A multi-stage randomized planning task offloading method based on energy harvesting in mobile Ad Hoc cloud

Abstract

The present invention belongs to the field of mobile communication technology and relates to a multi-stage randomized planning task offloading method based on energy harvesting in a mobile Ad Hoc cloud. The method comprises the following steps: considering a mobile Ad Hoc cloud network composed of a group of nearby terminal devices with EH functions, taking into account the uncertainty of Wi-Fi connection time of client terminals and proxy terminals, respectively establishing an offloading benefit model, a communication cost model, a computing cost model, and an energy harvesting model; establishing a randomized buying and selling game model based on multi-stage randomized planning, purchasing resources from proxy terminals according to the buyer's own computing task requirements, and establishing a problem of maximizing the buyer's revenue; providing different computing and storage resources to the client terminals through dynamic resource quotation, and establishing a problem of maximizing the seller's revenue; and calculating an optimal task offloading strategy for the buyer to the selected proxy terminal and an optimal quotation strategy for the seller using a multi-stage randomized planning Fargrange multiplier method and KKT conditions. The present invention effectively improves system revenue and stabilizes battery energy.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile communications, and in particular relates to a multi-stage random planning task offloading method based on energy collection in a mobile Ad Hoc cloud. Background Art

[0002] With the development of the Internet of Things (IoT), network computing resources and computing power demands have experienced explosive growth. In order to save computing power resources in the cloud, many tasks must be pre-processed before being offloaded to the cloud, which poses a severe challenge to the processing power and battery life of mobile terminals. The battery capacity of mobile terminals is very limited, and traditional power supply equipment will cause high communication costs. With the advent of the Internet of Things era and the exponential growth of "cloud" terminals, the demand for network computing power has also increased rapidly, and the problems of insufficient and unbalanced edge computing power still cannot be effectively solved. In some network scenarios (such as Ad Hoc networks, drone networks, vehicle cloud networks, etc.), there are no available cloud servers or local micro-clouds, or computing tasks cannot be processed in a timely manner due to network congestion.

[0003] Mobile Ad Hoc cloud computing has been proposed and widely studied as a new mobile computing paradigm. Unlike traditional cloud computing, which offloads local tasks to a network-centric cloud or edge cloud server, a mobile Ad Hoc cloud is a self-organizing cloud composed of a group of nearby end devices. Each end device can offload tasks to neighboring end devices and utilize their available computing resources. Limited by size and hardware cost, traditional battery-powered devices with limited battery capacity are unable to transmit and process tasks when battery power is low, which affects computing performance. When devices are distributed in remote or hazardous environments, it is difficult to power them with rechargeable batteries or the traditional power grid. Energy harvesting (EH) technology allows end devices to obtain green energy (such as solar, wind, and mechanical energy) from the environment, reducing reliance on the power grid or battery supply, further improving system energy efficiency, and achieving green communications. Therefore, the integration of mobile Ad Hoc cloud computing and EH technology is of great significance for improving network computing performance. Ad Hoc networks contain a wide variety of end devices. Due to their random mobility, the wireless connections between nodes often change dynamically, making the network topology highly uncertain. If a terminal device leaves the current Ad Hoc network while executing an offloaded task, it may cause the subtask to be reallocated, resulting in excessive task processing delays, high costs, and severe waste of network resources, or even leading to task offload failure. Therefore, it is necessary to study the problem of random user mobility in mobile Ad Hoc cloud environments.

[0004] In recent years, green communications combining MEC and EH technologies have also received widespread attention, which has greatly inspired the integration of EH technology and AdHoc mobile cloud. In view of the characteristics of dynamic changes in node locations, some major achievements are as follows: (1) Distributed computation offloading in IoT fog computing system with energy harvesting: DEC-POMDP approach (Reference: TANG Q, XIE R, YU FA, et al. Decentralized computation offloading in IoT fogcomputing system with energy harvesting: A DEC-POMDP approach [J]. IEEE Internet of Things Journal, 2020, 7 (6): 4898-4911. DOI: 10.1109 / JIOT.2020.2971323.): This algorithm proposes a learning-based distributed offloading algorithm for the problem of predictable distributed offloading in energy-harvesting IoT fog systems, which enables IoT devices to make approximately optimal decisions based on the predicted system state under the delay constraint. (2) A distributed game methodology for crowdsensing in uncertain wireless scenarios (Reference: Cao B, Xia SC, Han JW, et al. A distributed game methodology for crowdsensing in uncertain wireless scenarios [J]. IEEE Transactions on Mobile Computing, 2019, 19(1): 15-28. DOI: 10.1109 / TMC.2019.2892953): Since mobile devices are selfish and rational, the random arrival and departure of sensing tasks, and the random movement of mobile devices lead to random connections, a distributed game group sensing method based on multi-stage stochastic programming is proposed to obtain better group sensing response.(3) Multi-stage stochastic programming offloading strategy in IoT fog computing system (Reference: Zhang L, Cao B, Li Y, et al. A multi-stage stochastic programming based offloading policy for fog enabled IoT-eHealth[J]. IEEE Journal on Selected Areas in Communications, 2020. DOI: 10.1109 / JSAC.2020.3020659): In order to evaluate the impact of uncertainty on offloading strategy under random scenarios, the task offloading problem is formulated as a multi-stage stochastic programming problem (MSSP), and the joint decision of offloading, resource allocation and migration is studied to minimize the total delay of offloading. (4) Task allocation method based on multi-stage stochastic programming in mobile Ad Hoc cloud environment (Reference: Tham C K., Cao B. Stochastic programming methods for workload assignment in anad hoc mobile cloud[J]. IEEE Transactions on Mobile Computing, 2017, 17(7): 1709-1722. DOI: 10.1109 / TMC.2017.2762313): Considering the randomness of the connection time between devices in the mobile Ad Hoc cloud environment, a distributed multi-stage stochastic buying and selling game algorithm is proposed to maximize the benefits of mobile devices, which effectively promotes the collaboration between mobile devices and achieves the optimal overall performance.

[0005] The random mobility of users in Ad Hoc cloud networks can lead to unstable connections between mobile devices. When a terminal device assists nearby terminals in processing computing tasks, it is difficult to accurately predict whether it will move out of the current network. This can affect task offloading decisions and resource allocation strategies, thereby impacting the system's offloading benefits. Because each terminal device has limited resources and is selfish and rational, no terminal device is willing to provide services to other devices without compensation unless there is a reasonable incentive. Therefore, developing task offloading strategies with energy harvesting capabilities using multi-stage stochastic programming methods is of great research value. Summary of the Invention

[0006] In order to improve system benefits, the present invention proposes a multi-stage random planning task offloading method based on energy harvesting in a mobile Ad Hoc cloud, which specifically includes the following steps:

[0007] S1. Build a mobile Ad Hoc cloud network with EH functionality. Use the uncertainty of Wi-Fi connection time between terminal devices to represent the random mobility of users. Establish offloading benefit models, communication cost models, computation cost models, and energy harvesting models.

[0008] S2, taking the client terminal as the buyer, purchasing resources from the proxy terminal according to its own computing task requirements, and using Lyapunov optimization theory to establish the buyer's profit maximization problem;

[0009] S3: The proxy terminal is used as the seller, and different computing and storage resources are provided to the client terminal through dynamic resource quotation, so as to establish the seller's profit maximization problem;

[0010] S4. Establish a random buying and selling game model. According to the uncertainty of the connection time, establish a two-stage random programming model and a multi-stage random programming model respectively.

[0011] S5. Based on the task backlog, battery energy level, and quote of the agent terminal, the optimal task offloading strategy for the buyer to the selected agent terminal and the optimal quote strategy for the seller are calculated using the Lagrange multiplier method and the KKT condition in each sub-time slot.

[0012] S6. If the buyer's optimal task offloading strategy and the seller's optimal quotation strategy satisfy the Stackelberg equilibrium solution, the client terminal offloads the task to the agent terminal according to the optimal task offloading strategy.

[0013] Furthermore, the buyer's profit maximization problem includes:

[0014]

[0015] Constraints:

[0016]

[0017]

[0018] in, V represents the buyer's revenue maximization problem in the tth time slot; i represents the control parameters of the i-th client terminal; represents the total revenue of the i-th client terminal in time slot t; is the virtual energy queue of the EH device of the i-th client terminal, expressed as θ i is the disturbance parameter of the EH device, is the energy queue backlog of the EH device of the i-th client terminal at the beginning of time slot t; It is represented by the energy actually collected by the EH device of the i-th customer terminal in time slot t; is the energy consumption of the i-th client terminal in time slot t; E min is the minimum battery discharge energy; E max is the maximum battery discharge energy; is the energy queue backlog of the i-th client terminal in time slot t; represents the amount of tasks offloaded from the i-th client terminal to the j-th proxy terminal in the t-th time slot; It represents the backlog of the task queue of the i-th client terminal in the t-th time slot; N is the number of agent terminals.

[0019] Furthermore, the buyer's two-stage stochastic programming model includes:

[0020]

[0021] in, represents the revenue gained by the i-th client terminal from offloading the task in the t-th time slot; represents the payment cost paid by the i-th client terminal to the j-th agent terminal in the t-th time slot; w i.t A composite scenario is realized for the i-th client terminal, N proxy terminals, and the Wi-Fi connection time at time slot t; Ω i,t Indicates C i and A j A set of possible Wi-Fi connection times at time slot t; P(w i.t ) represents a composite scenario implemented as ω i,t probability; represents the communication cost of the i-th client terminal uploading the task in the t-th time slot; is the virtual energy queue of the EH device of the i-th client terminal in the t-th time slot, expressed as θ i is the disturbance parameter of the EH device, is the energy queue backlog of the EH device of the i-th client terminal at the beginning of time slot t; represents the actual energy collected by the EH device of the i-th customer terminal at time slot t; represents the local computing energy consumption of the i-th client terminal in the t-th time slot; represents the communication energy consumption of the i-th client terminal uploading the task in the t-th time slot.

[0022] Furthermore, the buyer's multi-stage stochastic programming problem is expressed as:

[0023]

[0024] Where, l represents dividing the time slot t into l sub-time slots; represents the payment cost paid by the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot in the t-th time slot; A composite scenario is realized for the Wi-Fi connection time of the i-th client terminal N proxy terminals and the k-th sub-time slot in time slot t; Indicates C i and A j A set of possible Wi-Fi connection times for the kth sub-slot in time slot t; Represents a composite scene implemented as probability; represents the communication cost of uploading the task of the i-th client terminal in the k-th sub-time slot in the t-th time slot; is the virtual energy queue of the EH device of the i-th client terminal in the k-th sub-time slot of the t-th time slot; represents the energy actually collected by the EH device of the i-th client terminal in the k-th sub-time slot in time slot t; represents the local computing energy consumption of the i-th client terminal in the k-th sub-time slot in the t-th time slot; It represents the communication energy consumption of uploading task of kth sub-time slot of i-th client terminal in t-th time slot.

[0025] Furthermore, the Lagrange multiplier method and KKT condition are used to calculate the optimal task offloading strategy for the buyer to unload the selected agent terminal, that is, the optimal task offloading amount is expressed as:

[0026]

[0027] in, represents the optimal task offloading amount of the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot of the t-th time slot; ξ i represents the task offloading benefit weight parameter; For the i-th client terminal C i Unit task communication cost of transmitting data via Wi-Fi; For the i-th client terminal C i Unit-task communication cost of transmitting data over cellular networks; For the jth agent terminal A j Time spent within Wi-Fi coverage area; For the i-th client terminal C i Amount of data transferred via Wi-Fi time; λ1 is the energy consumption per unit time for task transmission; λ2 is the energy consumption per unit time for calculation by the agent terminal; is the i-th client terminal C i and the jth agent terminal A jThe bandwidth of the Wi-Fi link between them; For the i-th client terminal C i and the jth agent terminal A j The bandwidth of the cellular network.

[0028] Furthermore, the seller's revenue maximization problem includes:

[0029]

[0030] Constraints:

[0031]

[0032]

[0033] in, It represents the seller’s revenue maximization problem; V represents the control parameter; represents the total revenue of the jth agent terminal in the tth time slot; is the virtual energy queue of the jth agent terminal in the tth time slot, expressed as θ j is the disturbance parameter of the EH device, is the energy queue backlog of the EH device carried by the jth proxy terminal at the beginning of time slot t; is the energy queue backlog of the EH device carried by the jth proxy terminal at the beginning of time slot t; Energy consumption of the jth agent terminal in time slot t; E max is the maximum battery discharge energy; represents the amount of tasks offloaded from the i-th client terminal to the j-th proxy terminal in the t-th time slot; It represents the backlog of the task queue of the i-th client terminal in the t-th time slot; N is the number of agent terminals.

[0034] Furthermore, the seller's two-stage stochastic programming model includes:

[0035]

[0036] Where M is the number of client terminals; Ω represents the payment cost paid by the i-th client terminal to the j-th proxy terminal in the t-th time slot; i,t Indicates C i and A j A set of possible Wi-Fi connection times at time slot t; P(w i.t ) represents a composite scenario implemented as ω i,t probability; represents the communication cost incurred when the jth proxy terminal returns the calculation result at time slot t; ηj L represents the unit time computation cost of the jth agent terminal; j represents the computing power of the jth agent terminal; is the virtual energy queue of the jth proxy terminal in the tth time slot; is the energy queue backlog of the EH device carried by the jth proxy terminal at the beginning of time slot t; represents the computational energy consumption of the jth agent terminal in time slot t; It represents the communication energy consumption generated when the j-th agent terminal returns the calculation result at time slot t.

[0037] Furthermore, the seller's multi-stage stochastic programming problem is expressed as:

[0038]

[0039] Where, l represents dividing the time slot t into l sub-time slots; represents the payment cost paid by the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot in the t-th time slot; represents the optimal task offloading amount of the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot of the t-th time slot; A composite scenario is realized for the Wi-Fi connection time of the i-th client terminal N proxy terminals and the k-th sub-time slot in time slot t; Indicates C i and A j A set of possible Wi-Fi connection times for the kth sub-slot in time slot t; Represents a composite scene implemented as probability; represents the communication cost incurred when the j-th proxy terminal returns the calculation result in the k-th sub-time slot in time slot t; is the virtual energy queue of the jth proxy terminal in the kth sub-time slot in the tth time slot; is the energy queue backlog of the EH device of the jth proxy terminal at the beginning of the kth sub-time slot in time slot t; represents the computational energy consumption of the jth proxy terminal in the kth sub-time slot in time slot t; It represents the communication energy consumption generated when the j-th proxy terminal returns the calculation result in the k-th sub-time slot in time slot t.

[0040] Furthermore, the Lagrange multiplier method and KKT conditions are used to calculate the seller's optimal bidding strategy, that is, the t-th k The optimal bid for a sub-time slot is expressed as:

[0041]

[0042] Among them, ξ i represents the task offloading benefit weight parameter; L j represents the processing capacity of the jth proxy terminal; For the i-th client terminal C i Unit task communication cost of transmitting data via Wi-Fi; For the i-th client terminal C i The unit task communication cost of transmitting data through the cellular network; z is the task compression rate when the task result is returned; λ1 is the unit time energy consumption for task transmission; λ2 is the unit energy consumption for calculation by the agent terminal; For the i-th client terminal C i and the jth agent terminal A j The bandwidth of the cellular network; is the i-th client terminal C i and the jth agent terminal A j The bandwidth of the Wi-Fi link between them; represents the optimal task offloading amount of the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot of the t-th time slot; f( ) represents The functional relationship between it and other variables is solved by MATLAB's fsolve function.

[0043] First, to address the mobility of nearby mobile terminals, represented by random connection times within a Wi-Fi area, the present invention employs a multi-stage stochastic programming algorithm to solve the task offloading problem. Taking into account the varying computing power and battery life of each mobile terminal, an optimal task offloading decision is generated among the mobile terminals. Second, to incentivize cooperation among mobile terminals, the problem is modeled as a buying and selling game, and the Stackelberg equilibrium strategy for the buying and selling game is determined. Simulation analysis verifies that the present solution can effectively improve system revenue. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a multi-stage randomized planning offloading method based on energy harvesting in a mobile Ad Hoc cloud in the present invention;

[0045] Figure 2 This is the mobile Ad Hoc cloud collaboration system model in the present invention;

[0046] Figure 3 This is a relationship diagram between communication cost and WiFi connection time in the present invention. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] The present invention proposes a multi-stage random planning task offloading method based on energy harvesting in a mobile Ad Hoc cloud, which specifically includes the following steps:

[0049] S1. Build a mobile Ad Hoc cloud network with EH functionality. Use the uncertainty of Wi-Fi connection time between terminal devices to represent the random mobility of users. Establish offloading benefit models, communication cost models, computation cost models, and energy harvesting models.

[0050] S2, taking the client terminal as the buyer, purchasing resources from the proxy terminal according to its own computing task requirements, and using Lyapunov optimization theory to establish the buyer's profit maximization problem;

[0051] S3: The proxy terminal is used as the seller, and different computing and storage resources are provided to the client terminal through dynamic resource quotation, so as to establish the seller's profit maximization problem;

[0052] S4. Establish a random buying and selling game model. According to the uncertainty of the connection time, establish a two-stage random programming model and a multi-stage random programming model respectively.

[0053] S5. Based on the task backlog, battery energy level, and quote of the agent terminal, the optimal task offloading strategy for the buyer to the selected agent terminal and the optimal quote strategy for the seller are calculated using the Lagrange multiplier method and the KKT condition in each sub-time slot.

[0054] S6. If the buyer's optimal task offloading strategy and the seller's optimal quotation strategy satisfy the Stackelberg equilibrium solution, the client terminal offloads the task to the agent terminal according to the optimal task offloading strategy.

[0055] This embodiment describes the solution of the present invention in detail from three aspects: system model, problem analysis based on multi-stage stochastic programming, and optimal strategy analysis based on multi-stage stochastic programming.

[0056] 1. System Model

[0057] Consider a mobile Ad Hoc cloud network with EH function, using the uncertainty of Wi-Fi connection time between terminal devices to represent the random movement of users. The task offloading model is shown in the figure below: Figure 1As shown, it includes M client terminals (Client, C i , ) and N agent terminals (Agent, A j , ) can share idle or excess computing resources. Assume that there are two wireless communication methods in the network, namely Wi-Fi and cellular network. The Wi-Fi coverage area is the inner circle range, and the cellular network coverage area is the outer circle range. i The computational tasks can be processed locally or offloaded to A j Collaborative computing, where j = 0 means the task is processed locally. Assuming that time can be slotted, the unit slot length is defined as τ, and the slot index is τ d Indicates C i The maximum tolerable delay of i Task offloading decision Indicates C i Offload the task to the jth agent A at time slot t j ,otherwise,

[0058] Assumption C i The task arrival process is subject to the parameter λ i Poisson distribution, and the computing tasks can be divided arbitrarily, defining the tth time slot, Indicates C i The total amount of tasks processed in time slot t, Indicates uninstallation to A j The amount of tasks, Indicates the amount of tasks processed locally and satisfies is the maximum amount of tasks that can be processed. i Indicates C i The unit processing capacity, A j CPU processing frequency, and meet and Respectively represent the maximum and minimum CPU processing frequency, Indicates C i CPU processing frequency.

[0059] 1. Uninstall revenue model

[0060] In order to evaluate the C i To A j The benefit degree after offloading the task, the present invention uses the logarithmic function widely used in the field of mobile computing and wireless communication to express C i The profit obtained by unloading the task in the tth time slot:

[0061]

[0062] in, It is C i The task Uninstall to A j The income obtained, i represents a task offloading benefit weight parameter greater than zero, It is in the tth time slot C i Uninstall to A j amount of tasks.

[0063] 2. Communication Cost Model

[0064] In mobile Ad Hoc clouds, the task offloading process primarily involves client terminals uploading tasks, proxy terminals collaboratively computing the offloaded tasks, and returning the computational results. Therefore, communication costs are incurred during both the client terminal uploading tasks and the computational results returning process.

[0065] First, assume that the tasks offloaded from the client terminal to the proxy terminal must be completely received before processing begins, and the results are returned only after all processing is completed. Assume that at the beginning of time slot t, all proxy terminals are within the Wi-Fi coverage area, and the cellular network can always be used for network communication. Only A j After moving out of the Wi-Fi coverage area, C i and A j It is assumed that the switching between Wi-Fi and cellular networks is fast enough to not interrupt data transmission. That is, if the proxy terminal moves out of the Wi-Fi coverage during data transmission, it only needs to switch to the cellular network to continue transmission. i and A j The Wi-Fi connection time between j The duration of stay in the Wi-Fi coverage area. The randomness of Wi-Fi connection time will affect the communication cost of the system, thus affecting C i uninstall decision.

[0066] According to the time the proxy terminal is within the Wi-Fi coverage area, the amount of data transmitted by the client terminal through Wi-Fi and cellular networks can be determined. i Upload the task to A j When A j In C i If the Wi-Fi coverage is within the range of t, the Wi-Fi with lower communication cost can be used. Otherwise, the cellular network with higher communication cost can be used. i Send A via Wi-Fi j The amount of data sent is:

[0067]

[0068] in, It's A j Time within Wi-Fi coverage, It is C i and A j The bandwidth of the Wi-Fi link between It is C i Amount of data transferred via Wi-Fi time, i.e. Similarly, C i A through the cellular network j The amount of data sent is:

[0069]

[0070] According to formulas (2) and (3), C i The communication cost of transmitting the task in time slot t is:

[0071]

[0072] in, and C i The unit communication cost of transmitting data via Wi-Fi and cellular networks. Since the cost of transmitting data via Wi-Fi is much lower than that via cellular networks,

[0073] C i To A j The energy consumed during the transmission task is:

[0074]

[0075] Among them, λ1 is the unit energy consumption for task transmission, C i and A j The bandwidth of the cellular network between. Assume A j Processing completed C i After unloading the task, return it to C i The amount of data for the calculation result is A j The amount of data transferred via Wi-Fi is:

[0076]

[0077] in, Return the result to C i and A jWi-Fi connection time, A j Assist in handling the processing delay of computing tasks, It's A j Data transfer via Wi-Fi ij time, It is the sum of communication delay and task processing delay. j The amount of data transferred over the cellular network is:

[0078]

[0079] According to equations (6) and (7), A j The communication cost of the transmission task is:

[0080]

[0081] Similar to the communication energy consumption during task uploading, A j Return the result to C i The communication energy consumption is

[0082]

[0083] 3. Calculation cost model

[0084] A j Assist C i Processing computing tasks will consume its own computing resources, so A j The computational cost of processing the computational task is:

[0085]

[0086] Where λ2 is A j Used for calculation-based unit energy consumption.

[0087] 4. Energy Harvesting Model

[0088] Assuming that each terminal device with EH can obtain green energy from the environment for battery power supply, the EH process is modeled as a continuous energy packet arrival process, where g = i represents the client terminal and g = j represents the agent terminal. represents the energy collected in time slot t, satisfying And they are independent and identically distributed in different time slots. The energy actually collected by the EH device is and satisfy Available for local and offloaded computation starting from the next time slot.

[0089] use and Represents the set of EH equipment energy queues of the client terminal and the proxy terminal respectively, where is the energy queue backlog of the g-th EH device at the beginning of time slot t. Usually, C i Considering only the energy consumption of local computing and transmission processes, it can be expressed as:

[0090]

[0091] A j Consider the energy consumption of the calculation and the return of the results

[0092]

[0093] To prevent the battery from over-discharging, the battery discharge constraints of equations (14) and (15) should be satisfied:

[0094]

[0095]

[0096] Among them, Emax and Em i n represents the maximum and minimum battery discharge energy, respectively. In addition, to ensure the battery life of the mobile terminal, the battery power at the beginning of time slot t must be greater than the energy consumption required by the mobile terminal, expressed as:

[0097]

[0098]

[0099] According to equations (12) and (14), C i The energy queue backlog at time slot t+1 is

[0100]

[0101] According to equations (13) and (15), A j The energy queue backlog at time slot t+1 is

[0102]

[0103] 2. Problem Analysis Based on Multi-stage Stochastic Programming

[0104] In a mobile Ad Hoc cloud, the terminal device offloading decision is constrained by the stability of the energy queue and the task offloading time. While considering the system offloading benefit, communication cost and computing cost, the present invention proposes a system benefit maximization problem, as shown in Equation (20).

[0105] max:

[0106] st(14),(15),(16),(17)

[0107]

[0108] Formula (21) indicates that the total amount of tasks unloaded to the agent terminal cannot exceed the backlog of its task queue.

[0109] In mobile Ad Hoc cloud networks, client terminals can offload computing tasks to neighboring proxy terminals and decide the amount of tasks to offload to each proxy terminal. The proxy terminals act as sellers and provide different computing and storage resources to client terminals through dynamic resource quotations; client terminals act as buyers and purchase resources from proxy terminals based on their own computing task requirements. This process can be regarded as a buying and selling game.

[0110] 1. Analysis of the buying and selling game model

[0111] Since battery energy is time-dependent, the terminal device's unloading decisions in different time slots are coupled. The perturbation weighting method is an effective way to solve the above problems.

[16] In order to eliminate the coupling effect, the disturbance parameters and virtual energy queues of the terminal devices are first defined.

[0112] The disturbance parameter θ of the EH device g is a bounded constant, namely:

[0113]

[0114] in, represents the maximum energy consumption of local computing, represents the maximum transmission energy consumption of the client terminal, represents the maximum energy consumption of agent calculation, V is a control parameter and satisfies 0<V<+∞.

[0115] The virtual energy queue is defined as Indicates the actual battery energy consumed by the mobile terminal device. By adjusting the disturbance parameter θ g and control parameter V, so that Stable at the disturbance parameter θ g nearby.

[0116] 1) Buyer Game Model Analysis

[0117] Define the tth time slot C i To A j The unit payment cost for purchasing computing resources is C i The cost paid is When tasks are processed locally, C iThe cost of C mainly includes the fee paid to the agent and the communication cost of unloading tasks to the agent. Therefore, the tth time slot C i The optimization goal is:

[0118]

[0119] st(14),(15),(16),(17),(21)

[0120] In order to balance the relationship between the client terminal revenue and the energy queue backlog, the Lyapunov function is introduced to model the queue backlog of each client terminal. The Lyapunov function is the C i Non-negative scalar representation of energy queue:

[0121]

[0122] Among them, L[Θ i (t)]≥0, the change of the Lyapunov function between two time slots is defined as the Lyapunov drift, which is expressed as:

[0123]

[0124] Equation (19) represents the queue backlog growth from time slot t to time slot t+1. By minimizing Δ[Θ i (t)] to ensure L[Θ i (t)] is stable. i The upper bound of [(t)] is expressed by formula (26):

[0125]

[0126] Lyapunov drift plus penalty is expressed as:

[0127]

[0128] The goal of optimizing the buyer's return is to minimize the Lyapunov drift plus the penalty function, which can be expressed as the P2 problem:

[0129] P2:

[0130] st(14),(16),(21)

[0131] 2) Analysis of the seller game model

[0132] For the proxy terminal, the profit obtained by providing computing resources to the client terminal in time slot t is The agent maximizes its own benefits through optimal pricing, A jConsidering only the computational cost of executing the computational task, the tth time slot A j The profit maximization problem is:

[0133]

[0134]

[0135] Similarly, the Lyapunov drift plus penalty function of the proxy terminal is:

[0136]

[0137] The seller's optimization problem is expressed as the P3 problem:

[0138] P3:

[0139] st(15),(17),(30)

[0140] 2. Analysis of random buying and selling game model

[0141] Because each terminal device in a mobile Ad Hoc cloud network exhibits random mobility, the Wi-Fi connection time between client and proxy terminals is uncertain, leading to uncertain communication costs during task offloading. Within Wi-Fi coverage areas, client and proxy connection times can be predicted based on historical observations, but simple predictions can be inaccurate. When the actual connection time between client and proxy is less than the predicted value, the decision workload is excessive, resulting in high communication costs. When the actual connection time between client and proxy is greater than the predicted value, the decision workload is too small, and the Wi-Fi connection cannot be fully utilized for data transmission, resulting in wasted resources. To address the uncertainty of connection time, a multi-stage stochastic programming approach is employed to take a posteriori actions to compensate for prediction inaccuracies.

[0142] 1) Uncertainty in connection time

[0143] Assume that the Wi-Fi connection time of each proxy terminal and the client terminal in the Wi-Fi coverage area of ​​the client terminal follows a probability distribution. ij,t Indicates C i and A j A set of possible Wi-Fi connection time sets at time slot t, i.e. individual scenarios, is easy to know. According to the Cartesian product, the present invention converts the set Ω i,t Defined as C i The set of possible Wi-Fi connection times of all proxy terminals at time slot t.

[0144]

[0145] The actual scenario after the uncertain parameters are observed is called a realization. i When offloading tasks to N proxy terminals, a composite scenario implementation of the connection time of N proxy terminals at time slot t is expressed as

[0146] 2) Two-stage stochastic programming model

[0147] C i The total cost includes communication cost and payment cost, where the communication cost includes uncertain parameters Assume that the connection time of the proxy terminal in the Wi-Fi coverage area of ​​the client terminal follows the probability distribution and satisfy We get a probability distribution of a composite scenario The buyer's two-stage stochastic programming problem is:

[0148]

[0149] st(14),(16),(21)

[0150] Similarly, the seller's two-stage stochastic programming problem is

[0151]

[0152] st(15),(17),(30)

[0153] 3) Multi-stage stochastic programming model

[0154] Using the two-stage randomized buying and selling game model, the optimal strategy is only decided once at the beginning of each time slot. It cannot guarantee that the task will be completely unloaded in one decision time slot, which will lead to inaccurate predictions and the inability to obtain the optimal unloading decision. In order to more accurately capture the information of the Wi-Fi connection time between the client terminal and the agent terminal, the two-stage randomized programming problem is expanded to a multi-stage randomized programming problem. In the multi-stage randomized programming model, the time slot t is divided into l sub-time slots, and t is defined. k is the kth sub-time slot. For the convenience of analysis, the variable subscript t in the text is changed to t k Indicates that this variable is in sub-slot t k The state below.

[0155] The buyer's multi-stage stochastic programming problem is:

[0156]

[0157] st(14),(16),(21)(37)

[0158] The seller's multi-stage stochastic programming problem is:

[0159]

[0160] st(15),(17),(30)

[0161] 3. Optimal Strategy Analysis Based on Multi-stage Stochastic Programming

[0162] In this example, we first analyze the optimal offloading strategy and optimal bid for the proposed multi-stage stochastic programming scheme. We also prove the Steinberg equilibrium for the optimal offloading strategy for the client terminal and the optimal bid for the agent terminal. Without loss of generality, this example analyzes the optimal strategies for both buyers and sellers in a single decision slot and a single possible scenario.

[0163] 1. Analysis of buying and selling game strategies

[0164] 1) Buyer strategy analysis

[0165] The buyer's optimization problem can be divided into EH optimization and task offloading strategy optimization. Since the two variables are independent of each other, the P2 problem can be transformed into two sub-problems Q1 and Q2.

[0166] According to formula (36), the optimal value of energy harvesting is solved:

[0167] Q1: min:

[0168] when hour, when hour,

[0169] 2) Task offloading optimization strategy

[0170] According to Equation (36), after decoupling the energy harvesting optimization problem, the task offloading optimization can be expressed as:

[0171] Q2:

[0172]

[0173] st(14),(16),(21)

[0174] In order to maximize its own interests, the client terminal adjusts the queue backlog Θ according to the control parameter V. i (t) and the seller’s quote and other status information to determine the purchase strategy. The buyer’s profit is a function of the offloading task volume and the quote. According to formula (40), Ask about The first-order derivative of right Ask about The second-order derivative of therefore, It's about The convex function of , the optimal task offloading amount is:

[0175]

[0176] in,

[0177] 2. Seller Strategy Analysis

[0178] Unit resource quotation of agent terminal The higher , the higher the agent's profit. However, if the client's payment is too high, it will reduce the willingness to buy, which will reduce the agent's profit. Therefore, there is an optimal bid for the agent that balances the buyer's and seller's profits. The P3 problem can be divided into the EH optimization problem and the resource bidding optimization problems Q3 and Q4.

[0179] 1) According to formula (26), solve the optimal value of energy harvesting:

[0180] Q3: min:

[0181] when hour, when hour,

[0182] 2) Resource quotation optimization strategy

[0183] According to formula (26), after decoupling the energy harvesting optimization problem, the resource bidding optimization can be expressed as:

[0184] Q4:

[0185]

[0186] st(15),(17),(30)

[0187] A j The benefit should be greater than zero, so when When the quote is the minimum value of the quotation, that is:

[0188]

[0189] right Find the first-order partial derivative:

[0190]

[0191] in, right Find the second-order partial derivative:

[0192]

[0193] right Find the second-order partial derivative:

[0194]

[0195] therefore, It's about The convex function of t is obtained by Lagrange multiplier method and KKT condition, and the constraints (15), (17), (30) are affine functions. k The optimal bid for a sub-time slot is:

[0196]

[0197] because The closed expression of is not easy to obtain, so express The functional relationship between the function and other variables. In the actual solution process, the solution can be obtained through the fsolve function of MATLAB.

[0198] 3. Stackelberg equilibrium analysis

[0199] According to the previous analysis, in order to maximize its own benefits, the client terminal will make offloading decisions based on the agent's attributes and channel resources, and select the appropriate agent to collaboratively calculate the offloading task; while the agent will decide the optimal resource pricing based on the relationship between the client terminal's task volume and its own benefits. Next, we prove the optimal solution It is the SE equilibrium solution.

[0200] Since the second-order derivative of the buyer's benefit function satisfies therefore It's about The convex function of exist The second-order derivative of the seller's profit function satisfies therefore It's about The convex function of exist Based on the equilibrium existence analysis, is the SE equilibrium solution, that is

[0201] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A multi-stage random planning task offloading method based on energy harvesting in mobile Ad Hoc cloud, characterized by: The following steps are involved: S1. Build a mobile Ad Hoc cloud network with EH functionality. Use the uncertainty of Wi-Fi connection time between terminal devices to represent the random mobility of users. Establish offloading benefit models, communication cost models, computation cost models, and energy harvesting models. S2. The client terminal is regarded as the buyer. It purchases resources from the proxy terminal according to its own computing task requirements. Lyapunov optimization theory is used to establish the buyer's profit maximization problem, namely: Constraints: in, It represents the buyer's revenue maximization problem in the tth time slot; V represents the control parameter; represents the total revenue of the i-th client terminal in time slot t; is the virtual energy queue of the EH device of the i-th client terminal, expressed as θ i is the disturbance parameter of the EH device, is the energy queue backlog of the EH device of the i-th client terminal at the beginning of time slot t; It is represented by the energy actually collected by the EH device of the i-th customer terminal in time slot t; is the energy consumption of the i-th client terminal in time slot t; E min is the minimum battery discharge energy; E max is the maximum battery discharge energy; is the energy queue backlog of the i-th client terminal in time slot t; represents the amount of tasks offloaded from the i-th client terminal to the j-th proxy terminal in the t-th time slot; represents the backlog of the task queue of the i-th client terminal in the t-th time slot; N is the number of agent terminals; The buyer's two-stage stochastic programming model includes: in, V represents the revenue gained by the i-th client terminal from unloading the task in the t-th time slot; i represents the control parameters of the i-th client terminal; represents the payment cost paid by the i-th client terminal to the j-th proxy terminal in the t-th time slot; ω i.t A composite scenario is realized for the i-th client terminal, N proxy terminals, and the Wi-Fi connection time at time slot t; Ω i,t Represents the i-th client terminal C i and the jth agent terminal A j A set of possible Wi-Fi connection times at time slot t; P(ω i.t ) represents a composite scenario implemented as ω i,t probability; represents the communication cost of the i-th client terminal uploading the task in the t-th time slot; represents the local computing energy consumption of the i-th client terminal in the t-th time slot; represents the communication energy consumption of the i-th client terminal uploading the task in the t-th time slot; Where, l represents dividing the time slot t into l sub-time slots; represents the payment cost paid by the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot in the t-th time slot; A composite scenario is realized for the Wi-Fi connection time of the i-th client terminal N proxy terminals and the k-th sub-time slot in time slot t; Indicates C i and A j A set of possible Wi-Fi connection times for the kth sub-slot in time slot t; Represents a composite scene implemented as probability; represents the communication cost of uploading the task of the i-th client terminal in the k-th sub-time slot in the t-th time slot; is the virtual energy queue of the EH device of the i-th client terminal in the k-th sub-time slot of the t-th time slot; represents the energy actually collected by the EH device of the i-th client terminal in the k-th sub-time slot in time slot t; represents the local computing energy consumption of the i-th client terminal in the k-th sub-time slot in the t-th time slot; represents the communication energy consumption of the i-th client terminal uploading the k-th sub-time slot in the t-th time slot; S3: The proxy terminal is regarded as the seller, and different computing and storage resources are provided to the client terminal through dynamic resource quotation. The seller's profit maximization problem is established, namely: Constraints: in, Represents the seller’s revenue maximization problem; represents the total revenue of the jth agent terminal in the tth time slot; is the virtual energy queue of the jth agent terminal in the tth time slot, expressed as θ j is the disturbance parameter of the EH device, is the energy queue backlog of the EH device carried by the jth proxy terminal at the beginning of time slot t; is the energy queue backlog of the EH device carried by the jth proxy terminal at the beginning of time slot t; Energy consumption of the jth agent terminal at time slot t; represents the benefit of the i-th client terminal offloading the task to the j-th agent terminal in time slot t; The seller's two-stage stochastic programming model includes: Among them, V j represents the control parameters of the jth proxy terminal, M is the number of client terminals; The seller's multi-stage stochastic programming problem is expressed as: Where, l represents dividing the time slot t into l sub-time slots; represents the payment cost paid by the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot in the t-th time slot; represents the optimal task offloading amount of the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot of the t-th time slot; A composite scenario is realized for the Wi-Fi connection time of the i-th client terminal N proxy terminals and the k-th sub-time slot in time slot t; Indicates C i and A j A set of possible Wi-Fi connection times for the kth sub-slot in time slot t; Represents a composite scene implemented as probability; represents the communication cost incurred when the j-th proxy terminal returns the calculation result in the k-th sub-time slot in time slot t; is the virtual energy queue of the jth proxy terminal in the kth sub-time slot in the tth time slot; is the energy queue backlog of the EH device of the jth proxy terminal at the beginning of the kth sub-time slot in time slot t; represents the computational energy consumption of the jth proxy terminal in the kth sub-time slot in time slot t; represents the communication energy consumption generated when the j-th proxy terminal returns the calculation result in the k-th sub-time slot in time slot t; S4. Establish a random buying and selling game model. According to the uncertainty of the connection time, establish a two-stage random programming model and a multi-stage random programming model respectively. S5. Based on the task backlog, battery energy level, and agent terminal quote of the client terminal, the optimal task offloading strategy for the buyer to the selected agent terminal and the optimal quote strategy for the seller are calculated using the Lagrange multiplier method and the KKT condition in each sub-time slot. The optimal task offloading amount is expressed as: in, represents the optimal task offloading amount of the i-th client terminal to the j-th proxy terminal in the k-th sub-time slot of the t-th time slot; ζ i represents the task offloading benefit weight parameter; For the i-th client terminal C i Unit task communication cost of transmitting data via Wi-Fi; For the i-th client terminal C i Unit-task communication cost of transmitting data over cellular networks; For the jth agent terminal A j Time spent within Wi-Fi coverage area; For the i-th client terminal C i Amount of data transferred via Wi-Fi time; λ1 is the energy consumption per unit time for task transmission; λ2 is the energy consumption per unit time for calculation by the agent terminal; is the i-th client terminal C i and the jth agent terminal A j The bandwidth of the Wi-Fi link between them; For the i-th client terminal C i and the jth agent terminal A j The bandwidth of the cellular network; No. t k The optimal bid for a sub-time slot is expressed as: Among them, ξ i represents the task offloading benefit weight parameter; L j represents the processing capacity of the jth agent terminal; z is the task compression rate when the task result is returned; For the i-th client terminal C i and the jth agent terminal A j The bandwidth of the cellular network; is the i-th client terminal C i and the jth agent terminal A j The bandwidth of the Wi-Fi link between them; represents the optimal task offloading amount from the i-th client terminal to the j-th proxy terminal in the t-th time slot; f( ) represents Functional relationships with other variables; S6. If the buyer's optimal task offloading strategy and the seller's optimal quotation strategy satisfy the Stackelberg equilibrium solution, the client terminal offloads the task to the agent terminal according to the optimal task offloading strategy.

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