation problem are proposed for different offloading decisions in the iterative process. Some offloading decisions and resource allocation are normalized to meet the constraints.

[0009] S4: The optimization algorithm of the equilibrium optimizer based on assimilation mutation algorithm and microhabitat improvement is used to iteratively optimize the solution matrix, divide the solution population into sub-populations according to the size of the fitness function, improve the equilibrium state pool based on the sub-population, and improve the mass generation rate based on the idea of ​​higher probability and smaller range exploration in the later stage of iteration. An expansion function is proposed to describe the task timeout and task failure, which together with the system cost constitutes the fitness function of the equilibrium optimizer.

[0010] Further, the traffic flow model is established in step S1, including: establishing a traffic flow model with the center of the intersection as the origin, assuming that the RSU is located at the origin, dividing the vehicles into four lanes along the positive direction of the X axis, along the negative direction of the X axis, along the positive and reverse direction of the Y axis, and along the negative direction of the Y axis, and each lane is divided into multiple sub-lanes, represented as Road = {road1, road2, ..., road 4×τ}, τ represents the number of sublanes, and the vehicle is represented by v j ={x j ,y j ,road i}, x j ,y j Indicates the horizontal and vertical coordinates of the vehicle, road i Indicates vehicle v j Driving on the road i Lane.

[0011] Furthermore, in step S1, the speed of the vehicle is related to the number of vehicles within the RSU range. The denser the vehicles in the same lane, the slower the speed of the vehicle. i The capacity is expressed as Cap i,max , the current number of vehicles is represented as Cap i , then road i The speed of the vehicle on s i It is expressed as:

[0012]

[0013] Where s min Indicates the minimum speed of the vehicle, s max Indicates the maximum speed of the vehicle; let rand i ∈(0.9, 1.1), road iThe speed of the vehicle on is rewritten as:

[0014]

[0015] When vehicles are driving on the road, the relative driving status between vehicles is described as: driving in the same lane, driving in different lanes in the same direction, driving in lanes in opposite directions, and driving in intersecting lanes. For two vehicles with known coordinates and driving speeds, moving or exchanging identities as a whole will not destroy their relative driving status. Based on this, the vehicles are first converted to the specified sub-lanes, and then a unified connection time calculation formula is used to solve it. The connection time calculation process is as follows:

[0016] S11: Initialize the vehicle and calculate the driving speed based on the lane information;

[0017] S12: Determine the relative driving state between vehicles according to the lane information of the vehicles;

[0018] S13: performing equivalent conversion on vehicles that are not in the designated lane according to the coordinate information of the vehicles;

[0019] S14: Calculate the connection time between vehicles using a unified connection calculation formula for the specified lane.

[0020] Further, step S2 includes establishing a task offloading model, in which the vehicle chooses to partially offload the computing task to the RSU and nearby idle vehicles through the PC5 interface, and the MEC server and the vehicle terminal carried by the RSU perform the calculation, or completely offload the computing task to the base station (BS) through the Uu interface, and transmit it to the cloud server for calculation; there are a total of N+M vehicles in the cell covered by the RSU, represented by V={v1, v2, v3, ..., v N+M}, where N vehicles generate computing tasks simultaneously, represented by Task = {task1, task2, task3, ..., task N}, the last M vehicles are idle vehicles; each task is represented by task n ={d n , z n , t n}, where d n Indicates the size of the data of the computing task itself, z n Indicates the number of CPU cycles required to complete the nth task, t n represents the maximum tolerable time of the nth task; tasks can be split and partially offloaded to edge servers and vehicles at the same time to speed up the calculation, but each task can only request one idle vehicle for assistance. Considering that the time consumption of offloading to the cloud server mainly comes from the propagation delay, the task is completely offloaded when offloading to the cloud server; for taskn , the unloading decision is defined as α n ={α n,0 , α n,1 , α n,2 , α n,3}, where α n,0 ∈{0, 1} indicates whether to offload the task to the cloud server.

[0021] Further, in step S2, according to the unloading vehicle v n With idle vehicle v N+m / RSU connection time, construct N×(M+1) connection time matrix, expressed as Matrix link , where the first M columns represent the unloaded vehicles v n With idle vehicle v N+m Connection time, Matrix link (n, M+1) represents the unloading vehicle v n The connection time with the RSU; the priority value of the computing task is defined as the weighted sum of its computing amount and data amount divided by the maximum tolerable delay, expressed as:

[0022]

[0023] where d n , z n , t n They are respectively computing tasks n The amount of data, the amount of computation and the maximum tolerable delay, θ represents the weight coefficient of the amount of data, and (1-θ) represents the weight coefficient of the amount of computation;

[0024] The unloading vehicles select the unmatched idle vehicles with the longest connection time in order of priority value, and the unloading vehicle set selected to be unloaded to the edge server and idle vehicles is represented as V rsu , the number is N rsu , the initial value of the idle vehicle matching state array Sta is 0, and the size of the vehicle matching matrix Match is min(N rsu , M)×2, the first column represents the unloaded vehicles, and the second column represents the matched idle vehicles; vehicle matching specifically includes the following steps:

[0025] S21: Calculate the priority value of each vehicle selected to be unloaded to the edge server;

[0026] S22: sorting the vehicles according to the priority values;

[0027] S23: The unloading vehicle with a large priority value selects the idle vehicle with the longest connection time in a greedy manner;

[0028] S24: Determine whether there are unmatched unloaded vehicles and idle vehicles. If so, go to step S23; otherwise, go to step S25;

[0029] S25: Output vehicle matching matrix.

[0030] Further, in step S3, there are N unloading vehicles within the coverage of the RSU, and the edge server has N′ tasks being calculated. The unloading decision includes four parameters: the decision to unload to the cloud server, the task ratio to be unloaded to nearby vehicles, the task ratio to be unloaded to the edge server, and the task ratio to be calculated locally. The side chain channel allocation includes two parameters: the channel ratio allocated for communication between the unloading vehicle and the RSU and the channel ratio allocated for communication between the unloading vehicle and the idle vehicle. The scheme is represented as a matrix of (N+N′)×7. The probabilistic mutation strategy is introduced to solve the problem of inconsistent binary unloading decisions. The maximum mutation probability is expressed as ε max , the minimum mutation probability is expressed as ε min , the maximum number of iterations is expressed as Iter max , the number of iterations is represented as iter, and the probability of binary decision variable mutation decreases linearly with the number of iterations, which is expressed as:

[0031]

[0032] According to ε iter Using Epsilon iter The -greedy strategy determines whether the binary decision variable mutates and generates a random number in [0, 1]. If the random number is greater than ε iter The binary decision variables remain unchanged, otherwise the unloading rate changes with the optimal solution. If at least one binary decision variable variation occurs, it means that the unloading vehicle has changed its choice of unloading to the cloud server for calculation or to the RSU / vehicle for local calculation. The vehicle matching algorithm is used to re-match the vehicle set; according to the results of the vehicle matching algorithm, the unloading rates and channel allocation rates of the unloading vehicles that are newly matched to idle vehicles and no longer matched to idle vehicles are transferred; the idle vehicle calculation has an additional process of transmitting data back and forth compared to the local calculation, and the time cost depends on the maximum calculation time. Therefore, the idle vehicle task unloading ratio should be less than the local calculation ratio, and the unloading rate of the unsatisfied unloading vehicle is transferred; finally, all unloading rates, channel allocations, and computing resource allocations are normalized.

[0033] Further, the assimilation mutation algorithm process in step S3 is as follows:

[0034] S31: Determine whether the binary uninstallation decision of the current solution is different from that of the optimal solution. If yes, go to step S32; otherwise, go to step S33.

[0035] S32: Calculate the mutation probability and calculate according to ε iter The -greedy policy determines whether to change the binary uninstall decision;

[0036] S33: Determine whether assimilation mutation has occurred, if yes, go to step S34, otherwise go to step S37;

[0037] S34: Update V according to the mutated solution rsu ,Use the vehicle matching algorithm to re-match the unloaded vehicles with the idle vehicles;

[0038] S35: Update the unloading decision of the unloading vehicle that loses the assistance of the idle vehicle, and transfer the share of the idle vehicle to the local and edge servers.

[0039] S36: The unloading decision of the unloading vehicle newly assisted by the idle vehicle is updated, and part of the computing task is transferred to the idle vehicle.

[0040] S37: Correct the situation where the idle vehicle unloading ratio is greater than the local calculated ratio;

[0041] S38: normalizing the offloading rate of each computing task;

[0042] S39: normalizing the channel resource allocation between the unloaded vehicle and the RSU / idle vehicle;

[0043] S310: Normalize resource allocation of edge servers.

[0044] Furthermore, in step S4, the population is first initialized and divided based on the microhabitat, each sub-population independently constructs an equilibrium state pool, and the optimal concentration particles of the adjacent sub-population are used to replace the average concentration particles in the original equilibrium state pool; then, based on the idea of ​​conducting higher probability and smaller range exploration in the later stage of iteration, the mass generation rate is improved, and an expansion function is proposed to inflate the system cost based on the calculation timeout and unloading failure. The concentration particles are updated as a fitness function, and the assimilation mutation algorithm is used to solve abnormal situations during the update process, and the equilibrium state pool is updated in real time; finally, after a round of updates, the sub-populations are mixed, and the sub-populations are re-divided according to adaptability for the next round of updates until the maximum number of iterations is reached.

[0045] Further, in step S4, the equilibrium optimizer concentration update formula is expressed as

[0046]

[0047]

[0048] Among them, C eqIndicates the concentration of the inflowing liquid, C′ now Indicates the concentration of the liquid in the container, V EO represents the size of the controlled volume, λ EO It is the ratio of liquid flow rate to controlled volume, indicating liquid flow rate;

[0049] The equilibrium state pool is improved by referring to the idea of ​​dividing populations in the microhabitat. The core of the microhabitat is to first classify all individuals in the population according to certain rules, then select some individuals from each category to form a subpopulation, sort the schemes according to the size of the fitness function, and divide the sorted schemes into N equal parts. sub intervals, and then randomly sort the solutions in the subintervals and divide them into M equal parts. sub subintervals, assuming there are Num plan The initial solution, the mth sub The subpopulation is represented by:

[0050]

[0051] Use The subpopulation represents the previous subpopulation of the msub-th subpopulation, satisfying

[0052]

[0053] mth sub The fifth element of the subpopulation equilibrium state pool is improved to The global optimal value of the subpopulation, and its equilibrium state pool is represented by “”

[0054]

[0055] in, They represent the four best concentration schemes in the msub-th subpopulation, represents the optimal concentration scheme of the previous subpopulation of the msub-th subpopulation;

[0056] In the early stage of iteration, the goal is to find the approximate range of the global optimal value. A larger exploration range can help the concentration particles to explore the search space more comprehensively. In the later stage of iteration, the concentration particles explore the search space in a smaller range with a higher probability, which can effectively improve the local optimization ability. F in formula (5) EO The function is a decreasing function with an initial value of 1, which converts the mass generation rate G EO It is expressed as:

[0057] G EO =GCP(C eq -λ EO ·C now )

[0058]

[0059] Where r1 and r2 are both random numbers between 0 and 1;

[0060] In addition to considering the system cost, the adaptability of the scheme also needs to consider whether the task completion time meets the maximum tolerable delay constraint of the task, and whether the unloading time meets the connection time constraint. Without loss of generality, the time constraint is converted into a penalty function. In order to make the value of the penalty function match the system cost, the penalty function is constructed in the form of an expansion function, that is, the value of the penalty function is determined based on the task cost;

[0061] First, for the maximum tolerable delay constraint, the actual completion time of a single task T n and the maximum tolerable delay t n The cost inflation function of a single task is constructed based on the ratio of

[0062]

[0063] For the connection time constraint, if the task is chosen to be offloaded to the RSU and the idle vehicle, and the connection time constraint is not met, the offloading will fail and the actual completion time of the task will be infinite, so it is classified into the else case in formula (10);

[0064] For the task that the edge server is computing n′ , the total computational cost cannot be known, and the penalty function is defined as a fixed value, expressed as:

[0065]

[0066] where t n′,rsu Represents task n′ The time that has been calculated, Represents task n′ The time required for calculation after computing resources are reallocated, t n′ Represents task n′ The maximum tolerable delay;

[0067] Finally, the total cost inflation function of the system is constructed based on the task timeout rate and task failure rate. sys and b sys Represents the timeout coefficient and failure coefficient, expressed as:

[0068]

[0069] where p overtime represents the ratio of the number of tasks that do not meet the maximum tolerable delay constraint to the total number of tasks, P failIt represents the ratio of the number of tasks that do not meet the connection time constraint to the total number of tasks;

[0070] The cost after the inflation of the single task cost and the total system cost is used as the fitness function of the balance optimizer. n The cost is denoted as H n , the fitness function is expressed as:

[0071]

[0072] H n represents the system cost of the newly arrived task, N represents the number of newly arrived tasks, and H′ n′ represents the system cost of the task being calculated, N′ represents the number of tasks being calculated, and Punish n′ represents the penalty function.

[0073] Further, the optimization algorithm process of the equilibrium optimizer based on the assimilation mutation algorithm and the microhabitat improvement in step S4 is as follows:

[0074] S41: Initialize the population composed of concentration particles;

[0075] S42: Calculate the fitness of particles at each concentration;

[0076] S43: Divide subpopulations according to fitness;

[0077] S44: Each subpopulation constructs a balanced state pool;

[0078] S45: Determine whether there is an optimal concentration particle in the iterative optimization process that is different from the binary decision of the current concentration particle. If yes, go to step S46, otherwise go to step S47;

[0079] S46: Use the assimilation mutation algorithm to mutate and repair abnormal situations;

[0080] S47: updating the concentration particles according to the improved equilibrium optimizer algorithm;

[0081] S48: Determine whether the current concentration particles are better than the equilibrium pool particles. If yes, go to S49, otherwise go to step 10:

[0082] S49: Update the balance state pool;

[0083] S410: Determine whether the maximum number of iterations has been reached, if yes, go to S412, otherwise go to S411;

[0084] S411: Mix sub-populations, and go to step S42;

[0085] S412: Obtain the optimal solution from the equilibrium state pool.

[0086] The channel capacity between the vehicle and the BS is expressed as:

[0087]

[0088] Among them B bs represents the bandwidth allocated by BS to each requesting vehicle, p n,bs Indicates vehicle v n Transmit power to BS, h n,bs Indicates vehicle v n The channel gain between the BS and N0 represents the power spectral density of the noise;

[0089] The channel capacity between vehicles and vehicles / RSUs is expressed as:

[0090]

[0091]

[0092] Among them B n,n+m , B n,rsu 、p n,n+m 、p n,rsu 、h n,n+m 、h n,rsu Represents vehicle v n With idle vehicle v n+m / Bandwidth, transmission power and channel gain between RSUs; the task vehicle can only select one idle vehicle for auxiliary calculation, and the communication bandwidth of all PC5 interfaces in the RSU cell meets

[0093]

[0094] Furthermore, the local computing model includes:

[0095] task n The local computation time is expressed as:

[0096]

[0097] where f n Indicates vehicle v n computing power;

[0098] task n The energy consumption of local vehicle calculation is expressed as

[0099] e n,local =κ(f n ) 2 α n,1 ·z n (19)

[0100] Where κ is the energy consumption coefficient of the vehicle computing chip;

[0101] task n The amount of data that needs to be transmitted to the edge server is α n,2 ·d n , the transmission time is expressed as

[0102]

[0103] The energy consumed by the vehicle during the transmission process is expressed as

[0104]

[0105] The edge server computing model includes:

[0106] The edge server computing time is expressed as:

[0107]

[0108] Among them, β n Refers to the edge server carried by RSU as task n The proportion of computing resources allocated, f rsu Refers to the computing power of the edge server;

[0109] task n The total time consumption of offloading to the edge server is expressed as:

[0110]

[0111] The total energy consumption of the edge server is the energy consumption of the vehicle during the transmission process, which is expressed as:

[0112]

[0113] Furthermore, the idle vehicle calculation model includes:

[0114] task n The amount of data that needs to be transmitted to the idle vehicle is α n,3 ·d n , the transmission time is expressed as:

[0115]

[0116] The energy consumed by the unloading vehicle during the transfer to the idle vehicle is expressed as:

[0117]

[0118] The idle vehicle calculation time is expressed as:

[0119]

[0120] Among them, f N+m Refers to the computing power of idle vehicles;

[0121] The energy consumption of idle vehicle auxiliary calculation is expressed as:

[0122]

[0123] Assuming that the amount of data in the calculation result is proportional to the amount of task data, the ratio is ω, and the idle vehicle uses the same transmission power as the unloaded vehicle, then the channel capacity is also R n,N+m , the time for the idle vehicle to return the calculation result is expressed as:

[0124]

[0125] The energy consumption of an idle vehicle returning the calculated result is expressed as:

[0126]

[0127] Therefore, the total time consumption of unloading to an idle vehicle is expressed as:

[0128]

[0129] The total energy consumption of unloaded vehicles and idle vehicles is expressed as:

[0130]

[0131] Furthermore, the cloud server computing model is:

[0132] task n The amount of data that needs to be transmitted to the BS is α n,0 ·d n , the transmission time is expressed as:

[0133]

[0134] The energy consumed by the unloading vehicle during transmission to the BS is expressed as:

[0135]

[0136] Denote the propagation delay between BS and cloud server as t bs,cloud , the total time consumption of offloading to the cloud server is expressed as:

[0137]

[0138] The total energy consumption is expressed as:

[0139]

[0140] Further, the optimization model is modeled as:

[0141] task n The total time consumption is expressed as:

[0142] T n =α n,0 ·t n,bs +(1-α n,0 )·max(t n,local , t n,rsu , t n,N+m ) (37)

[0143] task n The total energy consumption is expressed as:

[0144] E n =α n,0 ·e n,bs +(1-α n,0 )·(e n,local +e n,rsu +e n,N+m ) (38)

[0145] The system cost is defined as the weighted sum of the total energy consumption of all vehicles and the computing time of each computing task, with μ representing the weight coefficient, expressed as:

[0146]

[0147] There are N′ tasks being executed, task n′ The remaining computational effort is denoted as z′ n′ , assuming that the edge server is initially task n′ The proportion of computing resources allocated is r n′ , the proportion of computing resources allocated after adjustment is expressed as r′ n′ , edge server computing task n′ The time variation of is expressed as:

[0148]

[0149] Uninstall the task after the decision is made n′ The cost change caused by the change in edge server resource allocation is only related to the time change and is expressed as:

[0150]

[0151] The cost of all executing tasks is expressed as:

[0152]

[0153] The optimization function is established with the goal of minimizing the system cost, which is expressed as:

[0154]

[0155] The beneficial effects of the present invention are: the method effectively improves the stability of vehicle-to-vehicle connection and the success rate of task offloading, reduces the timeout rate and system cost, and realizes the effectiveness of vehicle networking task offloading.

[0156] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0157] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0158] Figure 1 Offload model for single RSU task. DETAILED DESCRIPTION

[0159] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0160] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0161] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0162] See also Figure 1 , describes a network model consisting of unloaded vehicles, idle vehicles, RSU / edge servers, and base stations. In this model, vehicles can choose to partially offload computing tasks to RSUs and nearby idle vehicles through the PC5 interface, and the MEC server and vehicle terminal carried by the RSU will perform the calculations, or completely offload to the base station (BaseStation, BS) through the Uu interface and transmit to the cloud server for calculation. The advantage of offloading to MEC servers and nearby vehicles is that the propagation delay is small and the task calculation time can be reduced through collaboration. However, MEC server resources are limited and cannot meet the offloading needs of all vehicles. Therefore, selectively offloading tasks to cloud servers can increase system benefits.

[0163] In the scenario of the present invention, there are a total of N+M vehicles in the cell covered by the RSU, which is represented by V={v1, v2, v3, ..., v N+M}, where N vehicles generate computing tasks simultaneously, represented by Task = {task1, task2, task3, ..., task N}, and the last M vehicles are idle vehicles. The coverage of the BS is the entire block, and the spectrum is divided using orthogonal frequency division multiplexing, so the communication between the vehicle and the BS can be done without considering interference. The BS allocates a fixed bandwidth for each requesting vehicle, denoted as B bs , then the channel capacity between the vehicle and the BS is expressed as

[0164]

[0165] where p n,bs Indicates vehicle v n Transmit power to BS, h n,bs Indicates vehicle v n The channel gain between BS and the receiver, and N0 represents the power spectral density of the noise.

[0166] The communication between vehicles and between vehicles and RSUs shares the same bandwidth B sl, then the channel capacity between vehicles and vehicles / RSUs is expressed as

[0167]

[0168]

[0169] In formula (15) and (16), B n,n+m , B n,rsu 、p n,n+m 、p n,rsu 、h n,n+m 、h n,rsu Represents vehicle v n With idle vehicle v n+m The bandwidth, transmission power and channel gain between RSUs. The task vehicle can only select one idle vehicle for auxiliary calculation, and the communication bandwidth of all PC5 interfaces in the RSU cell meets

[0170]

[0171] 1) Local computing

[0172] The local computing part only considers the time and energy consumption generated by vehicle computing.

[0173] Use f n Indicates vehicle v n The computing power of the task is in cycles / s. n The local computation time is expressed as

[0174]

[0175] Task n The energy consumption of local vehicle calculation is expressed as

[0176] e n,local =κ(f n ) 2 α n,1 ·z n (19)

[0177] In formula (19), κ is the energy consumption coefficient of the vehicle computing chip, which is generally 10 -26 .

[0178] 2) Edge Server Computing

[0179] The edge server calculation part needs to consider the time and energy consumption of the vehicle sending task data to the edge server, as well as the time consumption of the edge server computing tasks. Due to the large downlink transmission power of the edge server and the small amount of calculation result data, the time and energy consumption of the vehicle when returning the calculation result is not considered.

[0180] task n The amount of data that needs to be transmitted to the edge server is α n,2 ·d n , the transmission time is expressed as

[0181]

[0182] The energy consumed by the vehicle during the transmission process is expressed as

[0183]

[0184] The edge server computing time is expressed as

[0185]

[0186] In formula (22), β n Refers to the edge server carried by RSU as task n The proportion of computing resources allocated, f rsu Refers to the computing power of the edge server, and the unit is also cycles / s.

[0187] Therefore, task n The total time consumption of offloading to the edge server is expressed as

[0188]

[0189] The total energy consumption is the energy consumption of the vehicle during the transmission process, expressed as

[0190]

[0191] 3) Idle vehicle calculation model

[0192] When idle vehicles assist in computation, it is necessary to consider the time and energy consumed by vehicles sending data to idle vehicles. In addition, since idle vehicles have limited sending power when returning computation results, the process of unloaded vehicles receiving computation results cannot be ignored.

[0193] task n The amount of data that needs to be transmitted to the idle vehicle is α n,3 ·d n , the transmission time is expressed as

[0194]

[0195] The energy consumed by the unloading vehicle during the transfer to the idle vehicle is expressed as

[0196]

[0197] The idle vehicle calculation time is expressed as

[0198]

[0199] In formula (27), f N+m Refers to the computing power of idle vehicles.

[0200] The energy consumption of idle vehicle auxiliary calculation is expressed as

[0201]

[0202] Assuming that the amount of data in the calculation result is proportional to the amount of task data, the ratio is ω, and the idle vehicle uses the same transmission power as the unloaded vehicle, then the channel capacity is also R n,N+m , the time for the idle vehicle to return the calculation result is expressed as

[0203]

[0204] The energy consumption of the idle vehicle returning the calculated result is expressed as

[0205]

[0206] Therefore, the total time consumption of unloading to an idle vehicle is expressed as

[0207]

[0208] The total energy consumption of unloaded vehicles and idle vehicles is expressed as

[0209]

[0210] 4) Cloud Server Computing Model

[0211] When the cloud server calculates, it mainly considers the time and energy consumption of the vehicle sending the task to the BS, as well as the two-stage propagation delay consumption between the BS and the cloud server. Since the cloud server has extremely strong computing power, the time consumed by its computing tasks is ignored, and the time it takes for the calculation results to be transmitted back to the vehicle from the BS is also ignored.

[0212] task n The amount of data that needs to be transmitted to the BS is α n,0 ·d n , the transmission time is expressed as

[0213]

[0214] The energy consumed by the unloading vehicle during the transmission to the BS is expressed as

[0215]

[0216] Denote the propagation delay between BS and cloud server as tbs,cloud , the total time consumption of offloading to the cloud server is expressed as

[0217]

[0218] The total energy consumption is expressed as

[0219]

[0220] 3. Optimization Problem Modeling

[0221] Assuming that the vehicle can transmit data to the RSU and idle vehicles at the same time, the task n The total time consumption is expressed as

[0222] T n =α n,0 ·t n,bs +(1-α n,0 )·max(t n,local , t n,rsu , t n,N+m ) (37)

[0223] task n The total energy consumption is expressed as

[0224] E n =α n,0 ·e n,bs +(1-α n,0 )·(e n,local +e n,rsu +e n,N+m ) (38)

[0225] The system cost is defined as the weighted sum of the total energy consumption of all vehicles and the computing time of each computing task, with μ representing the weight coefficient, expressed as:

[0226]

[0227] The weight coefficient μ in the formula can be adjusted according to actual conditions. For example, when the computing task is sensitive to latency, μ can be increased, and when it is sensitive to energy, μ can be reduced.

[0228] The connection time between the vehicle and the RSU / vehicle is limited. If too many computing tasks are offloaded to the RSU / vehicle with a shorter connection time, the offloaded vehicle will not be able to receive the returned results and the calculation will fail. n Select an idle vehicle v N+m As an auxiliary vehicle, the vehicle v n With v N+m The connection time is represented by link n,N+m , vehicle v nThe connection time with RSU is represented by link n,rsu .

[0229] In an actual traffic environment, when a new batch of computing tasks is offloaded, the edge server has tasks that are being executed and cannot allocate all computing resources to the new tasks. However, the computing resources allocated to them can be adjusted under the condition of meeting the maximum tolerable delay of the tasks being executed, so as to meet the needs of the new tasks and minimize the system cost. Assume that there are N′ tasks being executed, task n′ The remaining computational effort is denoted as z′ n′ , assuming that the edge server is initially task n′ The proportion of computing resources allocated is r n′ , the proportion of computing resources allocated after adjustment is expressed as r′ n′ , then the edge server calculates the task n′ The time variation of

[0230]

[0231] From formula (23), we can get that the task after the offloading decision is determined is n′ The cost change caused by the change in edge server resource allocation is only related to the time change and is expressed as

[0232]

[0233] The cost of all executing tasks is expressed as

[0234]

[0235] The optimization function is established with the goal of minimizing system cost, which is expressed as

[0236]

[0237] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A task offloading method based on resource reallocation under connection time constraints in an Internet of Vehicles, characterized in that: The following steps are involved: S1: Establish a traffic flow model, deduce the driving speed based on the vehicle's location information, and calculate the connection time between vehicles based on equivalent conversion; Step S1 of establishing a traffic flow model includes: establishing a traffic flow model with the center of the intersection as the origin, assuming that the RSU is located at the origin, dividing vehicles into four lanes along the positive direction of the X axis, along the negative direction of the X axis, along the positive and reverse direction of the Y axis, and along the negative direction of the Y axis, and each lane is divided into multiple sub-lanes, represented as Road = {road1, road2, ..., road 4×τ }, τ represents the number of sublanes, and the vehicle is represented by v j ={x j ,y j ,road i }, x j ,y j Indicates the horizontal and vertical coordinates of the vehicle, road i Indicates vehicle v j Driving on the road i Lane; The speed of the vehicle is related to the number of vehicles within the RSU range. The denser the vehicles in the same lane, the slower the speed of the vehicle. i The capacity is expressed as Cap i,max , the current number of vehicles is represented as Cap i , then road i The speed of the vehicle on s i It is expressed as: Where s min Indicates the minimum speed of the vehicle, s max Indicates the maximum speed of the vehicle; let rand i ∈(0.9, 1.1), road i The speed of the vehicle on is rewritten as: When vehicles are driving on the road, the relative driving states between vehicles are described as: driving in the same lane, driving in different lanes in the same direction, driving in lanes in opposite directions, and driving in intersecting lanes. First, the vehicles are equivalently converted to the designated sub-lanes, and then a unified connection time calculation formula is used to solve the problem. The connection time calculation process is as follows: S11: Initialize the vehicle and calculate the driving speed based on the lane information; S12: Determine the relative driving state between vehicles according to the lane information of the vehicles; S13: performing equivalent conversion on vehicles that are not in the designated lane according to the coordinate information of the vehicles; S14: Calculate the connection time between vehicles using a unified connection calculation formula for a specified lane; S2: Match vehicles based on the greedy idea according to the connection time between vehicles; define the priority value of the computing task, and select the unmatched idle vehicle with the longest connection time in order of priority value; step S2 includes establishing a task offloading model, in which the vehicle chooses to offload part of the computing task to the RSU and nearby idle vehicles, and the MEC server and vehicle terminal carried by the RSU perform the calculation, or chooses to completely offload the computing task to the base station and transmit it to the cloud server for calculation; there are a total of N+M vehicles in the cell covered by the RSU, represented by V={v1, v2, v3, …, v N+M }, where N vehicles generate computing tasks simultaneously, represented by Task = {task1, task2, task3, ..., task N }, the last M vehicles are idle vehicles; each task is represented by task n ={d n , z n , t n }, where d n Indicates the size of the data of the computing task itself, z n Indicates the number of CPU cycles required to complete the nth task, t n represents the maximum tolerance of the nth task; tasks can be split and partially offloaded to edge servers and vehicles at the same time, but each task can only request one idle vehicle for assistance, and the task will be completely offloaded when offloading to the cloud server; for task n , the unloading decision is defined as α n ={α n,0 , α n,1 , α n,2 , α n,3 }, where α n,0 ∈{0, 1} indicates whether to offload the task to the cloud server; According to unloading vehicle v n With idle vehicle v N+m / RSU connection time, construct N×(M+1) connection time matrix, represented as Matrix link , where the first M columns represent the unloaded vehicles v n With idle vehicle v N+m Connection time, Matrix link (n, M+1) represents the unloading vehicle v n The connection time with the RSU; the priority value of the computing task is defined as the weighted sum of its computing amount and data amount divided by the maximum tolerable delay, expressed as: where d n , z n , t n They are respectively computing tasks n The amount of data, the amount of computation and the maximum tolerable delay, θ represents the weight coefficient of the amount of data, and (1-θ) represents the weight coefficient of the amount of computation; The unloading vehicles select the unmatched idle vehicles with the longest connection time in order of priority value, and the unloading vehicle set selected to be unloaded to the edge server and idle vehicles is represented as V rsu , the number is N rsu , the initial value of the idle vehicle matching state array Sta is 0, and the size of the vehicle matching matrix Match is min(N rsu , M)×2, the first column represents the unloaded vehicles, and the second column represents the matched idle vehicles; vehicle matching specifically includes the following steps: S21: Calculate the priority value of each vehicle selected to be unloaded to the edge server; S22: sorting the vehicles according to the priority values; S23: The unloading vehicle with a large priority value selects the idle vehicle with the longest connection time in a greedy manner; S24: Determine whether there are unmatched unloaded vehicles and idle vehicles. If so, go to step S23; otherwise, go to step S25; S25: output vehicle matching matrix; S3: Based on the assimilation mutation algorithm encoded in the offloading scheme, the offloading decision, channel resource allocation, resource allocation of newly generated tasks and tasks being calculated are comprehensively represented as a scheme matrix. A probabilistic mutation strategy and a correction algorithm for the mutation problem are proposed for different offloading decisions in the iterative process. Some offloading decisions and resource allocation are normalized to meet the constraints. In step S3, there are N unloading vehicles within the coverage of the RSU, and the edge server has N′ tasks being calculated. The offloading decision includes four parameters: the decision to offload to the cloud server, the proportion of tasks offloaded to nearby vehicles, the proportion of tasks offloaded to the edge server, and the proportion of tasks calculated locally. The side chain channel allocation includes two parameters: the proportion of channels allocated for communication between the offloading vehicle and the RSU and the proportion of channels allocated for communication between the offloading vehicle and the idle vehicle. The scheme is represented as a matrix of (N+N′)×7. The probabilistic mutation strategy is introduced to solve the problem of inconsistent binary offloading decisions. The maximum mutation probability is expressed as ε max , the minimum mutation probability is expressed as ε min , the maximum number of iterations is expressed as Iter max , the number of iterations is represented as iter, and the probability of binary decision variable mutation decreases linearly with the number of iterations, which is expressed as: According to ε iter Using Epsilon iter The -greedy strategy determines whether the binary decision variable mutates and generates a random number in [0, 1]. If the random number is greater than ε iter The binary decision variable remains unchanged, otherwise the unloading rate changes with the optimal solution. If at least one binary decision variable mutation occurs, the vehicle set is re-matched using the vehicle matching algorithm. According to the result of the vehicle matching algorithm, the unloading rate and channel allocation rate of the unloaded vehicles that are newly matched to idle vehicles and no longer matched to idle vehicles are transferred. The idle vehicle task unloading ratio should be less than the local calculation ratio, and the unloading rate of the unsatisfied unloading vehicles is transferred. Finally, all unloading rates, channel allocations, and computing resource allocations are normalized. The assimilation mutation algorithm process in step S3 is as follows: S31: Determine whether the binary uninstallation decision of the current solution is different from that of the optimal solution. If yes, go to step S32; otherwise, go to step S33. S32: Calculate the mutation probability and calculate according to ε iter The -greedy policy determines whether to change the binary uninstall decision; S33: Determine whether assimilation mutation has occurred, if yes, go to step S34, otherwise go to step S37; S34: Update V according to the mutated solution rsu ,Use the vehicle matching algorithm to re-match the unloaded vehicles with the idle vehicles; S35: updating the unloading decision of the unloading vehicle that loses the assistance of the idle vehicle, and transferring the share of the idle vehicle to the local and edge servers; S36: updating the unloading decision of the unloading vehicle newly assisted by the idle vehicle, and transferring part of the computing tasks to the idle vehicle; S37: Correct the situation where the idle vehicle unloading ratio is greater than the local calculated ratio; S38: normalizing the offloading rate of each computing task; S39: normalizing the channel resource allocation between the unloaded vehicle and the RSU / idle vehicle; S310: Normalizing resource allocation of edge servers; S4: The scheme matrix is ​​iteratively optimized based on the assimilation mutation algorithm and the microhabitat improved equilibrium optimizer optimization algorithm, the scheme population is divided into sub-populations according to the size of the fitness function, the equilibrium state pool is improved based on the sub-populations, the mass generation rate is improved based on the idea of ​​higher probability and smaller range exploration in the later stage of iteration, and the expansion function is proposed to describe the task timeout and task failure, which together with the system cost constitutes the fitness function of the equilibrium optimizer; in step S4, the population is first initialized and divided based on the microhabitat, each sub-population independently constructs the equilibrium state pool, and the average concentration particles in the original equilibrium state pool are replaced by the optimal concentration particles of the adjacent sub-population; then, the mass generation rate is improved based on the idea of ​​higher probability and smaller range exploration in the later stage of iteration, the expansion function is proposed to expand the system cost based on the calculation timeout and unloading failure, and the concentration particles are updated as the fitness function, the assimilation mutation algorithm is used to solve abnormal situations during the update process, and the equilibrium state pool is updated in real time; finally, after a round of update, the sub-populations are mixed, and the sub-populations are re-divided according to the adaptability for the next round of update until the maximum number of iterations is reached; In step S4, the equilibrium optimizer concentration update formula is expressed as Among them, C eq Indicates the concentration of the inflowing liquid, C′ now Indicates the concentration of the liquid in the container, V EO represents the size of the controlled volume, λ EO It is the ratio of liquid flow rate to controlled volume, indicating liquid flow rate; Referring to the idea of ​​dividing populations in microhabitats, the equilibrium state pool is improved; the schemes are sorted according to the size of the fitness function, and the sorted schemes are divided into N sub intervals, and then randomly sort the solutions in the subintervals and divide them into M equal parts. sub subintervals, assuming there are Num plan The initial solution, mth sub The subpopulation is represented by: Where Plan means plan; Use The subpopulation represents the mth sub The previous subpopulation of the subpopulation satisfies mth sub The fifth element of the subpopulation equilibrium state pool is improved to The global optimal value of the subpopulation, its equilibrium state pool is expressed as: in, Respectively represent the mth sub The four best concentration schemes among the subpopulations, Indicates the mth sub The optimal concentration scheme of the previous subpopulation of the subpopulation; The mass generation rate G EO It is expressed as: G EO =GCP(C eq -λ EO ·C' now ) Where r1 and r2 are both random numbers between 0 and 1; The time constraint is converted into a penalty function, and the penalty function is constructed as an expansion function, that is, the value of the penalty function is determined based on the task cost; First, for the maximum tolerable delay constraint, the actual completion time of a single task T n and the maximum tolerable delay t n The cost inflation function Exp of a single task is constructed based on the ratio of n , expressed as: For the connection time constraint, it is classified into the else case in formula (10); For the task that the edge server is computing n′ , the total computational cost cannot be known, and the penalty function is defined as a fixed value, expressed as: where t n′,rsu Represents task n′ The time that has been calculated, Represents task n′ The time required for calculation after computing resources are reallocated, t n′ Represents task n′ The maximum tolerable delay; Finally, the total cost inflation function of the system is constructed based on the task timeout rate and task failure rate. sys and b sys Represents the timeout coefficient and failure coefficient, expressed as: where p overtime represents the ratio of the number of tasks that do not meet the maximum tolerable delay constraint to the total number of tasks, P fail It represents the ratio of the number of tasks that do not meet the connection time constraint to the total number of tasks; The cost after the inflation of the single task cost and the total system cost is used as the fitness function of the balance optimizer. n The cost is denoted as H n , the fitness function is expressed as: H n represents the system cost of the newly arrived task, N represents the number of newly arrived tasks, and H′ n′ represents the system cost of the task being calculated, N′ represents the number of tasks being calculated, and Punish n′ represents the penalty function; The optimization algorithm process of the equilibrium optimizer based on the assimilation mutation algorithm and the microhabitat improvement in step S4 is as follows: S41: Initialize the population composed of concentration particles; S42: Calculate the fitness of particles at each concentration; S43: Divide subpopulations according to fitness; S44: Each subpopulation constructs a balanced state pool; S45: Determine whether there is an optimal concentration particle in the iterative optimization process that is different from the binary decision of the current concentration particle. If yes, go to step S46, otherwise go to step S47; S46: Use the assimilation mutation algorithm to mutate and repair abnormal situations; S47: updating the concentration particles according to the improved equilibrium optimizer algorithm; S48: Determine whether the current concentration particles are better than the equilibrium pool particles, if yes, go to S49, otherwise go to step 10; S49: Update the balance state pool; S410: Determine whether the maximum number of iterations has been reached, if yes, go to S412, otherwise go to S411; S411: Mix sub-populations, and go to step S42; S412: Obtain the optimal solution from the equilibrium state pool.

2. The method for task offloading based on resource reallocation under connection time constraints in the Internet of Vehicles according to claim 1, characterized in that: The channel capacity between the vehicle and the BS is expressed as: Among them B bs represents the bandwidth allocated by BS to each requesting vehicle, p n,bs Indicates vehicle v n Transmit power to BS, h n,bs Indicates vehicle v n The channel gain between the BS and N0 represents the power spectral density of the noise; The channel capacity between vehicles and vehicles / RSUs is expressed as: Among them B n,n+m , B n,rsu 、p n,n+m 、p n,rsu 、h n,n+m 、h n,rsu Represents vehicle v n With idle vehicle v n+m / Bandwidth, transmission power and channel gain between RSUs; the task vehicle can only select one idle vehicle for auxiliary calculation, and the communication bandwidth of all PC5 interfaces in the RSU cell meets 3. The method for task offloading based on resource reallocation under connection time constraints in the Internet of Vehicles according to claim 1, characterized in that: The local computing model includes: task n The local computation time is expressed as: where f n Indicates vehicle v n computing power; task n The energy consumption of local vehicle calculation is expressed as e n,local =κ(f n ) 2 α n,1 ·z n (19) Where κ is the energy consumption coefficient of the vehicle computing chip; task n The amount of data that needs to be transmitted to the edge server is α n,2 ·d n , the transmission time is expressed as The energy consumed by the vehicle during the transmission process is expressed as The edge server computing model includes: The edge server computing time is expressed as: Among them, β n Refers to the edge server carried by RSU as task n The proportion of computing resources allocated, f rsu Refers to the computing power of the edge server; task n The total time consumption of offloading to the edge server is expressed as: The total energy consumption of the edge server is the energy consumption of the vehicle during the transmission process, which is expressed as:

4. The method for task offloading based on resource reallocation under connection time constraints in the Internet of Vehicles according to claim 1, characterized in that: The idle vehicle calculation model includes: task n The amount of data that needs to be transmitted to the idle vehicle is α n,3 ·d n , the transmission time is expressed as: The energy consumed by the unloading vehicle during the transfer to the idle vehicle is expressed as: The idle vehicle calculation time is expressed as: Among them, f N+m Refers to the computing power of idle vehicles; The energy consumption of idle vehicle auxiliary calculation is expressed as: Assuming that the amount of data in the calculation result is proportional to the amount of task data, the ratio is ω, and the idle vehicle uses the same transmission power as the unloaded vehicle, then the channel capacity is also R n,N+m , the time for the idle vehicle to return the calculation result is expressed as: The energy consumption of an idle vehicle returning the calculated result is expressed as: Therefore, the total time consumption of unloading to an idle vehicle is expressed as: The total energy consumption of unloaded vehicles and idle vehicles is expressed as:

5. The method for task offloading based on resource reallocation under connection time constraints in the Internet of Vehicles according to claim 1, characterized in that: The cloud server computing model is: task n The amount of data that needs to be transmitted to the BS is α n,0 ·d n , the transmission time is expressed as: The energy consumed by the unloading vehicle during transmission to the BS is expressed as: Denote the propagation delay between BS and cloud server as t bs,cloud , the total time consumption of offloading to the cloud server is expressed as: The total energy consumption is expressed as:

6. The method for task offloading based on resource reallocation under connection time constraints in the Internet of Vehicles according to claim 1, characterized in that: The optimization model is constructed as: task n The total time consumption is expressed as: T n =α n,0 ·t n,bs +(1-α n,0 )·max(t n,local ,t n,rsu ,t n,N+m ) (37) task n The total energy consumption is expressed as: AND n =α n,0 ·And n,bs +(1-α n,0 )·(And n,local +e n,rsu +e n,N+m ) (38) The system cost is defined as the weighted sum of the total energy consumption of all vehicles and the computing time of each computing task, with μ representing the weight coefficient, expressed as: There are N′ tasks being executed, task n′ The remaining computational effort is denoted as z′ n′ , assuming that the edge server is initially task n′ The proportion of computing resources allocated is r n′ , the proportion of computing resources allocated after adjustment is expressed as r′ n′ , edge server computing task n′ The time variation of is expressed as: Uninstall the task after the decision is made n′ The cost change caused by the change in edge server resource allocation is only related to the time change and is expressed as: The cost of all executing tasks is expressed as: The optimization function is established with the goal of minimizing the system cost, which is expressed as:

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