A method for detecting the timeliness of information transmission system under PS strategy

Abstract

The present invention discloses a method for detecting the timeliness of an information transmission system under a PS strategy, comprising: modeling the information transmission system under the PS strategy as a discrete-time information transmission system; using an information age solution method to determine the timeliness range of the discrete-time information transmission system; the information age solution method comprises: establishing a two-dimensional discrete state vector to describe a random state transition scenario of the two-dimensional discrete state vector of each time slot: in the random state transition scenario, determining the state transition probability of the two-dimensional discrete state vector of the current time slot transferring to the two-dimensional discrete state vector of the next time slot, and obtaining a stable probability vector at any time slot in a scheduling cycle; based on this, obtaining an upper limit and a lower limit of the information age of the discrete-time information transmission system, and determining the timeliness range of the discrete-time information transmission system.

Description

Technical Field

[0001] The present invention belongs to the field of information communication technology, and in particular relates to a method for detecting the timeliness of an information transmission system under a PS strategy. Background Art

[0002] With the development of information and communication technology, the era of the Internet of Everything has arrived. Traditional data communications focus more on the delay of information transmission, while actual terminal devices and users are more concerned about the timeliness of information. Timeliness is crucial for IoT monitoring, data transmission systems, and Internet of Vehicles systems. Information with low timeliness will greatly reduce the accuracy and reliability of the system, posing challenges to system security and practicality.

[0003] Although the periodic scheduling (PS) strategy of information transmission systems can solve the timeliness problem of the system when the data transmission rate in the information transmission system is higher than the system service rate, there has been no effective solution for the timeliness indicator of the data transmission system under this strategy - Age of Information (AoI). Summary of the invention

[0004] Purpose of the invention: In order to solve the problem that the timeliness of the information transmission system under the PS strategy is difficult to quantify and thus the timeliness of the system cannot be determined, the present invention provides a method for detecting the timeliness of the information transmission system under the PS strategy, creatively solves the AoI closed formula under the scheduling strategy, and provides an effective solution method for the AoI of the data transmission system under the scheduling strategy.

[0005] Technical solution: A method for detecting the timeliness of an information transmission system under a PS strategy, comprising:

[0006] The information transmission system under the PS strategy is modeled as a discrete-time information transmission system, which defines that the data packets of the discrete-time information transmission system arrive only at the beginning of the time slot and the destination node is updated only at the end of the time slot;

[0007] The information age solution method is used to determine the timeliness range of discrete time information transmission systems;

[0008] Based on the timeliness range of the information transmission system in discrete time, determine the timeliness of the information transmission system under the PS strategy;

[0009] The method of solving the information age to determine the timeliness range of the discrete time information transmission system includes the following steps:

[0010] For discrete-time information transmission systems, a two-dimensional discrete state vector is established to represent the number of data packets in different time slots within a scheduling cycle;

[0011] According to the generation and service completion of data packets in each time slot, the random state transition scenario of the two-dimensional discrete state vector of each time slot is described as follows:

[0012] In a random state transition scenario, determine the state transition probability of the two-dimensional discrete state vector of the current time slot transferring to the two-dimensional discrete state vector of the next time slot;

[0013] Based on the state transition probability, determine the stability probability of the two-dimensional discrete state vector;

[0014] According to the stable probability of the two-dimensional discrete state vector, the stable probability vector at any time slot in the scheduling period is obtained;

[0015] Based on the stable probability vector at any time slot in the scheduling cycle, the upper and lower limits of the information age of the discrete-time information transmission system are obtained;

[0016] Based on the upper and lower limits of the information age of the discrete-time information transmission system, the timeliness range of the discrete-time information transmission system is determined.

[0017] Furthermore, the information transmission system for discrete time establishes a two-dimensional discrete state vector for representing the number of data packets in different time slots within a scheduling cycle, specifically comprising: establishing a two-dimensional discrete state vector To represent the number of data packets in different time slots within a scheduling cycle; Indicates the number of packets. Indicates the number of time slots, , , Indicated by time slots constitute a scheduling cycle; if the discrete time information transmission system is in an idle state, .

[0018] Furthermore, the random state transition scenario of the two-dimensional discrete state vector of each time slot is described according to the generation of the data packet and the service completion status in each time slot, and the specific operations include:

[0019] Let S represent whether a data packet is generated, S=0 means no data packet is generated in the current time slot, and S=1 means a data packet is generated in the current time slot;

[0020] Let C represent whether the destination node has completed the service and updated its information, C=1 means that the destination node has completed the service and updated the destination node's information, C=0 means that the destination node has not completed the service or the discrete-time information transmission system is in an idle state;

[0021] When the two-dimensional discrete state vector of the current time slot is , , , S=0, C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0022] When the two-dimensional discrete state vector of the current time slot is , , , S=0, C=1, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0023] When the two-dimensional discrete state vector of the current time slot is , , , S=1, C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0024] When the two-dimensional discrete state vector of the current time slot is , , , S=1, C=1, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0025] When the two-dimensional discrete state vector of the current time slot is , , when S=0, C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0026] When the two-dimensional discrete state vector of the current time slot is , , when S=1 and C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0027] When the two-dimensional discrete state vector of the current time slot is , , when S=0 and C=1, the two-dimensional discrete state vector of the next time slot is expressed as: ;

[0028] When the two-dimensional discrete state vector of the current time slot is , , when S=1, C=1, the two-dimensional discrete state vector of the next time slot is expressed as: .

[0029] Furthermore, in the random state transition scenario, determining the state transition probability of the two-dimensional discrete state vector of the current time slot transferring to the two-dimensional discrete state vector of the next time slot specifically includes:

[0030] In the random state transition scenario, assume that the probability of generating a data packet in each time slot is , the service completion probability of a data packet in each time slot is ;

[0031] When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0032] When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0033] When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0034] When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0035] When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0036] When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0037] When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ;

[0038] When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot .

[0039] Furthermore, the stability probability of the two-dimensional discrete state vector is determined based on the state transition probability, which is expressed as:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] In the formula, Indicates n Time slots, l The stability probability of a data packet; Indicates n -1 time slot, l The stability probability of a data packet, Indicates n -1 time slot, l +1 packet stability probability.

[0049] Furthermore, according to the stable probability of the two-dimensional discrete state vector, a stable probability vector at any time slot in the scheduling period is obtained, which is expressed as:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] In the formula, represents the stable probability vector of the nth time slot in a scheduling cycle, represents the stable probability vector of the initial time slot.

[0055] Furthermore, the above-mentioned stable probability vector at any time slot in the scheduling period is used to obtain the upper limit and lower limit of the information age of the discrete-time information transmission system. The specific operations include:

[0056] The mean number of packets at any time slot in the scheduling period is derived from the stable probability vector at any time slot in the scheduling period. Assuming that it is at time slot k, it is expressed as:

[0057] ;

[0058] make represents the upper limit of the information age of the discrete-time information transmission system, The lower limit of the information age of the discrete-time information transmission system is expressed as:

[0059] ;

[0060] ;

[0061] Among them, among them, M Indicates the length of the scheduling cycle, Indicates data packets, Indicates the arrival interval of data packets, represents the mean value of data packets in the kth time slot within the scheduling period, .

[0062] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0063] (1) The present invention provides a timeliness description indicator for the PS strategy, which is used to describe the freshness of the system transmission data packets. By establishing the upper and lower bound functions of AoI, the timeliness of the system can be evaluated more accurately, which is convenient for analyzing and optimizing system performance.

[0064] (2) The present invention establishes a new AoI closed-formula solution method based on two-dimensional discrete state vectors and state transfer matrices, which provides a new method and idea for the AoI solution method of discrete-time systems under subsequent burst scheduling strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A schematic diagram of the system's AoI and system data packet sampling path;

[0066] Figure 2 Schematic diagram of three-dimensional AoI with a scheduling period of 10 time slots. DETAILED DESCRIPTION

[0067] The technical solution of the present invention is now further described in conjunction with the accompanying drawings and embodiments.

[0068] This embodiment proposes a method for detecting the timeliness of an information transmission system under a PS policy, which mainly includes the following steps:

[0069] Step 1: In the system setting phase, the system is defined as a discrete time system, and the time axis is divided into time intervals of equal length, namely time slots. The generation, arrival, transmission and update of data packets can all be performed at the boundaries of time slots. The theoretical basis for such modeling and analysis is that actual communication devices, such as sensors and wireless transmission devices, are all based on discrete clock signals for synchronous operation; the system's queuing model selects geometrically distributed arrival process, geometrically distributed service time, and Geo / Geo / 1 queuing model of a single server; since the selection of the ingress protocol will not affect the analysis of the system's timeliness, and there is a clear relationship between different ingress protocols, the ingress protocol of the discrete time system needs to be specifically defined here. This embodiment focuses on analyzing the timeliness of the discrete time system under the ingress protocol; under this ingress protocol, data packets are only transmitted at the beginning of the time slot. Arrives, and the destination node is updated only at the end of the time slot happens; here, Indicates the start of a time slot, Indicates the end of the time slot; the results of other ingress protocols can be easily derived based on the conclusions of this embodiment, so they are not repeated here; PS strategy, specifically, the data transmission system operates with time slots as a scheduling cycle, and at the beginning of each scheduling cycle In each time slot, the processor maintains the original data packet service rate of the communication system and transmits data packets at a lower data transmission rate; those data packets that are not served in time will be queued and stored in the system's buffer; in the last time slot of each scheduling cycle, the server transmits all data packets that have not been delivered to the destination node in time during this scheduling cycle at a higher data transmission rate; this includes the data packets currently being transmitted by the system and the data packets accumulated in the buffer, thereby completing the information update of the destination node; compared with the traditional transmission system, the information transmission system under the PS strategy not only solves the congestion and data packet loss problems, but also improves the timeliness of information; in addition, in terms of resource allocation, the lower data transmission rate in the regular time slot allows narrower channel bandwidth allocation; the high-speed channels used during short scheduling periods are easier to implement, ultimately improving the overall resource utilization of the system.

[0070] Figure 1The figure shows the system's AoI and system data packet sampling path. Assuming the scheduling period is 10, data packets are generated in the 2nd, 4th, 7th, and 9th time slots and arrive at the system to wait for service. The system completes the service of the first data packet arriving at the system in the 5th time slot and transmits it to the destination node. The remaining three data packets arriving at the system have not completed the service until the end of the 9th time slot. The system PS strategy completes the transmission of the stranded data packets in the system at a high rate, which improves the timeliness of the system. It can be seen that at the 10th time slot, the system , which is greatly reduced compared to the AoI of the 9th time slot.

[0071] Step 2: A method for solving the AoI of the information transmission system under the PS strategy is used to obtain the upper and lower limit function formulas of the information age (AoI) of the discrete-time information transmission system, thereby providing a basis for determining the timeliness of the information transmission system under the PS strategy.

[0072] The present embodiment adopts an AoI solving method of an information transmission system under a PS strategy, which mainly includes the following steps:

[0073] STEP1: Create a two-dimensional discrete state vector To represent the number of data packets in different time slots within a scheduling cycle; Indicates the number of packets. Indicates the number of time slots, , , Indicated by time slots constitute a scheduling cycle; if the discrete time information transmission system is in an idle state, .

[0074] STEP 2: Generate a two-dimensional discrete state vector state transition table based on the generation and service completion of data packets in each time slot; the specific operations include:

[0075] According to the generation and service completion of data packets in each time slot, the random state transition process of the two-dimensional discrete state vector of each time slot is described as follows:

[0076] Let S represent whether the source node generates a data packet, where S = 0 means no data packet is generated in the current time slot, and S = 1 means a data packet is generated in the current time slot;

[0077] Let C represent whether the destination node has completed the service and updated its information, where C = 1 means that the destination node has completed the service and updated the destination node's information, and C = 0 means that the data packet has not received the complete service or the system is in an idle state;

[0078] Based on the generation and arrival of data packets, Table 1 lists the two-dimensional discrete state vectors in a scheduling cycle. All possible random state transition scenarios:

[0079] Table 1 Two-dimensional discrete state vector state transition scenarios

[0080]

[0081] STEP3: Considering the two-dimensional discrete state vector The Markov characteristics of the current two-dimensional discrete state vector and the transition probability of the next time slot to represent the subsequent time slot The transition state vector of ; the expression of transition probability is:

[0082] ;

[0083] In the formula, represents the number of data packets in the sth time slot; based on the above system settings, it is assumed that the probability of generating a data packet in each time slot is , the service completion probability of a data packet in each time slot is , using the PS strategy, we get the two-dimensional discrete state vector The corresponding state transition probability table:

[0084] Table 2 State transition probability table

[0085]

[0086] Figure 2 The schematic diagram of the three-dimensional AoI with a scheduling period of 10 time slots is shown. Assuming that the scheduling period is 10, the probability of generating a data packet is 0.8, and the service probability of the system is 0.4, the corresponding state transition table is shown in Table 3:

[0087] Table 3 State transition probability table ( , , )

[0088]

[0089] STEP 4: Due to the combination of random process and PS strategy, the packet count in the system is difficult to reach a stable state even after a long period of time; but since the scheduling period is a fixed value, the packet count in the same time slot in different scheduling periods will eventually converge to the stable probability distribution in the random process; in order to distinguish it from the steady-state probability, the stable probability distribution under the PS strategy is called the stable probability; therefore, the two-dimensional discrete state vector The stability probability is expressed as The stability probability is based on the state transition probability and follows the following formula:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] In the formula, Indicates n Time slots, l The stability probability of a data packet; Indicates n -1 time slot, l The stability probability of a data packet, Indicates n -1 time slot, l +1 packet stability probability.

[0099] According to the state transition probabilities in Table 2, the above eight state transition formulas are derived; there are several state transition processes that require special attention: due to the periodic scheduling of the random system, the data packet will be cleared from the system at the end of the last time slot of each cycle, and the destination node will be updated; therefore, if a data packet arrives in the first time slot of the new cycle, the system data packet count is 1, and the corresponding data packet generation probability is ,Right now ; Similarly, we can get ;when and , the number of system data packets is a non-negative integer; therefore, when the number of system data packets in the current time slot is 0, only two cases need to be considered: first, if the number of data packets in the previous time slot is 1 and the data packet has been served, and no new data packet arrives in the current time slot, the number of system data packets decreases by 1; second, if the number of data packets in the previous time slot is 0 and no data packet arrives in the current time slot, the number of system data packets remains unchanged at 0; the arrival and departure of data packets can increase or decrease the number of system data packets; since only one data packet can arrive or leave in a time slot, the number of time slots is greater than or equal to the number of system data packets, that is l ≤ n; This explains why the multiple equations in the above system of equations do not originate from three adjacent state transitions.

[0100] STEP5: According to the stable probability formula, obtain the stable probability vector at any time slot in the scheduling cycle, the stable probability vector of the initial time slot and the state transition matrix corresponding to the stable probability vector; the specific contents include: using letters to represent the transition probability, as shown below: Let C=(1-p)µ, B1=(1-p), B21=(1-p)(1-µ), B22=pµ, B2=B21+B22, A1=p, A2=p (1-µ); different letters represent the change of the system data packet count in the next time slot; the letter C represents a decrease of 1, the letter B represents unchanged, and the letter A represents an increase of 1; the above letters are used to represent the transition probabilities corresponding to different system packet transfer processes; based on the above 8 expressions, the stable probability vector at any time slot in the scheduling cycle is expressed as:

[0101] ;

[0102] ;

[0103] In the formula, represents the stable probability vector of the nth time slot in a scheduling cycle, Represents the stable probability vector of the initial time slot. When n≥2, replace the state transition probabilities in the 8 state transition formulas with the corresponding letters above to obtain the state transition matrix corresponding to the stable probability vector The expression is:

[0104] ;

[0105] ;

[0106] ;

[0107] in accordance with Figure 2 The three-dimensional AoI schematic diagram with a scheduling period of 10 time slots is shown, and the corresponding transition probability is shown in the following table:

[0108] Table 4 Transition probability alphabet

[0109]

[0110] The corresponding state transfer matrix The expression is as follows:

[0111] ;

[0112] ;

[0113] ;

[0114] STEP6: Get the stable probability vector of each time slot in the discrete time system under the PS strategy, consider the data transmission model of the discrete time system, and obtain the upper and lower limit function expressions of the AoI under the PS strategy. The specific contents include: Using the initial time slot stable probability vector and the state transition matrix (n≥2), we can get the stable probability vector of each time slot in the discrete time system under the periodic scheduling strategy; from the stable probability vector, we can deduce the mean value of any time slot data packet as follows:

[0115] ;

[0116] Consider again the discrete-time system under the periodic scheduling strategy, where the data arrival interval is subject to the parameter The geometric distribution of is the probability of packet generation; therefore, the packet arrival interval is ; The current information age can be expressed as:

[0117] ;

[0118] ;

[0119] in, Indicates the number of packets at the beginning of the scheduling period, represents the i-th data packet, represents the information age of the kth time slot in the scheduling period, represents the mean value of the data packets in the nth time slot within the cycle, ; Using the inequality mentioned above, we can get the upper and lower bounds of AoI for any period and any time slot: represents the upper limit function of AoI, Represents the lower limit function of AoI; the expressions of the upper and lower limit functions are as follows:

[0120] ;

[0121] ;

[0122] Wherein, M represents the length of the scheduling cycle.

[0123] Figure 2A three-dimensional AoI schematic diagram with a scheduling period of 10 time slots is shown. From top to bottom, the three figures in the figure are respectively a three-dimensional graph of the AoI upper limit function with a scheduling period of 10, a Monte Carlo simulation graph with a scheduling period of 10, and a three-dimensional graph of the AoI lower limit function with a scheduling period of 10. It can be clearly seen that the upper and lower limit functions proposed in this embodiment well complete the description of the AoI curve under the PS strategy, and the upper and lower limit threshold ranges provided also provide a new method for the timeliness study under the scheduling strategy.

Claims

1. A method for detecting the timeliness of an information transmission system under a PS strategy, characterized in that: include: The information transmission system under the PS strategy is modeled as a discrete-time information transmission system, which defines that the data packets of the discrete-time information transmission system arrive only at the beginning of the time slot and the destination node is updated only at the end of the time slot; The information age solution method is used to determine the timeliness range of discrete time information transmission systems; Based on the timeliness range of the information transmission system in discrete time, determine the timeliness of the information transmission system under the PS strategy; The method of solving the information age to determine the timeliness range of the discrete time information transmission system includes the following steps: For discrete-time information transmission systems, a two-dimensional discrete state vector is established to represent the number of data packets in different time slots within a scheduling cycle; According to the generation and service completion of data packets in each time slot, the random state transition scenario of the two-dimensional discrete state vector of each time slot is described as follows: In a random state transition scenario, determine the state transition probability of the two-dimensional discrete state vector of the current time slot transferring to the two-dimensional discrete state vector of the next time slot; Based on the state transition probability, determine the stability probability of the two-dimensional discrete state vector; According to the stable probability of the two-dimensional discrete state vector, the stable probability vector at any time slot in the scheduling period is obtained; Based on the stable probability vector at any time slot in the scheduling cycle, the upper and lower limits of the information age of the discrete-time information transmission system are obtained; Based on the upper and lower limits of the information age of the discrete-time information transmission system, the timeliness range of the discrete-time information transmission system is determined.

2. The method for detecting the timeliness of an information transmission system under a PS strategy according to claim 1, characterized in that: The information transmission system for discrete time establishes a two-dimensional discrete state vector to represent the number of data packets in different time slots in a scheduling cycle, specifically including: establishing a two-dimensional discrete state vector To represent the number of data packets in different time slots within a scheduling cycle; Indicates the number of packets. Indicates the number of time slots, , , Indicated by time slots constitute a scheduling cycle; if the discrete time information transmission system is in an idle state, .

3. The method for detecting the timeliness of an information transmission system under a PS strategy according to claim 2, characterized in that: The random state transition scenario of describing the two-dimensional discrete state vector of each time slot according to the generation and service completion of the data packet in each time slot specifically includes: Let S represent whether a data packet is generated, S=0 means no data packet is generated in the current time slot, and S=1 means a data packet is generated in the current time slot; Let C represent whether the destination node has completed the service and updated its information, C=1 means that the destination node has completed the service and updated the destination node's information, C=0 means that the destination node has not completed the service or the discrete-time information transmission system is in an idle state; When the two-dimensional discrete state vector of the current time slot is , , , S=0, C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , , S=0, C=1, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , , S=1, C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , , S=1, C=1, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , when S=0, C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , when S=1 and C=0, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , when S=0 and C=1, the two-dimensional discrete state vector of the next time slot is expressed as: ; When the two-dimensional discrete state vector of the current time slot is , , when S=1, C=1, the two-dimensional discrete state vector of the next time slot is expressed as: .

4. The method for detecting the timeliness of an information transmission system under a PS strategy according to claim 3, characterized in that: The state transition probability of determining the state transition of the two-dimensional discrete state vector of the current time slot to the two-dimensional discrete state vector of the next time slot in the random state transition scenario specifically includes: In the random state transition scenario, assume that the probability of generating a data packet in each time slot is , the service completion probability of a data packet in each time slot is ; When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot ; When the two-dimensional discrete state vector of the current time slot is , When , the state transition probability is , the two-dimensional discrete state vector transferred to the next time slot .

5. The method for detecting the timeliness of an information transmission system under a PS strategy according to claim 4, characterized in that: The stability probability of the two-dimensional discrete state vector is determined based on the state transition probability, which is expressed as: ； ； ； ； ； ； ； ； In the formula, Indicates n Time slots, l The stability probability of a data packet; Indicates n -1 time slot, l The stability probability of a data packet, Indicates n -1 time slot, l +1 packet stability probability.

6. The method for detecting the timeliness of an information transmission system under a PS strategy according to claim 5, characterized in that: According to the stable probability of the two-dimensional discrete state vector, the stable probability vector at any time slot in the scheduling period is obtained, which is expressed as: ； ； ； ； In the formula, represents the stable probability vector of the nth time slot in a scheduling cycle, represents the stable probability vector of the initial time slot.

7. The method for detecting the timeliness of an information transmission system under a PS strategy according to claim 6, characterized in that: The above-mentioned stable probability vector at any time slot in the scheduling cycle is used to obtain the upper limit and lower limit of the information age of the discrete-time information transmission system. The specific operations include: The mean number of packets at any time slot in the scheduling period is derived from the stable probability vector at any time slot in the scheduling period. Assuming that it is at time slot k, it is expressed as: ； make represents the upper limit of the information age of the discrete-time information transmission system, The lower limit of the information age of the discrete-time information transmission system is expressed as: ； ； Among them, among them, M Indicates the length of the scheduling cycle, Indicates data packets, Indicates the arrival interval of data packets, represents the mean value of data packets in the kth time slot within the scheduling period, .

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