An adaptive random access method for improving periodic data information age
By using an age-based adaptive random access strategy and a two-layer Markov chain model, the transmission probability of devices is dynamically adjusted, which solves the problem of high average AoI caused by device transmission contention and achieves a lower system average AoI and a higher device success transmission rate.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2023-05-26
- Publication Date
- 2026-07-31
AI Technical Summary
In existing technologies, when devices transmit data, it is assumed that the transmission behavior of each device is independent of the age of the information. This leads to intense competition among devices when the data update cycle is short. Devices with lower AoI cannot effectively reduce the system average AoI, while devices with higher AoI cannot transmit successfully for a long time, thus increasing the system average AoI.
An age-based adaptive random access strategy is adopted, in which devices send data with a certain probability only when the real-time AoI reaches a certain value. The transmission probability is dynamically adjusted by constructing a mutually coupled two-layer Markov chain model, and devices with larger AoIs are prioritized to reduce contention.
By optimizing the device's transmission probability and strategy, the probability of devices with a large AoI successfully transmitting data was increased, the average AoI of the system was reduced, and the probability of successful transmission by the device was increased, which is better than a fixed transmission probability setting.
Smart Images
Figure CN116546654B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of wireless network communication technology, specifically to an adaptive random access method for improving the age of periodic data information. Background Technology
[0002] Information age is a crucial performance indicator for measuring the real-time performance and freshness of data transmission. Its optimization is essential for real-time detection, monitoring, and precise decision-making control under the periodic data updates of the Industrial Internet of Things (IIoT). However, previous work has assumed that the transmission behavior of each device is independent of the age of its corresponding real-time information, leading to performance optimization bottlenecks. Bae et al. studied the average AoI performance of the system using an age-independent random access (AIRA) strategy, where all devices access the channel with a fixed probability at the beginning of each time slot and send data packets until successful transmission. Under this strategy, when the data update cycle is short, especially when the update cycle is much shorter than the number of devices, if all devices that have failed to transmit their data packets send them with the same probability, the competition between devices is significant, reducing the probability of successful transmission for all devices. Another problem with this strategy is that some devices with lower AoIs and devices with higher AoIs that have failed to transmit multiple times compete for transmission with the same probability. In this case, even if devices with lower AoIs successfully transmit, it cannot effectively reduce the system's average AoI; instead, it causes devices with higher AoIs to fail to transmit for a long time, thus increasing the system's average AoI. Summary of the Invention
[0003] This invention aims to propose an age-dependent random access (ADRA) strategy that allows each device to send data with a certain probability only when the corresponding real-time AoI reaches a certain value. The transmission probability of each active device is dynamically adjusted with the number of active devices. Furthermore, the system average AoI under this random access strategy is derived by constructing a mutually coupled two-layer Markov chain model, and the optimal AoI threshold under different network parameters is calculated.
[0004] The technical solution to achieve the objective of this invention is: an adaptive random access method for improving the age of periodic data information, the specific steps of which are as follows: S1: Initialize the relevant parameters, let Given N devices within the network and D data generation period, calculate the optimal information age threshold based on parameters N and D, and set the initial AoI and local age of data packets of any device n to 0; execute S2. S2: At the beginning of time slot t, device n obtains the number of active devices in the current time slot t based on channel feedback. This is used to calculate the probability of an active device sending data packets in the current time slot. ;Execute S3; S3: Determine whether the real-time AoI of device n is greater than or equal to the AoI threshold and greater than the local age of the existing data packet. If so, execute scheme A; otherwise, execute scheme B. Option A: Device n enters time slot t with probability... Send data packets; After executing plan A, determine whether a collision has occurred. If so, the data packet transmission fails and plan A1 is executed; otherwise, the data packet transmission succeeds and plan A2 is executed. Option A1: Let The real-time AoI of device n increases by 1 compared to the previous time slot, and S4 is executed; Option A2: Let The real-time AoI of device n is updated to the local age of the data packet in the previous time slot plus 1, and S4 is executed; Option B: Device n remains silent in time slot t, and option A1 is executed; S4: Determine whether device n generates a data packet at the beginning of time slot t. Since the data is generated periodically with a period of D, we can determine this by whether t is divisible by D. If it is, it means that a data packet has been generated, and we execute scheme C; otherwise, we execute scheme D. Solution C: The local age of data packets in device n becomes 0, and S2 is executed; Scheme D: The local age of data packets of device n increases by 1 compared to the previous time slot, and S2 is executed.
[0005] Furthermore, according to claim 1, the adaptive random access method for improving the age of periodic data information is characterized in that there are N independent devices in the network, the data generation period is D, and each device generates data packets only at the beginning of each period and does not generate data packets at other times.
[0006] Furthermore, according to claim 1, the adaptive random access method for improving the age of periodic data information is characterized in that, given any set of network parameters N and D, the optimal AoI threshold value under this random access method is calculated by constructing a mutually coupled two-layer Markov chain model. The specific derivation and calculation process 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, therefore and Can be re-identified as and , respectively representing time slots The number of active devices and the transmission probability of active devices; and set the AoI threshold value. ,in This represents the integer quotient obtained by dividing δ by D. Represent the corresponding remainder term; assume a stochastic process. This represents the state transition process of any tagged device in the real-time AoI at the beginning of each superframe, where This represents the real-time AoI of the tagging device at the start of superframe m; assuming the real-time AoI of the tagging device at the start of the first superframe is 0, i.e. , The recurrence relation is as follows: (1) Given a past state and current state Time, future state The conditional distribution of a stochastic process X depends only on the current state and is independent of past states. Therefore, X can be viewed as a discrete-time Markov chain (DTMC) with infinite states, and its state space is: ; S12. Derive the one-step transition probability of this Markov chain. For any superframe m, the tagging device generates data packets at the beginning of the superframe if... ,in Let represent any non-negative integer, and let Indicates the marking device in the time slot The probability of successfully transmitting the data packet is given by . This indicates the probability that the tagging device successfully transmits the data packet within superframe m; obviously... and The following equation applies between them: (2) Based on l, , Different values of , and The possible values of are represented as follows: (3) Among them, due to hour as well as The value of does not change with the value of l, therefore, any definition satisfying is given. of as well as For fixed variables and Specifically, express , Time marking devices in time slots The probability of successfully transmitting the data packet. express , The probability that the time-stamped device successfully transmits the data packet within superframe m; and subsequently, the one-step transition probability between the states of the DTMC. It is expressed as follows: (4) Where X m and X m+1 These represent the real-time AoI of the tagging device at the start of superframes m and m+1, respectively; x and x' represent X, respectively. m and X m+1 The specific value to be taken; This represents the conditional probability that the real-time AoI of the labeled device is x' at the start of superframe m+1, given that the real-time AoI of the labeled device is x at the start of superframe m. express The probability that the device successfully transmits the data packet within superframe m; express , The probability that the device successfully transmits the data packet within superframe m; S13. Write the recursive relationship between the steady-state probabilities of the Markov chain in each state, letting... This represents the stationary distribution of the DTMC, where Let l represent the steady-state probability of a random process X in state lD. According to equation (4), the recursive relationship between the steady-state probabilities of each state is calculated as follows: (5) in , , These represent the states of the stochastic process X. The steady-state probability, where i represents the set Any integer within; S14. Solve for each steady-state probability expression, and combine it with the equilibrium equations. The expressions for obtaining the steady-state probabilities of each state can be derived as follows: (6) S15. Derivation of the inner-layer absorbing Markov chain The expression, let These represent the real-time AoI (Aspect-Oriented Identifier) at the start of any superframe for devices other than the tagging device. And greater than The number of devices; They represent Any possible value; let express The joint probability mass function is expressed as follows: (7) make Indicates when At that time, the marking device is in the time slot The probability of successfully transmitting its existing data packets; let express Time stamping devices in time slots The probability of successfully transmitting its existing data packets; and then The following expression exists: (8) Define a stochastic process For a timeless homogeneous absorbing Markov chain with finite states, where express At that time, the system is in the time slot 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 marked device, have successfully transmitted their data packets, while the marked device has not yet successfully transmitted its data packets; It is an absorption state, meaning that when At time, in the time slot The beginning indicates that the device has successfully transmitted its data packet; here, 'suc' is an abbreviation for the word "success" and serves as an identifier to represent the absorption state; 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: (9) Where Y h and Y h+1 They represent Time system in time slot and The state; y and y' represent Y respectively. h and Y h+1 The specific value to be taken; express Time system in time slot Given a state of y, in time slot The conditional probability of state y'; 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: (10) in , Indicates the probability of transmission from an active device; The transition probabilities between states are defined as follows: (11) in , Indicates the probability of transmission from an active device; 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. For any , The expression is as follows: (12) Similarly, for any It can be calculated , used to represent is a state probability vector; where, Indicates time slot The one-step state transition matrix of a stochastic process Y, which contains all elements Therefore, for any , The expression is represented as follows: (13) in express The One element, express The One element; S16. 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 current data packet; let express , Time marking devices in time slots The probability of successfully transmitting the data packet; and then The following expression exists: (14) Define a stochastic process For a timeless homogeneous absorbing Markov chain with finite states, where express At that time, the system is in the time slot 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 tagging device has successfully transmitted its data packets, here Indicates time slot At the initial moment, the one-step state transition probability of the stochastic process Z is defined as follows: (15) Z h and Z h+1 They represent Time system in time slot and The states; z and z' represent Z respectively. h and Z h+1 The specific value to be taken; Indicates the system in time slots Under the condition that the state is z, in time slot The conditional probability of state z'; 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: (16) in , Indicates the probability of transmission from an active device; when The transition probabilities between states are defined as follows: (17) in ; express Time system in time slot Under the condition that the state is z, in time slot The conditional probability of the state being z'; 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. For any , The expression is defined as follows: (18) Similarly, for any It can be calculated , used to represent is a state probability vector; where, Let Z be the one-step state transition matrix of the random process Z in the j-th time slot within the superframe, containing all elements. Therefore, for any , The specific expression is as follows: (19) in express The One element, express The One element; S17. Solve the above-mentioned coupled two-layer Markov chain using Newton's iterative method, taking into account the derivation process in S11 to S16, when given any set of parameters... At that time, obtain information about The system of identities is as follows: (20) Since this system of equations is a nonlinear high-order system, an analytical solution cannot be obtained directly. Therefore, Newton's iteration method is used to solve the system of equations using approximate numerical solutions. Substituting the numerical solutions into equations (6), (8), and (14), we can obtain the steady-state distribution probability of the AoI of the tagging device at the beginning of any superframe. and , The specific value; S18. Calculate the average AoI of the system, based on the derivation process in S11 to S17, the average AoI of any tagging device n. The calculation 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 one device represents the average AoI of the system. S19. Solve for the optimal AoI threshold Due to the lack of a closed-form expression for the average AoI, it is impossible to obtain an answer by relating equation (21) to... To obtain the optimal AoI threshold, perform differentiation. The analytical solution is not provided here. Instead, a one-dimensional search algorithm from optimization theory is considered to find the optimal AoI threshold. .
[0007] Furthermore, according to claim 1, the adaptive random access method for improving the age of periodic data information is characterized in that each device obtains the number of active devices in each time slot through channel feedback. And use this to calculate the transmission probability of the corresponding active device. The calculation formula is: (twenty two).
[0008] Furthermore, according to claim 1, the adaptive random access method for improving the age of periodic data information is characterized in that data transmission can only be successfully completed when only a single device accesses and transmits the data packet within the channel; otherwise, a collision occurs and all devices fail.
[0009] Compared with existing age-independent access strategies, the present invention has the following significant advantages: the age-based adaptive random access strategy prioritizes scheduling devices with higher AoI to access the channel with a certain transmission probability p, while keeping devices with lower AoI silent. This reduces competition among devices, increases the probability of devices with higher AoI successfully sending data packets, thereby reducing the overall average AoI of the system. Furthermore, the transmission probability of each active device is dynamically adjusted according to the number of active devices, increasing the probability of successful transmission for each device. Therefore, the average AoI of the system is better than that of a fixed transmission probability setting.
[0010] 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
[0011] Figure 1 A flowchart illustrating the method design of the present invention is shown.
[0012] Figure 2 The simulation and theoretical comparison of the average AoI variation curves with the data update cycle under the optimal ADRA and AIRA strategies are shown. Detailed Implementation
[0013] 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.
[0014] This invention is applied in In a communication scenario involving N devices and a shared access point, assuming the N devices compete for a shared channel to send periodically generated latest data to the access point, interference occurs between the devices. Successful transmission occurs only if a single device accesses the channel; otherwise, a collision occurs, and all transmission devices fail to send. Given any set of network parameters, the optimal AoI threshold value under this random access method is derived and calculated by constructing a coupled two-layer Markov chain model. Each device is only active when its real-time AoI reaches a threshold 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 certain probability; otherwise, it remains silent. Each device obtains the number of active devices in the current time slot based on channel feedback at the beginning of each time slot. It also adaptively adjusts the transmission probability of each active device based on the number of active devices. .
[0015] like Figure 1 As shown, the specific implementation process includes: S1: Initialize the relevant parameters, let Given N devices within the network and D data generation period, calculate the optimal information age threshold based on parameters N and D, and set the initial AoI and local age of data packets of any device n to 0. S2: At the beginning of time slot t, device n obtains the number of active devices in the current time slot t based on channel feedback. This is used to calculate the probability of an active device sending data packets in the current time slot. ; S3: Determine whether the real-time AoI of device n is greater than or equal to the AoI threshold and greater than the local age of the existing data packet. If so, execute scheme A; otherwise, execute scheme B. Option A: Device n enters time slot t with probability... Send data packets; Determine if a collision has occurred. If so, the data packet transmission failed, and proceed with solution A1. Otherwise, the data packet was successfully transmitted, and proceed with solution A2. Option A1: Let The real-time AoI of device n increases by 1 compared to the previous time slot, and S4 is executed; Option A2: Let The real-time AoI of device n is equal to the local age of the data packet in the previous time slot plus 1, and S4 is executed; Option B: Device n remains silent in time slot t, and option A1 is executed; S4: Determine whether device n generates a data packet at the beginning of time slot t. Since the data is generated periodically with a period of D, we can determine this by whether t is divisible by D. If it is, it means that a data packet has been generated, and we execute scheme C; otherwise, we execute scheme D. Solution C: The local age of data packets in device n becomes 0, and S2 is executed; Scheme D: The local age of data packets of device n increases by 1 compared to the previous time slot, and S2 is executed.
[0016] As a preferred embodiment, the system network has N independent devices, the data generation period is D, and each device generates data packets only at the beginning of the period and does not generate data packets at other times.
[0017] As a preferred embodiment, given the network parameters N and D, the optimal AoI threshold value under this random access method is calculated by constructing a mutually coupled two-layer Markov chain model. The specific derivation and calculation process is as follows: S11. Construct the outer-layer stationary Markov chain model; S12. Derive the one-step transition probability of the Markov chain; S13. Write the recursive relationship between the steady-state probabilities of the Markov chain in each state; S14. Solve for each steady-state probability expression; S15. Establish the derivation of the inner-layer absorbing Markov chain. The expression; S16. Derivation of the inner-layer absorbing Markov chain. S17. Solve the mutually coupled two-layer Markov chain constructed in S11 to S16 using Newton's iteration method; S18. Calculate the average AoI of the system; S19. Solve for the optimal AoI threshold.
[0018] As a preferred embodiment, each device can obtain the number of active devices in each time slot through channel feedback. And use this to calculate the transmission probability of the corresponding active device. The calculation formula is: (twenty three).
[0019] As a preferred embodiment, when the N devices compete for transmission, 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.
[0020] Example 1
[0021] This invention uses MATLAB software to implement the method, setting the number of devices in the network. Data generation cycle The data packet length is 1, and the simulation time is... Time slot; Figure 2 Given any set of parameters The optimal AoI threshold and its corresponding optimal system average AoI under the age-based adaptive random access strategy proposed in this invention are solved respectively. The system average AoI is compared with that under the AIRA strategy proposed by Bae et al. It can be found that the theoretical system average AoI is basically consistent with the simulation results, which verifies the correctness of the theoretical derivation of this invention. At the same time, it can be found that the performance of the strategy proposed in this invention is significantly better than the existing AIRA strategy, and the AoI of periodic data is significantly improved.
Claims
1. An adaptive random access method for improving the age of periodic data information, characterized by the following specific steps: S1: Initialize relevant parameters, set time slots Given N devices within the network and D data generation period, calculate the optimal Age of Information (AoI) threshold based on parameters N and D, and set the initial AoI and local age of data packets of any device n to 0; execute S2; S2: At the beginning of time slot t, device n obtains the number of active devices in the current time slot t based on channel feedback. This is used to calculate the probability of an active device sending data packets in the current time slot. ;Execute S3; S3: Determine whether the real-time AoI of device n is greater than or equal to the AoI threshold and greater than the local age of the existing data packet. If so, execute scheme A; otherwise, execute scheme B. Option A: Device n enters time slot t with probability... Send data packets; After executing plan A, determine whether a collision has occurred. If so, the data packet transmission fails and plan A1 is executed; otherwise, the data packet transmission succeeds and plan A2 is executed. A1 scheme: Let the time slot The real-time AoI of device n increases by 1 compared to the previous time slot, and S4 is executed; A2 scheme: Let the time slot... The real-time AoI of device n is updated to the local age of the data packet in the previous time slot plus 1, and S4 is executed; Option B: Device n remains silent in time slot t, and option A1 is executed; S4: Determine whether device n generates a data packet at the beginning of time slot t. Since the data is generated periodically with a period of D, we can determine this by whether t is divisible by D. If it is, it means that a data packet has been generated, and we execute scheme C; otherwise, we execute scheme D. Solution C: The local age of data packets in device n becomes 0, and S2 is executed; Scheme D: The local age of data packets of device n increases by 1 compared to the previous time slot, and S2 is executed.
2. The adaptive random access method for improving the age of periodic data information according to claim 1, characterized in that, There are N independent devices in the network. The data generation period is D, and each device generates data packets only at the beginning of each period and does not generate data packets at other times.
3. The adaptive random access method for improving the age of periodic data information according to claim 1, characterized in that, Given any set of network parameters N and D, the optimal AoI threshold for this random access method is calculated by constructing a coupled two-layer Markov chain model. The specific derivation and calculation process are 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, therefore Can be re-identified as It represents a time slot. The probability of sending data from active devices within the network; and setting the AoI threshold value to [value missing]. ,in This represents the integer quotient obtained by dividing δ by D. Represent the corresponding remainder term; assume a stochastic process. This represents the state transition process of any tagged device in the real-time AoI at the beginning of each superframe, where This represents the real-time AoI of the tagging device at the start of superframe m; assuming the real-time AoI of the tagging device at the start of the first superframe is 0, i.e. , The recurrence relation is as follows: (1) Given a past state and current state Time, future state The conditional distribution of a stochastic process X depends only on the current state and is independent of past states. Therefore, X can be viewed as a discrete-time Markov chain (DTMC) with infinite states, and its state space is: ; S12. Derive the one-step transition probability of this Markov chain. For any superframe m, the tagging device generates data packets at the beginning of the superframe if... ,in Let represent any non-negative integer, and let Indicates the marking device in the time slot The probability of successfully transmitting the data packet is given by . This indicates the probability that the tagging device successfully transmits the data packet within superframe m; obviously... and The following equation applies between them: (2) Based on l, , Different values of , and The possible values of are represented as follows: (3) Among them, due to hour as well as The value of does not change with the value of l, therefore, any definition satisfying is given. of as well as For fixed variables and Specifically, express , Time marking devices in time slots The probability of successfully transmitting the data packet. express , The probability that the time-stamped device successfully transmits the data packet within superframe m; and subsequently, the one-step transition probability between the states of the DTMC. It is expressed as follows: (4) Where X m and X m+1 These represent the real-time AoI of the tagging device at the start of superframes m and m+1, respectively; x and x' represent X, respectively. m and X m+1 The specific value to be taken; This represents the conditional probability that the real-time AoI of the labeled device is x' at the start of superframe m+1, given that the real-time AoI of the labeled device is x at the start of superframe m. express The probability that the device successfully transmits the data packet within superframe m; express , The probability that the device successfully transmits the data packet within superframe m; S13. Write the recursive relationship between the steady-state probabilities of the Markov chain in each state, letting... This represents the stationary distribution of the DTMC, where Let l represent the steady-state probability of a random process X in state lD. According to equation (4), the recursive relationship between the steady-state probabilities of each state is calculated as follows: (5) in , , These represent the states of the stochastic process X. The steady-state probability, where i represents the set Any integer within; S14. Solve for each steady-state probability expression, and combine it with the equilibrium equations. The expressions for obtaining the steady-state probabilities of each state can be derived as follows: (6) S15. Derivation of the inner-layer absorbing Markov chain The expression, let These represent the real-time AoI (Aspect-Oriented Identifier) at the start of any superframe for devices other than the tagging device. And greater than The number of devices; They represent Any possible value; let express The joint probability mass function is expressed as follows: (7) make Indicates when At that time, the marking device is in the time slot The probability of successfully transmitting its existing data packets; let express Time stamping devices in time slots The probability of successfully transmitting its existing data packets; and then The following expression exists: (8) Define a stochastic process For a timeless homogeneous absorbing Markov chain with finite states, where express At that time, the system is in the time slot 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 marked device, have successfully transmitted their data packets, while the marked device has not yet successfully transmitted its data packets; It is an absorption state, meaning that when At time, in the time slot The beginning indicates that the device has successfully transmitted its data packet; here, 'suc' is an abbreviation of the word "success" and serves as an identifier to represent the absorption state; 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: (9) Where Y h and Y h+1 They represent Time system in time slot and The state; y and y' represent Y respectively. h and Y h+1 The specific value to be taken; express Time system in time slot Given a state of y, in time slot The conditional probability of state y'; 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: (10) in , Indicates the probability of transmission from an active device; The transition probabilities between states are defined as follows: (11) in , Indicates the probability of transmission from an active device; 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. For any , The expression is as follows: (12) Similarly, for any It can be calculated , express is a state probability vector; where, Indicates time slot The one-step state transition matrix of a stochastic process Y, which contains all elements Therefore, for any , The expression is represented as follows: (13) in express The One element, express The One element; S16. 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 current data packet; let express , Time marking devices in time slots The probability of successfully transmitting the data packet; and then The following expression exists: (14) Define a stochastic process For a timeless homogeneous absorbing Markov chain with finite states, where express At that time, the system is in the time slot 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 tagging device has successfully transmitted its data packets, here Indicates time slot At the initial moment, the one-step state transition probability of the stochastic process Z is defined as follows: (15) Z h and Z h+1 They represent Time system in time slot and The states; z and z' represent Z respectively. h and Z h+1 The specific value to be taken; express Time system in time slot Under the condition that the state is z, in time slot The conditional probability of state z'; 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: (16) in , Indicates the probability of transmission from an active device; when The transition probabilities between states are defined as follows: (17) in ; express Time system in time slot Under the condition that the state is z, in time slot The conditional probability of the state being z'; 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. For any , The expression is defined as follows: (18) Similarly, for any It can be calculated , express is a state probability vector; where, Let Z be the one-step state transition matrix of the random process Z in the j-th time slot within the superframe, containing all elements. Therefore, for any , The specific expression is as follows: (19) in express The One element, express The One element; S17. Solve the above-mentioned coupled two-layer Markov chain using Newton's iterative method, taking into account the derivation process in S11 to S16, when given any set of parameters... At that time, obtain information about The system of identities is as follows: (20) Since this system of equations is a nonlinear high-order system, an analytical solution cannot be obtained directly. Therefore, Newton's iteration method is used to solve the system of equations using approximate numerical solutions. Substituting the numerical solutions into equations (6), (8), and (14), we can obtain the steady-state distribution probability of the AoI of the tagging device at the beginning of any superframe. and , The specific value; S18. Calculate the average AoI of the system, based on the derivation process in S11 to S17, the average AoI of any labeled device n. The calculation is as follows: (21) Because the network is symmetrical, the average AoI of the N devices is the same, so the average AoI of any one device represents the average AoI of the system. S19. Solve for the optimal AoI threshold Due to the lack of a closed-form expression for the average AoI, it is impossible to obtain an answer by relating equation (21) to... To obtain the optimal AoI threshold, perform differentiation. The analytical solution is not provided here. Instead, a one-dimensional search algorithm from optimization theory is considered to find the optimal AoI threshold. .
4. The adaptive random access method for improving the age of periodic data information according to claim 1, characterized in that, Each device obtains the number of active devices in each time slot through channel feedback. And use this to calculate the transmission probability of the corresponding active device. The calculation formula is: (22)。 5. The adaptive random access method for improving the age of periodic data information according to claim 1, characterized in that, A data packet can be successfully transmitted if and only if a single device in the channel is connected to send the packet; otherwise, a collision occurs and all devices fail.