Method for estimating information age in an industrial internet of things scenario

Abstract

The application provides an information age estimation method for an industrial Internet of Things scene, comprising the following steps: proposing an age-based non-adaptive access strategy; constructing an outer two-dimensional stationary Markov chain model to depict the state transition process of real-time information age and local age of the latest generated data packet of a single device at the beginning of each cycle; constructing an inner one-dimensional absorbing Markov chain model to depict the transmission state transition process between time slots in any superframe of the single device; then, using a Newton iteration algorithm to solve the double-layer model, and further estimating the system average information age. The application can accurately estimate the system average information age under different network parameters, and thus can provide help for transmission strategy design and information age optimization research in the industrial Internet of Things scene.

Description

Technical Field

[0001] This invention relates to the field of wireless network communication technology, specifically to a method for estimating the age of information in an industrial Internet of Things (IoT) scenario. Background Technology

[0002] Data acquisition from industrial equipment is the foundation and prerequisite for intelligent manufacturing and the Industrial Internet of Things (IIoT). Information age, as a crucial performance indicator measuring the real-time performance and freshness of data transmission, is essential for real-time detection, monitoring, and precise decision-making control under the periodic data updates of the IIoT. Due to inter-device interference, information age estimation allows for the design of more rational transmission strategies, thereby optimizing system performance. However, previous studies on information age in periodically generated networks have assumed that each device generates data packets with a probability of 1 at the beginning of each period, neglecting the general case where the generation probability of each device is less than 1, significantly limiting the applicability of information age estimation methods. Furthermore, previous work assumed that transmission behavior is independent of its corresponding real-time information age, leading to performance optimization bottlenecks. Summary of the Invention

[0003] This invention aims to provide a method for estimating the information age in industrial IoT scenarios, targeting data periodicity generation probability of... Furthermore, a network employing an age-based random access strategy for transmission is constructed, and a two-layer Markov chain model is built to accurately estimate the average AoI of the system under different network parameters. Therefore, it can provide assistance for the design of transmission strategies and the optimization of information age in industrial IoT scenarios.

[0004] The technical solution to achieve the objective of this invention is as follows: a method for estimating the information age in an industrial Internet of Things (IIoT) scenario. The objective is to define an IIoT scenario with N mutually interfering devices and a common control center. The N devices send newly generated data packets to the control center through a shared channel. Each device generates a data packet with probability λ only at the beginning of each cycle, with a cycle length of D. Each device is allowed to send the latest, untransmitted data packet with a fixed probability p only when the corresponding real-time information age reaches a certain threshold δ. Successful transmission occurs only when a single device accesses the channel to send a data packet; otherwise, a collision occurs, affecting all devices. Failures occur; unsuccessfully transmitted data packets will be continuously retransmitted until replaced by newly generated data packets; after successful transmission, the device will remain silent until a new data packet is generated after receiving a feedback signal from the control center without errors or delays; the feature is that: an outer two-dimensional stationary Markov chain model is constructed to characterize the state transition process of a single device at the beginning of each cycle and the local age of the latest generated data packet; an inner one-dimensional absorbing Markov chain model is constructed to characterize the state transition process of a single device between each time slot in any superframe; then, the Newton-Raphson iteration algorithm is used to solve this two-layer model, and then the system average AoI is estimated.

[0005] Furthermore, according to claim 1, the information age estimation method for an industrial IoT scenario is characterized in that there are N independent devices in the network, the data generation period is D, and each device only generates data with probability at the beginning of each period. Generate data packets at other times, but not at other times.

[0006] Furthermore, according to claim 1, the information age estimation method for an industrial IoT scenario is characterized in that each device is allowed to only be used when its corresponding real-time AoI reaches a certain threshold value. A fixed probability approach can only be used if the newly generated data packet fails to be transmitted. Send data, otherwise remain silent.

[0007] Furthermore, according to the information age estimation method for an industrial IoT scenario as described in claim 1, the data packet can be successfully transmitted only when a single device accesses and sends the data packet within the channel; otherwise, a collision occurs and all devices fail. The data packet that has collided will continue to be retransmitted until it is successfully transmitted or replaced by a newly generated data packet. Once the control center successfully receives the data packet from the device, it will transmit a feedback signal through a control channel with no errors and no delays.

[0008] Furthermore, according to the information age estimation method for an industrial IoT scenario as described in claim 1, the construction of an outer two-dimensional stationary Markov chain model is used to characterize the state transition process of the real-time information age and the local age of the latest generated data packet of a single device at the beginning of each cycle. The specific model is as follows: S11. Construct an outer-layer stationary Markov chain model, first identifying any time slot t as a tuple. ,in This represents the m-th superframe. This represents the h-th time slot within superframe m, with the AoI threshold value set to [value]. ,in Arbitrarily label a device, and assume a random process. This indicates the changes in the real-time AoI and the local age of existing data packets at the beginning of each superframe by the tagging device. ,in This indicates the real-time AoI of the tagging device at the start of superframe m. This represents the local age of existing data packets at the start of superframe m for the tagging device; the initial values ​​for both the real-time AoI and the local age of existing data packets at the start of the first superframe are set to 0, i.e. To simplify the analysis, the AoI truncation model is used here to obtain a finite state space. It is assumed that at the beginning of any superframe, the maximum value of the real-time AoI of any device and the local age of the existing data packets is MD. The value of M can be as large as possible to reduce the impact of truncation. The evolution process satisfies the following recursive relation: (1) Then, The evolution process satisfies the following recursive relation: (2) Given a past state and current state Time, future state The conditional distribution of a stochastic process S depends only on the current state and is independent of past states. Therefore, the stochastic process S can be viewed as a discrete-time Markov chain with finite states, and its state space is: (3) S12. Derive the one-step transition probability of this Markov chain. At the beginning of any superframe m, if... ,make Indicates the time slot of the tagging device within superframe m. The probability of successfully transmitting its current data packet within the specified range is given by... This represents the probability that the tagging device successfully transmits its current data packet within superframe m. Obviously... and The following equation applies between them: (4) The one-step transition probabilities between the states of this DTMC are represented as follows: (5) Based on l, k, , Different values ​​of , and The possible values ​​of are represented as follows: (6) S13. Write the recursive relationship between the steady-state probabilities of the Markov chain in each state, letting... Let S represent the stationary distribution of a random process S, where This indicates that the random process S is in state S. Based on equations (5) and (6), the steady-state probability can be obtained as follows: (7).

[0009] Furthermore, according to the information age estimation method for an industrial IoT scenario as described in claim 1, the construction of the inner one-dimensional absorbing Markov chain model is used to characterize the transition process of the transmission state of a single device between time slots within any superframe, and the specific model is as follows: S21. Derivation of the inner-layer absorbing Markov chain The expression, let These represent the real-time AoI values ​​at the start of any superframe for devices other than the tagging device. Furthermore, the age of existing data packets is less than that of real-time AoI and greater than that of real-time AoI. Furthermore, the number of devices with an existing data packet age that is less than the number of devices with AoI makes express The joint probability mass function is expressed as follows: (8) make Indicates when At that time, the marking device is in the time slot The probability of successfully transmitting its existing data packets, and then... The following expression exists: (9) Define a stochastic process For a time-invariant homogeneous absorbing Markov chain with finite states, the state space is: , where the state It is a transit state, indicating that when At time, in the time slot At the beginning, y devices, excluding the tagged device, have successfully transmitted their data packets, while the tagged device has not yet successfully transmitted its data packets. It is an absorption state, meaning that when At time, in the time slot At the start, the tagging device has successfully transmitted its data packets. For ease of analysis, here... Indicates time slot At the initial moment, the one-step state transition probability of the stochastic process Y is defined as follows: (10) Based on the values ​​of h and ε, the state transition probability can be categorized into two cases: The transition probabilities between states are defined as follows: (11) in , ; The transition probabilities between states are defined as follows: (12) in , ; make express The state probability vector, where the i-th element corresponds to the state. The probability of , the probability of the last element corresponding to the state 'suc', and the initial state probability vector are. , The expression is as follows: (13) therefore The expression can be represented as follows: (14) S22. Derivation of the inner-layer absorbing Markov chain The expression, let Indicates when At that time, the marking device is in the time slot The probability of successfully transmitting its existing data packets, and then... The following expression exists: (15) Define a stochastic process For a time-invariant homogeneous absorbing Markov chain with finite states, the state space is: , where the state It is a transit state, indicating that when At time, in the time slot At the beginning, excluding the tagging device, z devices have successfully sent their data packets, while the tagging device has not yet successfully transmitted its data packet. It is an absorption state, meaning that when At time, in the time slot At the beginning, the device is marked as having successfully transmitted its data packet, as defined above, here Indicates time slot At the initial moment, the one-step state transition probability of the stochastic process Z is defined as follows: (16) Based on the values ​​of h and ε, the state transition probability can be categorized into two cases: The transition probabilities between states are defined as follows: (17) in , ; when The transition probabilities between states are defined as follows: (18) in ; make express The state probability vector, where the i-th element corresponds to the state. The probability of , the probability of the last element corresponding to the state 'suc', and the initial state probability vector are. , The expression is defined as follows: (19) therefore The specific expression is as follows: (20).

[0010] Furthermore, according to the information age estimation method for an industrial IoT scenario described in claim 1, the process of solving the above-mentioned mutually coupled two-layer Markov chain using the Newton iteration method is as follows: Considering the above derivation process, when any set of parameters is given... At that time, information about the unknown quantity can be obtained. and To reduce the time complexity of solving the system of simultaneous equations, we can... As a reference unknown, after simplification, the steady-state probability of all other states can be expressed as... The expression reduces the number of unknowns to... Then, the Newton-Raphson iteration method can be used to solve for each unknown quantity, and the steady-state probability of each state of the random process S and the probability of the marker device successfully transmitting in each time slot within the superframe under different conditions can be calculated.

[0011] Furthermore, according to the information age estimation method for an industrial IoT scenario as described in claim 1, based on the construction and solution of the above-mentioned two-layer Markov chain model, the average AoI estimate for any marked device n is as follows: (twenty one) Because the network is symmetrical, the average AoI of the N devices is the same, so the average AoI of any device can represent the average AoI of the system.

[0012] The analysis method proposed in this invention can be used to analyze data with a periodic update probability of... This method can accurately estimate the average AoI of a system under different network parameters in industrial IoT scenarios, thus providing assistance for the design of transmission strategies and the optimization of information age in industrial IoT scenarios.

[0013] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0014] Figure 1 A flowchart illustrating the method design of the present invention is shown.

[0015] Figure 2 The changes were shown When taking the value, the system average AoI varies with the transmission probability. Changing situation .

[0016] Figure 3 The changes were shown When taking the value, the system average AoI varies with the transmission probability. Changes . Detailed Implementation

[0017] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0018] This invention is applied in In an Industrial Internet of Things (IIoT) scenario where N industrial devices equipped with wireless sensors communicate with a common control center, assuming the N devices compete for a shared channel to send their latest generated data to the control center, each device only sends data probabilistically at the beginning of each cycle. Data packets are generated, but not at other times; the period length is D, meaning a superframe consists of D time slots; devices interfere with each other, and successful transmission occurs only when a single device accesses the channel; otherwise, a collision occurs, and all transmission devices fail to send; if a device successfully sends its data packet, the control center can send a feedback signal to the device through an error-free and delay-free channel. The device receiving the feedback will remain silent until it generates a new data packet and its real-time AoI reaches a threshold value; if a data packet fails to be sent, it will continue to be retransmitted until successful or replaced by a newly generated data packet; in this invention, each device uses an age-based random access strategy to transmit its data packets. Each device is only active when its real-time AoI reaches a threshold value and the current data packet has not been successfully transmitted (the device's real-time AoI is greater than the local age of the current data packet), and sends data packets with a fixed probability p; otherwise, it remains silent; given any set of network parameters... The system average AoI under this random access strategy can be estimated by constructing a mutually coupled two-layer Markov chain model. The key feature is that: an outer two-dimensional stationary Markov chain model is constructed to characterize the state transition process of a single device at the beginning of each cycle, which includes the real-time information age and the local age of the latest generated data packet; an inner one-dimensional absorbing Markov chain model is constructed to characterize the transmission state transition process of a single device between each time slot in any superframe; and then the Newton-Raphson iteration algorithm is used to solve this two-layer model to estimate the system average AoI.

[0019] As a preferred embodiment, the network has N independent devices, the data generation period is D, and each device generates data only at the beginning of each period with probability. Generate data packets at other times, but not at other times.

[0020] As a preferred option, the age-based random access policy allows each device to access the device only when the corresponding real-time AoI reaches a certain threshold. A fixed probability approach can only be used if the newly generated data packet fails to be transmitted. Send data, otherwise remain silent.

[0021] As a preferred embodiment, when the N devices transmit data, the transmission can only be successful if only a single device accesses and sends a data packet within the channel; otherwise, a collision occurs and all devices fail. The data packets involved in the collision will be retransmitted until they are successfully transmitted or replaced by newly generated data packets. Once the control center successfully receives the data packets from the devices, it will transmit a feedback signal through an error-free and delay-free control channel.

[0022] As a preferred embodiment, the construction of the outer two-dimensional stationary Markov chain model is used to characterize the state transition process of a single device at the beginning of each cycle, including the real-time information age and the local age of the latest generated data packet. The specific model is as follows: S11. Construct the outer stationary Markov chain model; S12. Derive the one-step transition probability of the Markov chain; S13. Write out the recursive relationship between the steady-state probabilities of the Markov chain in each state.

[0023] As a preferred embodiment, the construction of the inner one-dimensional absorbing Markov chain model is used to characterize the transition process of the transmission state of a single device between time slots within any superframe. Specifically, the model is as follows: S21. Establishment and derivation of the inner absorbing Markov chain. The expression; S22. Derivation of the inner-layer absorbing Markov chain. The expression.

[0024] As a preferred solution, the process of solving the above-mentioned mutually coupled two-layer Markov chain using Newton's iteration method is as follows: Considering the above derivation process, when given any set of parameters... At that time, information about the unknown quantity can be obtained. and To reduce the time complexity of solving the simultaneous equations, we can... As a reference unknown, after simplification, the steady-state probability of all other states can be expressed as... The expression reduces the number of unknowns to... Then, the Newton-Raphson iteration method can be used to solve for each unknown quantity, and the steady-state probability of each state of the random process S and the probability of the marker device successfully transmitting in each time slot within the superframe under different conditions can be calculated.

[0025] As a preferred approach, based on the construction and solution of the above two-layer Markov chain model, the average AoI estimate for any tagging device n is as follows: (twenty two) Because the network is symmetrical, the average AoI of the N devices is the same, so the average AoI of any device can represent the average AoI of the system.

[0026] Figure 1 The flowchart of the method design of the present invention is shown. The present invention first constructs an outer two-dimensional stationary Markov chain model to characterize the state transition process of a single device at the beginning of each cycle, including the real-time information age and the local age of the latest generated data packet. Secondly, it constructs an inner one-dimensional absorbing Markov chain model to characterize the transmission state transition process of a single device between time slots within any superframe. Then, it uses the Newton-Raphson iterative algorithm to solve this coupled two-layer model, thereby estimating the system average AoI.

[0027] Example 1

[0028] This invention uses MATLAB software to implement the method, setting the number of devices in the network. Data generation cycle length The data packet length is 1, and the simulation time is... Time slot.

[0029] Figure 2 , Figure 3 While keeping all other parameters unchanged, change the parameters sequentially. , By observing the theoretical and simulation results of the curve of the average AoI of the system changing with the transmission probability p, it can be found that the theory and simulation are basically matched, indicating that the information age estimation method of the present invention in the industrial Internet of Things scenario is accurate.

Claims

1. A method for estimating the information age in an industrial Internet of Things (IIoT) scenario, wherein the IIoT scenario comprises N mutually interfering devices and a common control center; characterized in that: The N devices send the latest generated data packets to the public control center through a shared channel. Each device generates a data packet with probability λ only at the beginning of each period. The period length is fixed at D. Each device is allowed to send the latest data packet that has not been successfully transmitted, using a fixed probability p, only when the corresponding real-time information age reaches a certain threshold value δ. Transmission is successful only if a single device accesses the channel to send a data packet; otherwise, a collision occurs, and all devices fail. Unsuccessfully transmitted data packets will be continuously retransmitted until they are replaced by newly generated data packets. After successfully transmitting, the device will remain silent until it generates a new data packet after receiving a feedback signal from the control center that is error-free and without delay. The information age estimation method can be decomposed into the following steps: Step 1: Construct an outer two-dimensional stationary Markov chain model to characterize the state transition process of a single device at the beginning of each cycle for its real-time Age of Information (AoI) and the local age of the latest generated data packet. The specific model is as follows: Step 1-1: Construct an outer-layer stationary Markov chain model. First, label any time slot t as a tuple. ,in This represents the m-th superframe. This represents the h-th time slot within superframe m, with the AoI threshold value set to [value]. ,in ; Arbitrarily label a device, and assume a random process. This indicates the changes in the real-time AoI and the local age of existing data packets at the beginning of each superframe by the tagging device. ,in This indicates the real-time AoI of the tagging device at the start of superframe m. This represents the local age of existing data packets at the start of superframe m for the tagging device; the initial values ​​for both the real-time AoI and the local age of existing data packets at the start of the first superframe are set to 0, i.e. ; To simplify the analysis, an AoI truncation model is used here to obtain a finite state space. It is assumed that at the start of any superframe, the maximum value of the real-time AoI of any device and the local age of existing data packets is MD. The value of M is as large as possible to reduce the impact of truncation. The evolution process satisfies the following recursive relation: (1) Then, The evolution process satisfies the following recursive relation: (2) Given a past state and current state Time, future state Since the conditional distribution of a stochastic process S depends only on the current state and is independent of past states, the stochastic process S can be viewed as a discrete-time Markov chain (DTMC) with finite states, and its state space is: (3) Step 1-2: Derive the one-step transition probability of the Markov chain. At the beginning of any superframe m, if... ,make Indicates the time slot of the tagging device within superframe m. The probability of successfully transmitting its current data packet within the specified range is given by... This represents the probability that the tagging device successfully transmits its current data packet within superframe m. Obviously... and The following equation applies between them: (4) The one-step transition probabilities between the states of this DTMC are represented as follows: (5) Based on l, k, , Different values ​​of , and The possible values ​​of are represented as follows: (6) Steps 1-3: Write out the recursive relationship between the steady-state probabilities of the Markov chain in each state, let... Let S represent the stationary distribution of a random process S, where This indicates that the random process S is in state S. Based on equations (5) and (6), the steady-state probability can be obtained from the following recursive formulas for the steady-state distribution: (7) Step 2: Construct an inner one-dimensional absorbing Markov chain model to characterize the state transition process of a single device between time slots within any superframe. The specific model is as follows: Step 2-1: Derivation of the inner-layer absorbing Markov chain The expression, let These represent the real-time AoI values ​​at the start of any superframe for devices other than the tagging device. Furthermore, the age of existing data packets is less than that of real-time AoI and greater than that of real-time AoI. Furthermore, the number of devices with an existing data packet age that is less than the number of devices with AoI makes express The joint probability mass function is expressed as follows: (8) make Indicates when At that time, the marking device is in the time slot The probability of successfully transmitting its existing data packets, and then... The following expression exists: (9) Define a stochastic process For a time-invariant homogeneous absorbing Markov chain with finite states, the state space is: , where the state It is a transit state, indicating that when At time, in the time slot At the beginning, y devices, excluding the tagged device, have successfully transmitted their data packets, while the tagged device has not yet successfully transmitted its data packets. It is an absorption state, meaning that when At time, in the time slot At the start, the tagging device has successfully transmitted its data packets. For ease of analysis, here... Indicates time slot At the initial moment, the one-step state transition probability of the stochastic process Y is defined as follows: (10) Based on the values ​​of h and ε, the state transition probability has the following two cases: The transition probabilities between states are defined as follows: (11) in ; The transition probabilities between states are defined as follows: (12) in ; make express The state probability vector, where the i-th element corresponds to the state. The probability of , the probability of the last element corresponding to the state 'suc', and the initial state probability vector are. , The expression is as follows: (13) therefore The expression can be represented as follows: (14) Step 2-2: Derivation of the inner-layer absorbing Markov chain The expression, let Indicates when At that time, the marking device is in the time slot The probability of successfully transmitting its existing data packets, and then... The following expression exists: (15) Define a stochastic process For a time-invariant homogeneous absorbing Markov chain with finite states, the state space is: , where the state It is a transit state, indicating that when At time, in the time slot At the beginning, excluding the tagging device, z devices have successfully sent their data packets, while the tagging device has not yet successfully transmitted its data packet. It is an absorption state, meaning that when At time, in the time slot At the beginning, the device is marked as having successfully transmitted its data packet, as defined above, here Indicates time slot At the initial moment, the one-step state transition probability of the stochastic process Z is defined as follows: (16) Based on the values ​​of h and ε, the state transition probability has the following two cases: The transition probabilities between states are defined as follows: (17) in ; when The transition probabilities between states are defined as follows: (18) in ; make express The state probability vector, where the i-th element corresponds to the state. The probability of , the probability of the last element corresponding to the state 'suc', and the initial state probability vector are. , The expression is defined as follows: (19) therefore The specific expression is as follows: (20) Step 3: Solve the coupled two-layer Markov chain constructed in Steps 1 and 2 using the Newton-Raphson iterative algorithm. The specific process is as follows: Considering the derivation process in Steps 1 and 2, given any set of parameters... At that time, information about the unknown quantity can be obtained. and To reduce the time complexity of solving the simultaneous equations, we can... As a reference unknown, after simplification, the steady-state probability of all other states can be expressed as... The expression reduces the number of unknowns to... Then, the Newton iteration method can be used to solve for each unknown quantity, and the steady-state probability of each state of the random process S and the probability of the marker device successfully transmitting in each time slot within the superframe under different conditions can be calculated. Step 4: Estimate the system's average AoI; Based on the construction and solution of the two-layer Markov chain model in steps 1, 2, and 3, the average AoI of any labeled device n is estimated as follows: (21) Because the network is symmetrical, the average AoI of the N devices is the same, so the average AoI of any device can represent the average AoI of the system.

2. The method for estimating the information age in an industrial IoT scenario according to claim 1, characterized in that, There are N independent devices in the network, with a data generation period of D, and each device generates data only at the beginning of each period with probability. Generate data packets at other times, but not at other times.

3. The method for estimating the information age in an industrial IoT scenario according to claim 1, characterized in that, Each device is allowed to only operate when its corresponding real-time AoI reaches a certain threshold. A fixed probability approach can only be used if the newly generated data packet fails to be transmitted. Send data, otherwise remain silent.

4. The method for estimating the information age in an industrial IoT scenario according to claim 1, characterized in that, Data packets can only be successfully transmitted if and only if a single device accesses and sends data packets within the channel; otherwise, a collision occurs and all devices fail. Data packets involved in a collision will be retransmitted until they are successfully transmitted or replaced by newly generated data packets. Once the control center successfully receives a data packet from a device, it will transmit a feedback signal through an error-free and delay-free control channel.

Images