A differentiated time slot access method for risk-sensitive status update services

Abstract

The present invention belongs to the field of wireless status update technology and relates to a differentiated time slot access method for risk-sensitive status update services, comprising: step 1, statistical AoI definition, step 2: using ε(τ k ) indicates that, in step 3, when the status data packet is successfully received at the destination, the AoI is updated to τ k ; Otherwise, the AoI increases continuously and linearly with time. Step 4: record the corresponding maximum statistical AoI minimization problem as problem P1. Step 5: simplify problem P1 to problem P2. Step 6: solve problem P2 using a two-step method. Step 7: calculate the statistical AoI value related to #imgabs0#. The present invention can obtain the optimal transmission time allocation scheme, which reduces the system delay while ensuring system reliability, and can better meet the diverse needs of different risk-sensitive status update services. By comparing with the benchmark method, the proposed scheme has great potential for improving information freshness.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless status update, and relates to a differentiated time slot access method for risk-sensitive status update services. Background Art

[0002] Wireless state update systems are a typical time-sensitive application. In particular, some state update systems are risk-sensitive, and critical state information on the target side should always be as fresh as possible. Otherwise, even a small amount of outdated information can lead to undesirable system behavior or even damage.

[0003] In wireless state update systems, methods for assessing the freshness of state information are crucial. Age of Information (AoI), defined as the time elapsed since the source generated the last received state information, is a recently emerging and highly anticipated concept in the field of state information updates. AoI exhibits a sawtooth-like function characteristic over time and is affected not only by end-to-end network latency but also by the source's sampling rate. By fine-tuning the source's sampling rate, the freshness of information can be significantly improved, with relatively low associated costs compared to implementing semantic communication designed to improve information freshness.

[0004] Average AoI is widely used to evaluate the long-term performance of information freshness in various state update systems. However, due to the coupling between the arrival interval of state packets and system time, the derivation of average AoI is often complex. In contrast, since AoI is a sawtooth function of time, peak AoI captures the core characteristics of the aging process. Therefore, average peak AoI can serve as an alternative long-term performance metric to circumvent the complex derivation caused by the correlation between arrival interval and system time. Although the average AoI statistic well reflects the long-term performance of information freshness and is often used as an objective function for resource allocation in wireless state update systems, it cannot meet the requirements of critical state update systems. This is because even if the average AoI or average peak AoI is minimized, the instantaneous age or peak age will still fluctuate frequently due to time-varying conditions such as wireless channel fading. Therefore, it is impossible to determine the proportion of peak ages that exceed the average AoI or average peak AoI. In addition, there is the uncontrollable risk that the information age will often be too large, leading to adverse consequences. Minimizing the maximum peak AoI can mitigate the worst effects of outdated information. However, minimizing the maximum peak AoI often leads to bias, allocating too much resources to the worst case scenario, significantly reducing overall performance. In short, average AoI or average peak AoI are insensitive to risk, while maximum peak AoI is overly sensitive to some critical state update systems.

[0005] To meet the requirements of various critical status update systems, the minimum peak AoI achievable at a given violation probability can be used as an alternative and more comprehensive metric. The level of the violation probability can be correlated with the risk sensitivity of the status update system. The higher the risk sensitivity, the lower the violation probability should be, and vice versa. This metric can be further expanded to reflect the statistical properties of the peak AoI after it exceeds a certain threshold. For example, the average of the tail peak AoI can be used to better indicate overall performance and risk level. However, since the probability distribution function of the peak AoI generally lacks a closed-form expression, it is difficult to derive the minimum peak AoI achievable at a given violation probability, and even more difficult to optimize it.

[0006] Existing technologies have the following drawbacks: average AoI or average peak AoI are insensitive to risk and are therefore unsuitable for use in wireless status update systems. Maximum peak AoI is overly sensitive to certain critical status update systems, potentially allocating excessive resources to worst-case scenarios, significantly reducing overall system performance. The probability distribution function for the minimum peak age achievable under a given violation probability often lacks a closed-form expression, making it difficult to derive the minimum peak AoI achievable under a given violation probability, and even more difficult to optimize.

[0007] Therefore, a time slot access method is needed to ensure system reliability while reducing system latency and better meet the needs of different risk-sensitive status update services to solve the above technical problems. Summary of the Invention

[0008] The technical solution adopted by the present invention to solve the technical problem is: a differentiated time slot access method for risk-sensitive status update services, the method comprising the following steps:

[0009] Step 1. Statistical AoI definition: A tight upper bound on the average peak age of the tail under a given violation probability is defined as Δ(ρ), which is expressed as:

[0010]

[0011] In formula (1), A represents the peak information age, θ represents the age information index, and M A (θ) represents the moment generating function MGF of peak age, which is e θA The mathematical expectation of

[0012] Step 2: Denote the peak age violation probability requirement of source k as ρ k ,in and The duration of a TDMA frame is expressed as T TDMA ; Denote the transmission time allocated to the kth source in each frame as τ k; Express the transmission error probability ε(τk) of each transmission as: Among them, e -c express τ s represents the transfer duration of one copy, represents the transmission error probability of a single state data packet within a frame; where the TDMA system contains K sources and 1 destination;

[0013] Step 3: When the status data packet is successfully received at the destination, the AoI is updated to τ k Otherwise, AoI increases continuously and linearly with time; the peak age of the destination A k Expressed as: A k =τ k +nT TDMA , Where n represents the number of transmissions from the start of transmission to successful reception. represents the set of positive integers;

[0014] Step 4: The corresponding maximum statistical AoI minimization problem is recorded as problem P1, which is expressed as:

[0015]

[0016] In (6a), problem P1 is a min-max optimization problem, and each part of the objective Δk(ρk) exhibits τ k and θ k High coupling between them;

[0017] Step 5: Simplify problem P1 to problem P2, expressed as:

[0018]

[0019] in Represents τ k The upper bound of the time threshold T of TDMA TDMA ;

[0020] Step 6: Solve the P2 problem in two steps; in the first step, set θ k Consider it as a constant and find the optimal τ k ; Then, at the optimal τ k Based on this, we search for the optimal θ k ;

[0021] Step 7: Calculate and Related statistical AoI values.

[0022] Preferably, in step 3, A k =τ k+nT TDMA The probability is expressed as:

[0023] Pr(A k =τ k +nT TDMA )=ε(τ k ) n-1 (1-ε(τ k ))(2)

[0024] The peak age of the destination A k The moment generating function MGF is expressed as:

[0025]

[0026] In formulas (3) and (4), θ k Represents the AoI index of source k and must satisfy

[0027] The statistical AoI of source k at the destination is denoted as Δ k (ρ k ), expressed as:

[0028]

[0029] The goal is to obtain the optimal transmission time allocation scheme to minimize the maximum statistical AoI among K sources.

[0030] Preferably, in step 6, the sub-problem corresponding to the first step is denoted as P3 and is expressed as:

[0031]

[0032] Solve problem P3 and get the optimal transmission time Expressed as:

[0033]

[0034] In formula (9)

[0035]

[0036] In formulas (9) and (10), the smaller the violation probability, the larger the corresponding statistical AoI.

[0037] Preferably, in step 4, the solution to the P1 problem satisfies:

[0038] Δ1(ρ1)=Δ2(ρ2)=...=Δ K (ρ K )(11)

[0039] Use binary search to find the minimum maximum statistical AoI and the corresponding (τ1,τ2,...τ K ); In binary search, Δ k The range is [Δ min ,Δ max ], for k calculation and Δ k =(Δ min +Δ max ) / 2 corresponds to if Then Δ min Update to Δ k , otherwise Δ max Update to Δ k , until Converges to T TDMA .

[0040] The beneficial effects of the present invention are:

[0041] The present invention can obtain the optimal transmission time allocation scheme, which reduces system latency while ensuring system reliability, and can better meet the diverse needs of different risk-sensitive status update services. By comparing with the benchmark method, the proposed scheme has great potential for improving information freshness. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a model diagram of a multi-source status update system using time division multiple access (TDMA) for a differentiated time slot access method for risk-sensitive status update services of the present invention;

[0043] Figure 2 This is a time-sensitive process diagram of source k at the destination when TDMA is used to schedule K sources in the present invention;

[0044] Figure 3 The statistical AoI under different peak age violation probabilities of the present invention is The change curve diagram of

[0045] Figure 4 It is the optimal transmission time diagram of different sources under their respective violation probabilities in the present invention;

[0046] Figure 5 : This is a comparison curve of the maximum statistical AoI corresponding to the proposed scheme and the fixed time allocation scheme under different violation probabilities of the present invention;

[0047] Figure 6 1 is a curve diagram showing the variation of the maximum statistical AoI with the TDMA frame period under different source numbers and violation probabilities in the present invention. DETAILED DESCRIPTION

[0048] The following will provide a clear and complete description of the relevant technologies in the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0049] refer to Figures 1 to 6 This paper proposes a differentiated time slot access method for risk-sensitive state update services. Taking into account the risk insensitivity of average AoI and average peak AoI, and inspired by the entropy value-at-risk, a statistical AoI is used for state updates. The statistical AoI is used to study the impact of unreliable transmission at the media access control (MAC) layer on the time-sensitive process. To mitigate the impact of unreliable transmission while meeting the needs of various risk-sensitive applications, the problem of minimizing the maximum statistical AoI in multiple state updates using time division multiple access (TDMA) technology is studied.

[0050] The statistical AoI is defined as a tight upper bound on the average peak age of the tail under a given violation probability, defined as Δ(ρ), and its mathematical expression is shown in Equation (1).

[0051]

[0052] Where A represents the peak information age, θ is the age information index, M A (θ) is the moment generating function MGF of peak age, which is e θA The mathematical expectation of .

[0053] Consider Figure 1 In the scenario shown, there are K sources and 1 destination in the TDMA system. The K sources want to update their real-time status to the destination. The peak age violation probability requirement of source k is expressed as ρ k ,in and The duration of a TDMA frame is denoted as T TDMA The transmission time allocated to the kth source in each frame is denoted as τ k , the transmission error probability of each transmission is expressed as ε(τk), ε(τk) is about τ k Assume that multiple copies of the state data packet are transmitted in each transmission time to improve transmission reliability. The transmission error probability of each copy is denoted as p, and the multiple copies are independent and identically distributed. When all copies of the data packet fail to be transmitted, it is considered that an error occurs. Therefore, the transmission error probability of a single state data packet in a frame is where τ s is the transmission duration of one copy. -c express get

[0054] Figure 2 It shows the time-efficiency process of source k at the destination. According to the definition of AoI, when the state data packet is successfully received at the destination, the AoI is updated to τ k Otherwise, AoI will increase continuously and linearly with time. The peak age of the destination is denoted by A k , represented by A k =τ k +nT TDMA , Where n represents the number of transmissions from the start of transmission to successful reception. A represents a set of positive integers. k =τ k +nT TDMA The probability of is expressed as formula (2).

[0055] Pr(A k =τ k +nT TDMA )=ε(τ k ) n-1 (1-ε(τ k ))(2)

[0056] According to formula (2) k The probability distribution function, A k The moment generating function (MGF) can be expressed as

[0057]

[0058] Among them, θ k is the AoI index of source k, and must satisfy To ensure A k MGF exists. Then, according to the statistical AoI defined in equation (1), the statistical AoI of source k at the destination is denoted as Δ k (ρ k ), expressed as:

[0059]

[0060] The goal of this embodiment is to obtain the optimal transmission time allocation scheme to minimize the maximum statistical AoI among K information sources. The corresponding maximum statistical AoI minimization problem is denoted as problem P1 and is expressed as follows:

[0061]

[0062] Problem P1 is a min-max optimization problem, and each part Δ in the objective k (ρk ) show that τ k and θ k The high coupling between them. First consider the special case K = 1, and then generalize the results to the case K> 1. In practical applications, the probability of error transmission is usually small, and mathematically it is suggested that and Then we get 1-ε(τ k )≈1. Therefore, problem P1 is simplified to problem P2, which is expressed as follows:

[0063]

[0064] in is τ k The upper bound of the time threshold T of TDMA TDMA Therefore, this embodiment proposes a two-step method to solve the P2 problem. In the first step, θ k Consider it as a constant and find the optimal τ k Then, at the optimal τ k Based on this, we search for the optimal θ k The subproblem corresponding to the first step is denoted as P3 and is as follows:

[0065]

[0066] Solve problem P3 and get the optimal transmission time The expression is

[0067]

[0068] in

[0069]

[0070] Based on the above The theoretical results of Related statistical AoI values. Figure 3 Given a given peak age violation probability, as from Increase to T TDMA , the statistical AoI first decreases and then remains constant, with the turning point being It can be seen that the smaller the violation probability, the larger the corresponding statistical AoI. Based on this idea, an effective method to solve the P1 problem is proposed. Since P1 is a minimum-maximum problem, if Δ k (ρ k )<Δ j (ρ j ),k, Then the transmission time originally allocated to source k can be partially allocated to source j, so that Δ k (ρ k ) increases, Δ j (ρ j ) decreases, which leads to a further decrease in the objective value of the P1 problem. Therefore, in most cases, the solution to the P1 problem satisfies:

[0071] Δ1(ρ1)=Δ2(ρ2)=...=Δ K (ρ K ) (11)

[0072] Therefore, the binary search method is used to find the minimum maximum statistical AoI and the corresponding (τ1, τ2, ... τ K ).like Figure 3 As shown, taking K = 3 as an example, the corresponding ρ1, ρ2, ρ3 are set to 0.1, 0.01 and 0.001 respectively. In the binary search, Δ k The range is [Δ min ,Δ max ], for k from 1 to 3, calculate the difference between Δ k =(Δ min +Δ max ) / 2 corresponds to if Then Δ min Update to Δ k , otherwise Δ max Update to Δ k , until Converges to T TDMA The bisection method is repeatedly used in the solution process, which makes the corresponding computational complexity low.

[0073] The effectiveness of the proposed algorithm is verified by numerical simulation. The simulation parameters are set as follows: average transmission power P is 0.1W, bandwidth B is 1MHz, number of sources K is 3, error factor c is 1000, and duration of one TDMA frame T is 0. TDMA is 10ms.

[0074] Figure 4 This figure shows the optimal transmission time for each source while satisfying its own violation probability requirement. The violation probabilities of Sources 1 and 2 vary between 0.001 and 0.1, while the violation probability of Source 3 is fixed at 0.001. The figure shows that as the violation probability of User 1 and / or User 2 decreases, the optimized transmission time of Source 1 and / or Source 2 increases accordingly. At the same time, the transmission time of Source 3 decreases. When ρ1 = ρ2 = ρ3 = 0.001, the transmission time for each user becomes the same. This result suggests that sources with more stringent violation probability requirements should be allocated more transmission time.

[0075] Figure 5 Comparison curves of the maximum statistical AoI of the proposed scheme and the fixed-time allocation scheme are shown for three sources with different violation probabilities. In the simulation, the violation probability of source 3 is set to 0.001, while the violation probabilities of sources 1 and 2 vary between 0.001 and 0.1. The simulation results show that the maximum statistical AoI of the proposed scheme increases as the violation probability of source 1 and / or source 2 decreases. In contrast, the maximum statistical AoI of the fixed-time allocation scheme remains constant regardless of the variation in the violation probability of source 1 and / or source 2. This is because the statistical AoI of source 3, which has the lowest violation probability, dominates the maximum statistical AoI. The fixed-time allocation scheme performs identically to the proposed scheme only when ρ1 = ρ2 = ρ3 = 0.001.

[0076] Figure 6 The maximum statistical AoI changes with the TDMA frame period under different source numbers and corresponding violation probabilities. The simulation results show that as the TDMA frame length increases, the maximum statistical AoI decreases first and then increases, which indicates that there is an optimal TDMA frame period. TDMA It can reduce the information age, but it will also reduce the transmission reliability. In addition, it can be seen from the simulation results that as the number of sources increases, the optimal T TDMA This is because in order to accommodate more sources and improve transmission reliability, the TDMA frame period needs to be extended.

[0077] In summary, the present invention can obtain the optimal transmission time allocation scheme, which reduces system latency while ensuring system reliability, and can better meet the diverse needs of different risk-sensitive status update services. By comparing with the benchmark method, the proposed scheme has great potential for improving information freshness.

[0078] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A differentiated time slot access method for risk-sensitive status update services, characterized in that: The method comprises the following steps: Step 1. Statistical AoI definition: A tight upper bound on the average peak age of the tail under a given violation probability is defined as Δ(ρ), which is expressed as: In formula (1), A represents the peak information age, θ represents the age information index, and M A (θ) represents the moment generating function MGF of peak age, which is e θA The mathematical expectation of Step 2: Denote the peak age violation probability requirement of source k as ρ k ,in and The duration of a TDMA frame is expressed as T TDMA ; Denote the transmission time allocated to the kth source in each frame as τ k ; The transmission error probability ε(τ k ) is expressed as: Among them, e -c express τ s represents the transfer duration of one copy, represents the transmission error probability of a single state data packet within a frame; where the TDMA system contains K sources and 1 destination; Step 3: When the status data packet is successfully received at the destination, the AoI is updated to τ k Otherwise, AoI increases continuously and linearly with time; the peak age of the destination A k Expressed as: Where n represents the number of transmissions from the start of transmission to successful reception. represents the set of positive integers; Step 4: The corresponding maximum statistical AoI minimization problem is recorded as problem P1, which is expressed as: In (6a), problem P1 is a min-max optimization problem, and each part of the objective Δ k (ρ k ) show that τ k and θ k High coupling between them; Step 5: Simplify problem P1 to problem P2, expressed as: in Represents τ k The upper bound of the time threshold T of TDMA TDMA ; Step 6: Solve the P2 problem in two steps; in the first step, set θ k Consider it as a constant and find the optimal τ k ; Then, at the optimal τ k Based on this, we search for the optimal θ k ; Step 7: Calculate and Related statistical AoI values.

2. A differentiated time slot access method for risk-sensitive status update services according to claim 1, characterized in that: In step 3, A k =τ k +nT TDMA The probability is expressed as: Pr(A k =t k +nT TDMA )=e(t k ) n-1 (1-e(t) k )) (2) The peak age A of the destination k The moment generating function MGF is expressed as: In formulas (3) and (4), θ k Represents the AoI index of source k and must satisfy The statistical AoI of source k at the destination is denoted as Δ k (ρ k ), expressed as: The goal is to obtain the optimal transmission time allocation scheme to minimize the maximum statistical AoI among K sources.

3. A differentiated time slot access method for risk-sensitive status update services according to claim 1, characterized in that: In step 6, the sub-problem corresponding to the first step is denoted as P3 and is expressed as: Solve problem P3 and get the optimal transmission time Expressed as: In formula (9) In formulas (9) and (10), the smaller the violation probability, the larger the corresponding statistical AoI.

4. A differentiated time slot access method for risk-sensitive status update services according to claim 1, characterized in that: In step 4, the solution to the P1 problem satisfies: Δ1(ρ1)=Δ2(ρ2)=...=Δ K (r K ) (11) Use binary search to find the minimum maximum statistical AoI and the corresponding (τ1,τ2,...τ K ); In binary search, Δ k The range is [Δ min ,Δ max ], for k calculation and Δ k =(Δ min +Δ max ) / 2 corresponds to if Then Δ min Update to Δ k , otherwise Δ max Update to Δ k , until Converges to T TDMA .

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