An industrial internet of things wireless resource optimization method based on random network calculus

Abstract

The application discloses an industrial internet of things wireless resource optimization method based on random network calculus, comprising the following steps: according to the differentiated quality of service requirement of heterogeneous services in the industrial internet of things edge network, a system queue evolution model containing delay guarantee services and throughput enhancement services is established; according to the system queue evolution model, the statistical delay violation probability boundary of the delay guarantee services is obtained by using the random network calculus theory, and the minimum effective service capability threshold value meeting the statistical delay constraint is determined based on the statistical delay violation probability boundary; according to the minimum effective service capability threshold value, the optimization problem is constructed with the optimization objective of maximizing the long-term average quality of experience of the throughput enhancement services and the statistical delay violation probability constraint of the delay guarantee services being met; and the optimization problem is solved to obtain the optimization result. The application realizes real-time resource scheduling under the statistical performance constraint.

Description

Technical Field

[0001] This invention belongs to the field of wireless resource optimization technology, and particularly relates to an industrial Internet of Things wireless resource optimization method based on random network calculus. Background Technology

[0002] With the continuous development of the Industrial Internet of Things (IIoT), the data services carried by terminal nodes are increasingly exhibiting significant heterogeneity. For practical dynamic network scheduling scenarios, heterogeneous services with differentiated QoS requirements are divided into two categories: one category targets industrial control, status feedback, and closed-loop regulation scenarios, and due to its strict end-to-end latency requirements, it is defined as Delay-Guaranteed (DG) services; the other category focuses more on data transmission efficiency and service experience, placing higher demands on system throughput and long-term service quality, and is defined as Throughput-Enhanced (TE) services. In complex industrial wireless networks, both service arrival and channel service processes are highly random. How to rationally allocate limited wireless resources in a randomly and dynamically changing network environment, while meeting the stringent statistical performance requirements of DG services and maximizing the long-term experience of TE services, has become an important research problem in current IIoT resource optimization.

[0003] While existing research has extensively addressed resource allocation and quality of service (QoS) assurance in industrial wireless networks, most methods primarily model and solve for average latency, instantaneous capacity, or deterministic constraints, neglecting the long-term statistical QoS constraints of distributed generation (DG) services under random arrival and service conditions. Particularly when considering latency default probability constraints, these constraints are determined by network states and system decisions over long timescales, while system resource allocation needs to be dynamically completed within each time slot based on queue and channel states, resulting in a timescale inconsistency. This makes it difficult for long-term statistical latency constraints to directly apply to the resource allocation process in each time slot, and also makes it difficult for traditional optimization frameworks to balance long-term QoS assurance with real-time dynamic control. Therefore, the core problem to be solved is how to transform the long-term statistical constraints of latency-assured services into quantifiable conditions that can be applied to decisions in each time slot, and on this basis, achieve dynamic resource optimization for heterogeneous services. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes an industrial IoT wireless resource optimization method based on stochastic network calculus (SNC). This method utilizes SNC to derive the minimum effective service capacity threshold required for latency-guaranteed services. By constructing a virtual queue, the latency default probability constraint is transformed into a virtual queue stability condition. Furthermore, combining Lyapunov optimization theory, the long-term optimization problem is decoupled into a slot-by-slot subproblem. Finally, under the premise of satisfying the statistical performance constraints of latency-guaranteed services and system stability, Lagrange dual decomposition is used to jointly iteratively solve for bandwidth and transmit power, achieving real-time resource scheduling under statistical performance constraints.

[0005] To achieve the above objectives, this invention provides an industrial IoT wireless resource optimization method based on random network calculus, comprising: Based on the differentiated quality of service requirements of heterogeneous services in the industrial IoT edge network, a system queue evolution model including latency-guaranteed services and throughput-enhanced services is established. Based on the system queue evolution model, the statistical delay default probability boundary of the delay guarantee service is obtained using the random network calculus theory, and the minimum effective service capacity threshold that satisfies the statistical delay constraint is determined based on the statistical delay default probability boundary. Based on the minimum effective service capacity threshold, with the optimization objective of maximizing the long-term average experience quality of throughput enhancement services and the latency guarantee services satisfying the statistical latency default probability constraint, an optimization problem is constructed. The optimization problem is solved to obtain the optimization results.

[0006] Optionally, establishing a system queue evolution model that includes latency-guaranteed services and throughput-enhanced services includes: Based on the Poisson arrival characteristics of the latency guarantee service and the periodic arrival characteristics of the throughput enhancement service, cumulative arrival models for the two types of services are established respectively. An instantaneous transmission rate model for the uplink wireless link is established based on the block fading channel model, and the actual service volume of the two types of services in each time slot is determined based on the instantaneous transmission rate model. Based on the cumulative arrival volume model and the actual service volume, update equations are established for the latency-guaranteed service queue and the throughput-enhanced service queue, resulting in the system queue evolution model.

[0007] Optionally, based on the system queue evolution model, the statistical delay default probability boundary of the delay guarantee service is obtained using stochastic network calculus theory, including: Based on the system queue evolution model, and according to the moment generating function characteristics of the Poisson arrival process of the delay guarantee service, the upper bound form of the moment generating function of the cumulative arrival amount is determined; Based on the power gain distribution characteristics of the Rayleigh fading channel, the upper bound of the moment generating function of the actual service process is determined; Based on the upper bound of the moment generating function of the cumulative arrivals and the upper bound of the moment generating function of the actual service process, the statistical delay default probability boundary of the delay guarantee service is obtained using the delay boundary theory in random network calculus.

[0008] Optionally, the minimum effective service capacity threshold is: ; in, The minimum effective service capacity threshold, To ensure the average arrival rate of services with low latency, For the size of the business data packet, For the free parameters of random network calculus, For the time delay threshold, This is the threshold for the probability of default. For Lambert- W The main branch of the function.

[0009] Optionally, solving the optimization problem to obtain the optimization result includes: Construct a virtual queue for statistical service deficit, and transform the long-term statistical latency constraints of the latency guarantee service into stability conditions for the virtual queue; Based on the stability condition of the virtual queue, Lyapunov optimization theory is introduced to construct a drift plus penalty function, which decouples the long-term resource optimization problem into a time-slot dynamic decision problem. Based on the aforementioned time-slot dynamic decision problem, the joint bandwidth and power allocation problem is decomposed into a delay guarantee service subproblem and a throughput enhancement service subproblem using the Lagrange dual decomposition method, and the local optimal solutions of each subproblem are solved based on the KKT conditions. Based on the local optimal solution, the dual variable is iteratively updated using the subgradient method until convergence, thus obtaining the optimization result.

[0010] Optionally, constructing a virtual queue for statistical service deficit includes: Based on the minimum effective service capacity threshold and the instantaneous effective service rate of the current time slot, the evolution equation of the statistical service deficit virtual queue is defined, wherein the instantaneous effective service rate is jointly determined by the bandwidth allocated to the current time slot, the transmit power, and the instantaneous channel state. According to the evolution equation, when the instantaneous effective service rate is lower than the minimum effective service capacity threshold, the virtual queue grows; when the instantaneous effective service rate is higher than the minimum effective service capacity threshold, the virtual queue decreases.

[0011] Optionally, based on the stability condition of the virtual queue, a drift plus penalty function is constructed by introducing Lyapunov optimization theory, including: Based on the stability conditions of the latency-guaranteed service queue, the throughput-enhanced service queue, and the virtual queue, construct the Lyapunov function of the system; Based on the Lyapunov function, a conditional Lyapunov drift is defined, and the upper bound expression of the conditional Lyapunov drift is derived using the queue update equation. Based on the upper bound expression of the conditional Lyapunov drift and the utility function of the throughput enhancement service, the drift plus penalty function is constructed, wherein the drift plus penalty function includes control parameters for balancing system stability and long-term experience quality optimization.

[0012] Optionally, the long-term resource optimization problem can be decoupled into a time-slot-by-time dynamic decision problem, including: Based on the upper bound expression of the drift plus penalty function, minimizing the upper bound of the drift plus penalty function is equivalently transformed into maximizing the decision objective function that includes the coupling relationship between queue backlog weight and instantaneous service volume in each time slot; Based on the decision objective function, the long-term resource optimization problem is decoupled into a time-slot-by-time dynamic decision problem that depends only on the current time-slot queue state and the channel state.

[0013] Optionally, based on the aforementioned time-slot-by-time dynamic decision problem, the joint bandwidth and power allocation problem is decomposed into a latency-guaranteed service sub-problem and a throughput-enhanced service sub-problem using the Lagrange dual decomposition method, including: Based on the total system bandwidth constraint, dual variables are introduced, and based on the transmit power constraint of each terminal, dual variables are introduced to construct the Lagrangian function of the time-slot dynamic decision problem. Based on the separable structure of the Lagrange function, the joint bandwidth and power allocation problem is decomposed into local optimization problems that are independent of each terminal. The local optimization problem of each terminal is further decomposed into the latency guarantee service sub-problem and the throughput enhancement service sub-problem.

[0014] Optionally, based on the local optimum, the dual variable is iteratively updated using the subgradient method until convergence, and the optimization results obtained include: Based on the concavity of the objective function and the linearity of the constraint conditions of the latency guarantee service subproblem and the throughput enhancement service subproblem, the optimal bandwidth allocation and optimal power allocation of each terminal under the current dual variables are obtained by using the KKT conditions respectively. Based on the optimal bandwidth allocation and the optimal power allocation, the dual variables corresponding to the total bandwidth constraint and the dual variables corresponding to the power constraints of each terminal are updated using the subgradient method. Based on the updated dual variable, the local optimal solution based on KKT conditions and the dual variable update by the subgradient method are repeatedly executed until the dual variable converges or the preset number of iterations is reached. The convergence result is used as the optimal bandwidth allocation and power allocation result for the current time slot. The optimization result is obtained based on the optimal bandwidth and power allocation results of the current time slot.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: Existing industrial IoT wireless resource optimization solutions are mostly based on average latency, instantaneous channel capacity, and deterministic latency constraints for modeling and scheduling. These solutions struggle to adapt to the dual randomness of industrial scenarios, characterized by random service arrival and time-varying fading of wireless channels. Furthermore, long-term statistical QoS constraints such as latency default probability are long-term metric indicators, while resource allocation requires real-time decision-making on a per-slot basis. This time-scale mismatch prevents the long-term latency guarantee requirement from being directly embedded in the online scheduling process, making it difficult to simultaneously ensure the reliability of latency-sensitive control services and the long-term transmission experience of data acquisition services. To address these shortcomings, this invention utilizes random network calculus, virtual queue transformation, Lyapunov stochastic optimization, and Lagrange duality to form a complete scheduling framework, possessing the following core innovative advantages and technical effects: 1. Based on random network calculus, accurate quantitative modeling of statistical latency for heterogeneous services is completed, yielding closed-form analytical service thresholds: To distinguish between two typical heterogeneous services in the Industrial Internet of Things (IIoT): for the differentiated characteristics of Poisson random arrival in delay-assured (DG) industrial control services and periodic arrival in throughput-enhanced (TE) data acquisition services, standardized cumulative arrival models are established for each; and an instantaneous transmission rate model is constructed by combining Rayleigh block fading uplink channel to fully characterize the system queue evolution law under random traffic and time-varying channel coupling.

[0016] By utilizing the upper bound of the moment generating function of Poisson arrival and Rayleigh fading, a closed boundary of the statistical delay default probability of DG services is derived. With the help of the Lambert-W function, the minimum effective service capacity analytical threshold that satisfies the delay and default probability constraints is given. This can quantify the statistical service margin required to suppress the delay tail effect under random networks, and solve the shortcoming of traditional schemes that cannot quantify the delay default risk by relying only on average rate and deterministic delay. This provides a unified quantitative constraint benchmark for resource scheduling.

[0017] 2. A virtual queue mechanism for statistical service deficit is proposed to break down the time scale barrier between long-term statistical constraints and single-slot real-time decision-making: This invention constructs a virtual queue for statistical service deficit, using the minimum effective service threshold derived from SNC as the evaluation criterion: when the instantaneous effective service rate of a time slot is lower than the threshold, the virtual queue accumulates service deficit; when it is higher than the threshold, historical deficits are automatically deducted. Furthermore, it rigorously proves that the stability of the virtual queue mean is equivalent to the validity of the long-term delay default probability constraint of DG services.

[0018] This design transforms probabilistic QoS constraints that span time slots and long-term scales into queue stability conditions that can be observed in real time and adjusted on a time slot basis. This completely solves the core pain point in traditional methods where long-term statistical constraints cannot be directly applied to bandwidth and power allocation in each time slot, enabling online real-time scheduling to meet statistical latency guarantee requirements.

[0019] 3. By integrating Lyapunov optimization to decouple long-term global optimization problems, the computational complexity of online scheduling at the edge is significantly reduced: The original optimization objective is to maximize the long-term average Quality of Experience (QoE) over an infinite time domain. Given the strong coupling of queue states across time slots, this is a highly complex stochastic global optimization problem. This invention combines the DG physical service queue, TE physical service queue, and statistical deficit virtual queue to construct a unified Lyapunov function, derives the upper bound of conditional drift, and introduces the TE service utility function to construct a drift plus penalty function. By flexibly balancing system queue stability and long-term TE service experience quality with a single adjustable trade-off parameter V, the scheduling tendency of "prioritizing control latency" or "prioritizing improving acquisition throughput" can be freely switched according to the priority of industrial scenarios. The complex long-term optimization in the infinite time domain is equivalently decomposed into an independent single-time-slot decision subproblem that depends only on the current time-slot channel and queue state. This eliminates the state coupling between time slots, significantly reduces the amount of online scheduling computation, and adapts to the lightweight real-time computing needs of industrial edge access points.

[0020] 4. Lagrange dual hierarchical decomposition to achieve joint distributed optimal allocation of bandwidth and transmit power: For the two types of globally coupled constraints—total system bandwidth and maximum terminal transmit power—a hierarchical dual decomposition method is used to simplify the solution process: By introducing bandwidth and power as corresponding dual variables to construct a Lagrangian function, and utilizing the separability of the objective function, the global joint optimization is decomposed into independent local optimization problems for each terminal; within a single terminal, it is further decomposed into two types of service sub-problems: DG and TE, which do not interfere with each other. Both subproblems are concave optimization and linearly constrained convex programming. The KKT conditions are used to quickly solve the closed-form solution of the optimal bandwidth and power allocation for a single terminal. Then, the dual variables are iteratively updated through the subgradient method until convergence, and the globally optimal resource allocation scheme of the time slot is obtained.

[0021] This distributed solution architecture does not require a centralized high-performance computing center. Multiple terminals can perform parallel local computations, taking into account both the overall global resource constraints and the differentiated QoS requirements of terminal services. It also features fast scheduling and convergence speed and low engineering implementation difficulty.

[0022] 5. Multi-scenario simulation verification shows that the overall performance is superior to traditional benchmark scheduling algorithms: Using three mainstream traditional schemes—static uniform allocation, maximum queue backlog priority, and channel queue awareness ratio heuristic—as benchmarks, simulation results demonstrate significant performance advantages: DG service latency reliability is stronger: Under the same service load, the average queue backlog of DG is reduced by up to 27.9%, and the physical service queue and the statistical deficit virtual queue remain bounded and stable in the long term; under the dual random disturbances of Poisson burst traffic and deep Rayleigh fading, the latency default probability is always strictly controlled to meet the hard requirements of high reliability statistical latency for industrial closed-loop control services. TE services offer a superior long-term experience: When system bandwidth resources are sufficient, the long-term average QoE of TE services is significantly higher than that of the comparison algorithm; by balancing parameter V, the trade-off between latency assurance and throughput experience can be precisely controlled. It exhibits outstanding resource adaptability and robustness: in scenarios with low bandwidth and scarce resources, it automatically prioritizes resource allocation to ensure the latency safety threshold of DG services; after bandwidth expansion, it fully releases the throughput gain of TE services and adapts to the dynamic fluctuation conditions of industrial network bandwidth; under long-term online simulation with thousands of time slots, the virtual service deficit can be quickly self-compensated, without queue divergence or continuous congestion issues, and has strong resistance to random disturbances.

[0023] 6. The model closely matches the real-world business characteristics of the Industrial Internet of Things (IIoT), making it highly practical for implementation. This invention fully matches typical industrial edge uplink transmission scenarios, covering two core heterogeneous services: closed-loop control of industrial robots and equipment status monitoring. All key thresholds and optimal resource allocation have analytical closed expressions, eliminating the need for offline big data training. Online iterative convergence is fast, and it can be directly deployed at industrial wireless access points to complete millisecond-level real-time time slot scheduling. While ensuring the hard latency statistical constraints of industrial control services, it maximizes the monitoring data transmission experience, taking into account both industrial system reliability and data transmission efficiency. Attached Figure Description

[0024] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a diagram of an industrial IoT edge network uplink transmission system according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the change of the statistical effective service rate threshold concept with arrival rate in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the changes in the long-term utility of TE services and the backlog of DG service queues as a function of the trade-off parameter V in an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the performance of the Lyapunov and Lagrange duality algorithm proposed in this embodiment of the invention as a function of the total system bandwidth; Figure 5 This is a schematic diagram illustrating the change in queue backlog control performance based on the Lyapunov and Lagrange dual algorithm as a function of DG service arrival rate in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating an actual demonstration of the algorithm proposed in this invention within 1000 online decision slots according to an embodiment of the invention; Figure 7 This is a schematic diagram of an industrial IoT wireless resource optimization method based on random network calculus, according to an embodiment of the present invention. Detailed Implementation

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0027] This embodiment proposes an industrial IoT wireless resource optimization method based on random network calculus, such as... Figure 7 As shown, the specific steps include: Based on the differentiated quality of service requirements of heterogeneous services in the industrial IoT edge network, a system queue evolution model including latency-guaranteed services and throughput-enhanced services is established. Based on the system queue evolution model, the statistical delay default probability boundary of the delay guarantee service is obtained using the random network calculus theory, and the minimum effective service capacity threshold that satisfies the statistical delay constraint is determined based on the statistical delay default probability boundary. Based on the minimum effective service capacity threshold, with the optimization objective of maximizing the long-term average QoE of throughput enhancement services and the latency guarantee services satisfying the statistical latency default probability constraint, an optimization problem is constructed. The optimization problem is solved to obtain the optimization results.

[0028] Specifically, this embodiment comprehensively considers the random arrival characteristics of services and the random service process of wireless channels, establishes a system queue evolution model, and derives the latency default probability boundary of latency-guaranteed services using stochastic network calculus theory. Addressing the problem that statistical latency constraints are difficult to directly apply to dynamic decision-making, the minimum service capacity threshold required to meet statistical latency requirements is derived using SNC and transformed into a constraint condition for per-slot resource allocation. By constructing a virtual queue, long-term statistical latency constraints are transformed into a queue stability problem, establishing a connection between long-term statistical performance indicators and current time-slot decision variables. A joint resource scheduling algorithm based on Lyapunov optimization is designed, decoupling the complex long-term optimization problem into a low-complexity per-slot dynamic decision problem. The proposed method enables the system to improve the long-term experience quality of the system throughput enhancement service while satisfying the statistical latency constraints of latency-guaranteed services and system queue stability.

[0029] Furthermore, establishing a system queue evolution model that includes latency-guaranteed services and throughput-enhanced services includes: Based on the Poisson arrival characteristics of the latency guarantee service and the periodic arrival characteristics of the throughput enhancement service, cumulative arrival models for the two types of services are established respectively. An instantaneous transmission rate model for the uplink wireless link is established based on the block fading channel model, and the actual service volume of the two types of services in each time slot is determined based on the instantaneous transmission rate model. Based on the cumulative arrival volume model and the actual service volume, update equations are established for the latency-guaranteed service queue and the throughput-enhanced service queue, resulting in the system queue evolution model.

[0030] Specifically, consider an uplink transmission system for industrial IoT edge networks, such as... Figure 1 As shown, the system consists of a wireless access point and multiple terminal devices, with the devices grouped together using... This indicates that industrial robots and other terminals generate two distinct service needs during operation: one is latency-assured services for scenarios such as industrial control, status feedback, and closed-loop regulation; the other is throughput-enhancing services for scenarios such as data acquisition and monitoring feedback. The former is more sensitive to transmission latency and its default risk, while the latter focuses more on continuous transmission capabilities and long-term service experience.

[0031] Assume the system uses a discrete time-slot model, with time divided into equal-length time slots. time slot The total bandwidth shared by all devices' DG and TE services is [missing information]. The uplink radio access resources. The DG service generated by device n can be represented by a binary array. express, Indicates the size of the task data packet. This represents the upper limit threshold for task latency. Control commands, alarm messages, and other DG services are generated per time slot according to a Poisson distribution, with an average arrival rate of [missing information]. For TE services such as data acquisition and monitoring feedback, the model is based on periodic arrival, with a period of [period missing]. The data packet size is Unlike DG services, TE services focus more on the continuous transmission capabilities that can be obtained during the radio access phase.

[0032] Business arrival model: For terminal devices For DG services, service packets arrive in each time slot according to a Poisson process, with an average arrival rate of Record the first The number of data packets arriving in each time slot for DG service is Then we have: ; Therefore, the first The arrival volume of DG services in a time slot can be expressed as: ; In the interval The cumulative arrivals are: ; Since the Poisson arrival process has the property of independent increments, its moment generating function can be written as: ; Therefore, for The arrival process of DG services satisfies the upper bound form of the Moment Generating Function (MGF) in random network calculus, that is: ; in, ; For TE services that arrive periodically at terminal devices, the definition is... For TE business in The cumulative arrivals over the interval are: ; in This represents the floor function.

[0033] Wireless transmission and queue evolution model: Assuming the uplink wireless link follows a block fading channel model, meaning the channel state remains constant within a single time slot but changes independently between different time slots, the channel is modeled as a Rayleigh fading channel with additive white Gaussian noise and small-scale fading. Follow the variance The Rayleigh distribution. The distance between the base station and the terminal device is... Large-scale fading path loss is , This is the path loss factor. The model uses orthogonal frequency division multiplexing (OFDM) technology and ignores co-channel interference, therefore the terminal... The DG business and TE business in the first The instantaneous transmission rates of each time slot are as follows: ; ; in and These represent the bandwidth allocated by the system to device n for DG and TE services, respectively. and These are the transmit powers for DG and TE services, respectively. It is a constant related to antenna gain and carrier frequency. It is noise power.

[0034] In the Within each time slot, the actual service volume of the two types of services can be expressed as follows: , ; in This refers to the length of a unit time slot. Because both the service arrival process and the wireless service process are random, the system state needs to be described through queue evolution. These are defined separately. and For the first Terminal at the start of each time slot Given the backlog of the DG and TE queues, the queue update equations for both types of services can be uniformly written as: ; ; The queue evolution equations above show that the queue length is determined by both the number of incoming services and the wireless service volume. When the service volume in a given time slot is less than the sum of the current backlog and newly arrived services, the queue will continue to grow; conversely, if the service volume can process arriving services in a timely manner, the system queue can remain stable. For any... and All of them have: ; Then the corresponding business queue is said to be stable.

[0035] Unlike DG services, TE services do not focus on statistical latency default probability, but rather on long-term transmission experience. Therefore, this embodiment uses a square root utility function to characterize its service experience quality, namely: ; in It is the rate sensitivity factor. Indicates the first The instantaneous transmission rate obtained by the TE service in each time slot. This utility function has the characteristic of diminishing marginal returns, and can well characterize the actual law of how throughput improvement improves service experience.

[0036] Furthermore, based on the system queue evolution model, the statistical delay default probability boundary of the delay guarantee service is obtained using stochastic network calculus theory, including: Based on the system queue evolution model, and according to the moment generating function characteristics of the Poisson arrival process of the delay guarantee service, the upper bound form of the moment generating function of the cumulative arrival amount is determined; Based on the power gain distribution characteristics of the Rayleigh fading channel, the upper bound of the moment generating function of the actual service process is determined; Based on the upper bound of the moment generating function of the cumulative arrivals and the upper bound of the moment generating function of the actual service process, the statistical delay default probability boundary of the delay guarantee service is obtained using the delay boundary theory in random network calculus.

[0037] Specifically, for DG services, the core objective is not simply to increase the average transmission rate, but to meet given statistical delay guarantees under conditions of random arrival and random radio service. Based on the above modeling, the end-to-end service process of DG services can be characterized by the uplink radio transmission service process. Definition For interval The cumulative service volume on the platform, Represented as: ; The MGF for the DG service offloading transmission queue service process is: ; For Rayleigh fading channels, power gain Follow the mean The exponential distribution, let Under the assumption of independent block fading, it can be written in the product form of the generating functions of the service process moments in each time slot: ; To simplify the calculation, let The formula can be further written as: ; To solve for the integral term in the above equation, let: ; in , Let be a constant. By making appropriate variable substitutions, the above equation can be transformed into the standard integral form of an upper incomplete gamma function. According to the definition of an upper incomplete gamma function, the integral result can be expressed as: ; in It is an incomplete gamma function. Its effect can be obtained. The upper bound of the constraint MGF is: ; terminal equipment latency of DG services This includes latency for devices queuing in the queue and latency for communication to the edge server.

[0038] Assuming the arrival and service processes are independent, the latency default probability of DG services can be expressed as follows, based on random network calculus: ; Expanding the above equation further, we get: ; in By utilizing the joint boundary inequality, The Chernov inequality was used. The MGF theorem was used, that is, for Constraint arrival process and dynamic servers ,have and , It is a polynomial summation. It is a stability condition.

[0039] ; From the above formula, we can see that The statistical arrival intensity of DG services in the sense of the moment generating function characterizes the arrival process. The statistical service capability characterizes the wireless service process. When the statistical service capability is lower than the statistical arrival strength, the system queue is more prone to backlog, leading to an increased probability of latency default. Conversely, when the statistical service capability can meet the service arrival requirements, the latency default probability of DG services can be stably controlled within a given constraint range.

[0040] Furthermore, the minimum effective service capacity threshold is: ; in, The minimum effective service capacity threshold, To ensure the average arrival rate of services with low latency, For the size of the business data packet, For the free parameters of random network calculus, For the time delay threshold, This is the threshold for the probability of default. For Lambert- W The main branch of the function.

[0041] Furthermore, the optimization problem is solved to obtain the optimization results, including: Construct a virtual queue for statistical service deficit, and transform the long-term statistical latency constraints of the latency guarantee service into stability conditions for the virtual queue; Based on the stability condition of the virtual queue, Lyapunov optimization theory is introduced to construct a drift plus penalty function, which decouples the long-term resource optimization problem into a time-slot dynamic decision problem. Based on the aforementioned time-slot dynamic decision problem, the joint bandwidth and power allocation problem is decomposed into a delay guarantee service subproblem and a throughput enhancement service subproblem using the Lagrange dual decomposition method, and the local optimal solutions of each subproblem are solved based on the KKT conditions. Based on the local optimal solution, the dual variable is iteratively updated using the subgradient method until convergence, thus obtaining the optimization result.

[0042] Furthermore, constructing a virtual queue for statistical service deficit includes: Based on the minimum effective service capacity threshold and the instantaneous effective service rate of the current time slot, the evolution equation of the statistical service deficit virtual queue is defined, wherein the instantaneous effective service rate is jointly determined by the bandwidth allocated to the current time slot, the transmit power, and the instantaneous channel state. According to the evolution equation, when the instantaneous effective service rate is lower than the minimum effective service capacity threshold, the virtual queue grows; when the instantaneous effective service rate is higher than the minimum effective service capacity threshold, the virtual queue decreases.

[0043] Furthermore, based on the stability condition of the virtual queue, a drift plus penalty function is constructed using Lyapunov optimization theory, including: Based on the stability conditions of the latency-guaranteed service queue, the throughput-enhanced service queue, and the virtual queue, construct the Lyapunov function of the system; Based on the Lyapunov function, a conditional Lyapunov drift is defined, and the upper bound expression of the conditional Lyapunov drift is derived using the queue update equation. Based on the upper bound expression of the conditional Lyapunov drift and the utility function of the throughput enhancement service, the drift plus penalty function is constructed, wherein the drift plus penalty function includes control parameters for balancing system stability and long-term experience quality optimization.

[0044] Furthermore, the long-term resource optimization problem is decoupled into a time-slot-by-time dynamic decision-making problem, including: Based on the upper bound expression of the drift plus penalty function, minimizing the upper bound of the drift plus penalty function is equivalently transformed into maximizing the decision objective function that includes the coupling relationship between queue backlog weight and instantaneous service volume in each time slot; Based on the decision objective function, the long-term resource optimization problem is decoupled into a time-slot-by-time dynamic decision problem that depends only on the current time-slot queue state and the channel state.

[0045] Furthermore, based on the aforementioned time-slot-by-time dynamic decision-making problem, the Lagrange dual decomposition method is used to decompose the joint bandwidth and power allocation problem into a latency-guaranteed service sub-problem and a throughput-enhanced service sub-problem, including: Based on the total system bandwidth constraint, dual variables are introduced, and based on the transmit power constraint of each terminal, dual variables are introduced to construct the Lagrangian function of the time-slot dynamic decision problem. Based on the separable structure of the Lagrange function, the joint bandwidth and power allocation problem is decomposed into local optimization problems that are independent of each terminal. The local optimization problem of each terminal is further decomposed into the latency guarantee service sub-problem and the throughput enhancement service sub-problem.

[0046] Furthermore, based on the local optimal solution, the dual variable is iteratively updated using the subgradient method until convergence, yielding the following optimization results: Based on the concavity of the objective function and the linearity of the constraint conditions of the latency guarantee service subproblem and the throughput enhancement service subproblem, the optimal bandwidth allocation and optimal power allocation of each terminal under the current dual variables are obtained by using the KKT conditions respectively. Based on the optimal bandwidth allocation and the optimal power allocation, the dual variables corresponding to the total bandwidth constraint and the dual variables corresponding to the power constraints of each terminal are updated using the subgradient method. Based on the updated dual variable, the local optimal solution based on KKT conditions and the dual variable update by the subgradient method are repeatedly executed until the dual variable converges or the preset number of iterations is reached. The convergence result is used as the optimal bandwidth allocation and power allocation result for the current time slot. The optimization result is obtained based on the optimal bandwidth and power allocation results of the current time slot.

[0047] Specifically, based on the service arrival model, wireless transmission model, and statistical delay analysis results constructed above, the goal of this section is to optimize the bandwidth resource allocation for each time slot in the system. and transmission power The optimization objective is to maximize the long-term average QoE of the TE (Transportation, Service) business, while simultaneously requiring the DG (Delivery, Service) business to meet the statistical latency default probability constraint, and maintaining the stability of both business queues. The optimization problem can be expressed as P1: ; Among the constraints This represents the statistical delay default probability constraint for DG business. Indicates and These represent the stability constraints of the DG service queue and the TE service queue, respectively. This indicates the system's total bandwidth resource constraint. This indicates the transmit power limit for a single terminal.

[0048] The difficulties in solving the aforementioned optimization problem mainly lie in two aspects. First, the statistical delay constraint of DG services is essentially a long-term probabilistic constraint, which is difficult to transform into a deterministic condition for single-slot resource scheduling. Second, the evolution of system queues is tightly coupled in the time dimension, making long-term stochastic optimization problems difficult to solve directly.

[0049] This embodiment derives the minimum statistical service capacity threshold that satisfies a given statistical latency requirement based on the statistical latency default probability constraint of DG services. This threshold is then transformed into a virtual queue stability constraint, providing theoretical guidance for real-time resource scheduling.

[0050] Based on system modeling, consider the terminal For DG services, the arrival of data packets follows a Poisson distribution with an average arrival rate of [missing information]. The size of a single data packet is Let the interval be... The cumulative arrivals are Based on the analysis results of the arrival process given above, for any The arrival process satisfy Upper bound form: ; in ; On the service side, let the first... The bandwidth allocated to the DG service in the time slot is The amount of wireless service provided by DG services in this time slot can be expressed as: ; The analysis of the wireless service process shows that its instantaneous effective service rate is: ; If the channel state within the current time slot is determined, it is denoted as... .

[0051] According to the delay boundary theory in random network calculus, the delay default probability of DG services satisfies the following upper bound: ; in This represents the statistical effective service rate of DG's business. When it is less than a given default probability threshold... When this condition is met, the business can be considered to satisfy the statistical latency constraint. Therefore, the original statistical latency constraint can be transformed into the following deterministic inequality regarding the statistical effective service rate: ; This embodiment uses the Lambert W function to provide an analytical closed-form expression for the threshold, facilitating its subsequent embedding into an online decision-making framework. This yields the minimum effective service rate threshold required for the DG service to meet statistical latency requirements: ; The minimum statistical service capability required for DG services is related to its arrival rate, packet size, latency threshold, default probability threshold, and QoS index. Commonly related. Parameters The value of is the parameter with the smallest value, that is It can be obtained using one-dimensional search using optimization algorithms such as grid search or Nelder-Mead.

[0052] Given these parameters, the statistical latency constraint for DG services can be transformed into ensuring that the instantaneous effective service rate is not lower than the minimum statistical effective service rate threshold under the long-term average meaning. The inequality constraints are as follows: ; The statistical latency guarantee requirement for DG services can essentially be equated to the problem of ensuring the system continuously provides sufficient service capacity during long-term operation. The instantaneous effective service rate is determined by bandwidth allocation, power allocation, and instantaneous channel conditions. .

[0053] To embed this long-term statistical constraint into the dynamic decision-making process for each time slot, a virtual queue for statistical service deficit is constructed for each DG service. The queue evolution equation is defined as: ; This virtual queue is used to characterize the historical deficiencies in the statistical service capabilities of DG services. When the actual effective service rate falls below a threshold within a certain time slot... When the virtual queue grows, the effective service rate provided by that time slot is higher than expected. When this happens, the virtual queue decreases. The system can transform long-term statistical latency requirements into a virtual queue stability problem through dynamic accumulation and subsequent compensation. If the virtual queue... Satisfies mean rate stability: ; Therefore, the original long-term statistical constraints must hold.

[0054] So far, the original question The long-term latency constraints were transformed into virtual queues. Stability dynamic decision problem : ; The long-term statistical delay constraint, which is the most difficult part of the original problem, has been transformed into a deterministic constraint concerning the stability of the virtual queue and the decision variables per time slot.

[0055] By introducing Lyapunov optimization theory, and constructing a Lyapunov function for queue states, the long-term average QoE of TE services is maximized and integrated with queue stability constraints into the same trade-off framework, transforming the original long-term optimization problem into a decision problem solvable on a time-slot basis.

[0056] set up and They represent time slots respectively. The lengths of the DG service queue and TE service queue of device n. and These represent the arrival volume of the two types of services within the same time slot. and These represent the actual service volume provided by the system for the two types of services within this time slot. The queue update equations for the two types of services can be written as: ; ; The above queue update relationship shows that the resource allocation result of the system in each time slot directly affects the dynamic change trend of each service queue. Defining Time Slots The queue state vector is: ; Based on this, the Lyapunov function of the system is defined as follows: ; The larger this function value is, the more severe the current data backlog in the system, or the more significant the deficiency in the statistical services of the DG business. To ensure queue stability while also considering the long-term performance of the TE business, conditional Lyapunov drift is introduced: ; Update equations and inequalities using queues Expandable: ; Given the current queue state Under the given conditions, taking the conditional expectation of both sides simultaneously, we obtain the upper bound of the Lyapunov drift: ; The system's arrival volume, service volume, and instantaneous effective service rate are all bounded, meaning they are finite constants. .

[0057] Based on the Lyapunov drift upper bound obtained from the current queue update model, a drift penalty term is constructed to maintain queue stability and improve the long-term average QoE of TE services: ; Substituting into the above formula, we get: ; in This is a trade-off parameter used to balance system stability with long-term QoE optimization. As can be seen from the formula, the constant term... It doesn't affect resource control decisions for each time slot; what it truly impacts is the coupling relationship between queue backlog and instantaneous service volume. Minimizing the upper bound of the drift plus penalty function is equivalent to... Maximize the following expression: ; Control parameters The larger the value, the more the system tends to improve the efficiency of TE services; The smaller the value, the more the system tends to prioritize ensuring queue stability. (Problem) Can be equivalently transformed into a problem : ; Although problem P3 has a good convex structure, different terminals are still coupled to each other through the total bandwidth constraint, making direct separation and solution difficult. To reduce the solution complexity, this embodiment uses the Lagrange dual decomposition method. Regarding the total bandwidth constraint... Introducing dual variables Terminal power constraints Introducing dual variables The Lagrangian function for question P3 is: ; Summarized as follows: ; The local Lagrange term for terminal n is: ; Given dual variables and Under these conditions, the terminal local problem can be decomposed into two independent optimization subproblems.

[0058] For the terminal The optimization problem is decomposed into DG (Demand, Service) business sub-problems and TE (Service, TE) business sub-problems. The DG business sub-problem is as follows: ; The TE business sub-problem is: ; The objective functions of both subproblems are concave, and the constraints are both linear, ensuring that their optimal solutions exist uniquely. By combining the KKT conditions, the optimal bandwidth and power allocation for each terminal under the current dual variables can be obtained.

[0059] For the DG business subproblem, the definition is as follows: ; Its optimal solution satisfies: ; Similarly, for the TE business sub-problem, the definition is: ; Its optimal solution satisfies: ; Since each local subproblem is a convex optimization problem, this embodiment uses a numerical iterative method based on KKT conditions to solve it, thereby obtaining the optimal local decision variables for each terminal.

[0060] After obtaining the local optimal solutions for each terminal, the dual variables can be updated using the subgradient method. The dual variable update corresponding to the total bandwidth constraint is as follows: ; The dual variables corresponding to the power constraints of each terminal are updated as follows: ; in, For the first The step size of the next iteration. Since the original problem is a convex optimization problem and satisfies strong duality, when the dual variables converge iteratively, the bandwidth and power allocation results obtained from the local subproblems are the global optimal solutions to the original per-slot joint optimization problem.

[0061] In summary, the algorithm for solving problem P3 is shown in Table 1.

[0062] Table 1 To verify the effectiveness of the proposed algorithm, this embodiment selects the following three benchmark schemes for comparison: (1) Static uniform allocation scheme. The system uniformly allocates bandwidth and power resources in each time slot, without considering queue state differences and long-term QoE targets.

[0063] (2) Maximum queue backlog priority scheme. In each time slot, the system prioritizes allocating resources to the service with the largest current queue backlog in order to minimize the instantaneous backlog level.

[0064] (3) Channel and queue awareness ratio heuristic scheme. The system observes the current channel state and queue length in each time slot, and the resource allocation weight of each service is defined as the product of the current physical queue length and the instantaneous channel gain. The system allocates the total bandwidth and total power according to the normalized ratio of this dynamic weight.

[0065] This embodiment uses Python 3.10 to simulate an IIoT wireless uplink transmission system consisting of one base station and two terminal devices. The simulation parameters are shown in Table 2. Table 2 Figure 2 Demonstrates maximum tolerable latency milliseconds (ms) are the probability of a default due to latency. The minimum statistical effective service rate required by the system is as follows. With DG's average reach rate The change in arrival rate can be observed. The minimum statistical effective service rate threshold is consistently higher than the average arrival rate, and the gap between the two increases with the arrival rate. The statistical service margin increases with the increase in traffic arrival rate. This indicates that in a random network environment, to overcome the suddenness of Poisson traffic arrival and suppress the long-tail effect of queuing delay distribution, the system cannot simply handle the average traffic and must allocate additional statistical service margin. As the service arrival rate increases, the statistical service margin required by the system also increases to meet strict statistical QoS constraints.

[0066] Figure 3 This intuitively reveals the theoretical trade-off mechanism between utility and time delay within the Lyapunov stochastic optimization framework. In the earlier stages, the system prioritizes maintaining network stability, with less emphasis on DG (Demand for Goods) services. and This dominance results in the system allocating very little bandwidth and power to TE services. At this point, TE utility is suppressed to around 850. With... As the order of magnitude increases, the penalty for TE utility terms begins to grow, and the system allocates more bandwidth resources to TE services, resulting in a decrease in TE utility. A monotonous increase. In a larger... Within the region, while the long-term average QoE of the TE business continues to rise, the rate of increase is slowing down, while the average queue backlog of the DG business continues to increase significantly, indicating that... The value needs to be set reasonably in combination with the needs of business latency protection and experience enhancement, so as to achieve a trade-off between system stability and long-term utility.

[0067] Figure 4 This paper demonstrates the evolution of four algorithms in terms of long-term utility for TE services and queue backlog for DG services as the total available bandwidth of the system expands from 400kHz to 900kHz. At extremely low bandwidths of 400-500kHz, the system is in a resource-scarce state, and the algorithm proposed in this embodiment performs worse than the static uniform allocation and maximum queue priority algorithms in terms of TE service utility. However, as the available bandwidth of the system increases, this algorithm demonstrates the optimal performance.

[0068] Figure 5 The study demonstrates how the average queue backlog of DG services changes with the average arrival rate of DG services using four different resource allocation algorithms. Figure 5 This directly reflects the system's ability to control backlog in DG (Delivery and Gauge) traffic. As the arrival rate increases, the queue backlog for all algorithms shows an upward trend. Performance differences are not significant during periods of low system load, but... The algorithms exhibited divergent performance. The static uniform allocation algorithm, lacking dynamic scheduling capabilities, saw its backlog grow to approximately 5100 bits; the maximum queue first algorithm, due to local greed, resulted in a backlog exceeding 4000 bits. In contrast, the algorithm proposed in this embodiment consistently maintained the lowest queue backlog among all schemes, with a backlog of only 3676 bits, representing a maximum reduction of 27.9% compared to the static uniform allocation. This demonstrates the effectiveness of introducing a backlog queue and a virtual queue derived from random network computation in this embodiment. This ensures strong system stability, preventing the average backlog from diverging, thus guaranteeing the system's efficiency in resource allocation. Figure 5 While improving efficiency, resource allocation will be limited to a safe range that does not exceed the statistical latency limit of DG business.

[0069] Figure 6 Demonstrates the physical queues of DG services within 1000 online decision slots. With virtual queues The dynamic evolution trajectory. As can be seen from the figure, under the dual random process of sudden Poisson arrival and Rayleigh fading channel, and The system exhibits high-frequency sawtooth-like fluctuations, with physical queue backlogs mainly concentrated between 250 and 2000 bits, reaching an extreme peak of approximately 2700 bits, but consistently remaining strictly within a certain upper bound, indicating good system stability. The SNC virtual queue characterizes the statistical service deficit. The values ​​remain in the 0 to 1200 bit range for most of the time and can drop rapidly. It always remains bounded. In resource-constrained scenarios, bursty traffic and time-varying channels can easily lead to delay violations and virtual queue collapses. The virtual queues in the figure remain stable over a long period, proving that the algorithm in this paper effectively avoids instantaneous congestion and ensures the strict statistical QoS requirements of DG services under limited bandwidth and power.

[0070] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for optimizing wireless resources in the Industrial Internet of Things based on random network calculus, characterized in that, include: Based on the differentiated quality of service requirements of heterogeneous services in the industrial IoT edge network, a system queue evolution model including latency-guaranteed services and throughput-enhanced services is established. Based on the system queue evolution model, the statistical delay default probability boundary of the delay guarantee service is obtained using the random network calculus theory, and the minimum effective service capacity threshold that satisfies the statistical delay constraint is determined based on the statistical delay default probability boundary. Based on the minimum effective service capacity threshold, with the optimization objective of maximizing the long-term average experience quality of throughput enhancement services and the latency guarantee services satisfying the statistical latency default probability constraint, an optimization problem is constructed. The optimization problem is solved to obtain the optimization results.

2. The industrial IoT wireless resource optimization method based on random network calculus according to claim 1, characterized in that, Establishing a system queue evolution model that includes latency-guaranteed services and throughput-enhanced services includes: Based on the Poisson arrival characteristics of the latency guarantee service and the periodic arrival characteristics of the throughput enhancement service, cumulative arrival models for the two types of services are established respectively. An instantaneous transmission rate model for the uplink wireless link is established based on the block fading channel model, and the actual service volume of the two types of services in each time slot is determined based on the instantaneous transmission rate model. Based on the cumulative arrival volume model and the actual service volume, update equations are established for the latency-assured service queue and the throughput-enhanced service queue, thus obtaining the system queue evolution model.

3. The industrial IoT wireless resource optimization method based on random network calculus according to claim 2, characterized in that, Based on the system queue evolution model, the statistical delay default probability boundary of the delay guarantee service is obtained using stochastic network calculus theory, including: Based on the system queue evolution model, and according to the moment generating function characteristics of the Poisson arrival process of the delay guarantee service, the upper bound form of the moment generating function of the cumulative arrival amount is determined; Based on the power gain distribution characteristics of Rayleigh fading channels, the upper bound of the moment generating function for the actual service process is determined. Based on the upper bound of the moment generating function of the cumulative arrivals and the upper bound of the moment generating function of the actual service process, the statistical delay default probability boundary of the delay guarantee service is obtained using the delay boundary theory in random network calculus.

4. The industrial IoT wireless resource optimization method based on random network calculus according to claim 1, characterized in that, The minimum effective service capacity threshold is: ； in, The minimum effective service capacity threshold, To ensure the average arrival rate of services with low latency, For the size of the business data packet, For the free parameters of random network calculus, For the time delay threshold, This is the threshold for the probability of default. For Lambert- W The main branch of the function.

5. The industrial IoT wireless resource optimization method based on random network calculus according to claim 1, characterized in that, Solving the optimization problem and obtaining the optimization results includes: Construct a virtual queue for statistical service deficit, and transform the long-term statistical latency constraints of the latency guarantee service into stability conditions for the virtual queue; Based on the stability condition of the virtual queue, Lyapunov optimization theory is introduced to construct a drift plus penalty function, which decouples the long-term resource optimization problem into a time-slot dynamic decision problem. Based on the aforementioned time-slot dynamic decision problem, the joint bandwidth and power allocation problem is decomposed into a delay guarantee service subproblem and a throughput enhancement service subproblem using the Lagrange dual decomposition method, and the local optimal solutions of each subproblem are solved based on the KKT conditions. Based on the local optimal solution, the dual variable is iteratively updated using the subgradient method until convergence, thus obtaining the optimization result.

6. The industrial IoT wireless resource optimization method based on random network calculus according to claim 5, characterized in that, Constructing a virtual queue for statistical service deficit includes: Based on the minimum effective service capacity threshold and the instantaneous effective service rate of the current time slot, the evolution equation of the statistical service deficit virtual queue is defined, wherein the instantaneous effective service rate is jointly determined by the bandwidth allocated to the current time slot, the transmit power, and the instantaneous channel state. According to the evolution equation, when the instantaneous effective service rate is lower than the minimum effective service capacity threshold, the virtual queue grows; when the instantaneous effective service rate is higher than the minimum effective service capacity threshold, the virtual queue decreases.

7. The industrial IoT wireless resource optimization method based on random network calculus according to claim 6, characterized in that, Based on the stability condition of the virtual queue, a drift plus penalty function is constructed using Lyapunov optimization theory, including: Based on the stability conditions of the latency-guaranteed service queue, the throughput-enhanced service queue, and the virtual queue, the Lyapunov function of the system is constructed. Based on the Lyapunov function, a conditional Lyapunov drift is defined, and the upper bound expression of the conditional Lyapunov drift is derived using the queue update equation. Based on the upper bound expression of the conditional Lyapunov drift and the utility function of the throughput enhancement service, the drift plus penalty function is constructed, wherein the drift plus penalty function includes control parameters for balancing system stability and long-term experience quality optimization.

8. The industrial IoT wireless resource optimization method based on random network calculus according to claim 7, characterized in that, Decoupling the long-term resource optimization problem into a time-slot-by-time dynamic decision-making problem includes: Based on the upper bound expression of the drift plus penalty function, minimizing the upper bound of the drift plus penalty function is equivalently transformed into maximizing the decision objective function that includes the coupling relationship between queue backlog weight and instantaneous service volume in each time slot; Based on the decision objective function, the long-term resource optimization problem is decoupled into a time-slot-by-time dynamic decision problem that depends only on the current time-slot queue state and the channel state.

9. The industrial IoT wireless resource optimization method based on random network calculus according to claim 8, characterized in that, Based on the aforementioned time-slot-by-time dynamic decision-making problem, the Lagrange dual decomposition method is used to decompose it into a delay-assurance service sub-problem and a throughput-enhancing service sub-problem, including: Based on the total system bandwidth constraint, dual variables are introduced, and based on the transmit power constraint of each terminal, dual variables are introduced to construct the Lagrangian function of the time-slot dynamic decision problem. Based on the separable structure of the Lagrange function, the joint bandwidth and power allocation problem is decomposed into local optimization problems that are independent of each terminal. The local optimization problem of each terminal is further decomposed into the latency guarantee service sub-problem and the throughput enhancement service sub-problem.

10. The industrial IoT wireless resource optimization method based on random network calculus according to claim 9, characterized in that, Based on the local optimum, the dual variable is iteratively updated using the subgradient method until convergence, yielding the following optimization results: Based on the concavity of the objective function and the linearity of the constraint conditions of the latency guarantee service subproblem and the throughput enhancement service subproblem, the optimal bandwidth allocation and optimal power allocation of each terminal under the current dual variables are obtained by using the KKT conditions respectively. Based on the optimal bandwidth allocation and the optimal power allocation, the dual variables corresponding to the total bandwidth constraint and the dual variables corresponding to the power constraints of each terminal are updated using the subgradient method. Based on the updated dual variable, the local optimal solution based on KKT conditions and the dual variable update by the subgradient method are repeatedly executed until the dual variable converges or the preset number of iterations is reached. The convergence result is used as the optimal bandwidth allocation and power allocation result for the current time slot. The optimization result is obtained based on the optimal bandwidth and power allocation results of the current time slot.

Images