Service interruption based information age analysis method

Abstract

This invention provides a method for information age analysis based on service interruption. The method includes: constructing a dual-queue state update system; the dual-queue state update system includes two sensors and a monitor; defining the on / off state transition rate and service rate for each sensor; calculating the steady-state probability of the two sensors in various discrete states based on the discrete state transition rules, on / off state transition rate, and service rate for multiple trigger generation strategies; calculating the information age vector under each trigger generation strategy based on the steady-state probability, on / off state transition rate, and service rate, and determining the average information age from the information age vector; and determining the target trigger generation strategy for the two sensors based on the average information age under the multiple trigger generation strategies. This invention can provide new theoretical basis and practical methods for improving the information update efficiency in real-time IoT applications.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically, to a method for analyzing information age based on service interruption. Background Technology

[0002] With the rapid development of Internet of Things (IoT) technology, the demand for real-time sensor status updates is increasing. To ensure the timeliness of information, Information Age (AoI), as an important indicator of information freshness, is widely used in various latency-sensitive communication systems. AoI is defined as the time interval from information generation to successful reception of the update, reflecting the "freshness" of the information. Therefore, AoI has become a key indicator for evaluating and optimizing system performance. However, sensors in status update systems are inevitably affected by factors such as power consumption, quality, and lifespan, leading to service interruptions and thus impacting AoI performance.

[0003] Most existing research focuses on single-queue systems, analyzing the impact of service interruptions on AoI performance. For example, studies on service interruption problems in continuous-time and discrete-time queuing systems have shown that service interruptions have a significant impact on AoI.

[0004] However, these studies typically assume that the service process is continuous, neglecting the practical impact of service interruptions. In contrast, multi-queue systems, by processing multiple data streams in parallel, exhibit greater system robustness and flexibility. Under certain conditions, they can reduce information latency and maintain good AoI performance even in the event of service interruptions. Therefore, studying the impact of service interruptions on AoI performance in multi-queue systems has significant practical implications. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a method for information age analysis based on service interruption, thus offering a new theoretical basis and practical approach to improve the information update efficiency in real-time IoT applications.

[0006] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows: First, embodiments of the present invention provide a method for information age analysis based on service interruption, the method comprising: A dual-queue state update system is constructed; the dual-queue state update system includes: two sensors and a monitor, the two sensors are used to monitor the same physical process and generate state update data packets, and the monitor is used to receive the state update data packets; Define the on / off state transition rate and service rate for each sensor, wherein the on / off state transition rate is the rate at which each sensor changes between an on and off state, and the service rate is the rate at which the state update data packet for each sensor is successfully transmitted and serviced. For multiple trigger generation strategies, based on the discrete state transition rules of the two sensors, the switch state transition rate, and the service rate, the steady-state probability of the two sensors being in multiple discrete states is calculated. The multiple discrete states correspond to multiple combinations of the working states of the two sensors. Each trigger generation strategy is used to indicate the triggering method for the two sensors to send the state update data packet to the monitor. Based on the steady-state probabilities of the various discrete states, the switching state transition rate, and the service rate, calculate the information age vector under each trigger generation strategy, and determine the average information age from the information age vector; Based on the average information age under the various trigger generation strategies, the target trigger generation strategy for the two sensors is determined.

[0007] Optionally, the multiple trigger generation strategies include at least: The delivery-triggered generation strategy is used to instruct each sensor to generate a new state update data packet immediately after the previous state update data packet is successfully sent; A state-triggered generation strategy is used to instruct each sensor to generate a new state update data packet when it switches from the off state to the on state. A dual-trigger generation strategy is used to indicate that a new state update data packet is generated when either the delivery-triggered generation strategy or the state-triggered generation strategy occurs.

[0008] Optionally, calculating the steady-state probability of the two sensors being in multiple discrete states based on the discrete state transition rules of the two sensors, the switching state transition rate, and the service rate includes: Based on the discrete state transition rules of the two sensors, the switching state transition rate, and the service rate, a diagonal matrix and an off-diagonal matrix are constructed. The diagonal elements of the diagonal matrix represent the total outflow rate of each discrete state transitioning to other discrete states, and the elements of the off-diagonal matrix represent the inflow rate of other discrete states transitioning to each discrete state. Based on the diagonal matrix and the off-diagonal matrix, construct the Markov chain balance equations for the various discrete states; Solve the Markov chain equilibrium equations to determine the steady-state probabilities of the various discrete states.

[0009] Optionally, if the triggering generation strategy corresponds to four discrete states, the Markov chain balance equation is expressed as:

[0010] in, and The service rate of the two sensors. To enable state transition rate, To disable state transition rate, , , and These are the steady-state probabilities of the four discrete states, respectively.

[0011] Optionally, if the triggering generation strategy corresponds to eight discrete states, the Markov chain balance equation is expressed as:

[0012] in, , , , , , , and These are the steady-state probabilities for eight discrete states.

[0013] Optionally, the step of calculating the information age vector under each trigger generation strategy based on the steady-state probabilities of the various discrete states, the switching state transition rate, and the service rate, and determining the average information age from the information age vector, includes: Based on the steady-state probability of each discrete state, the outflow rate of each discrete state to other discrete states, the age growth rate of each discrete state, the inflow rate of other discrete states to each discrete state, and the reset mapping matrix of each triggering generation strategy, an information age vector balance equation is constructed. The reset mapping matrix is ​​used to indicate the age change matrix when transitioning from other discrete states to each discrete state. Solve the information age vector balance equation to obtain the information age vector under each trigger generation strategy. The information age vector includes: the expected value of the instantaneous information age in the monitor under the various discrete states and the expected value of the information age of the current state update data packet in the sensor. The average information age is determined based on the expected instantaneous information age of multiple discrete states under each trigger generation strategy.

[0014] Optionally, if the trigger generation strategy is a delivery trigger generation strategy, the reset mapping matrix includes: The status update data packet completes the first reset mapping matrix corresponding to the service. The second reset mapping matrix corresponding to the switching of the sensor's working state .

[0015] Optionally, the information age vector balance equation corresponding to the delivery trigger generation strategy is expressed as:

[0016] in, This refers to the information age vector corresponding to the four discrete states of the delivery trigger generation strategy. The outflow rate of the four discrete states including the delivery-triggered generation strategy. ,matrix The age growth rate of the four discrete states including the delivery-triggered generation strategy. Steady-state probabilities of the four discrete states including the delivery-triggered generation strategy, matrix The inflow rate matrix of the four discrete states including the delivery-triggered generation strategy. It includes the first reset mapping matrix and the second reset mapping matrix, the matrix and the matrix They are respectively:

[0017]

[0018] in, for The first order matrix, its second order matrix All row elements are 1, and all other row elements are 0.

[0019] Optionally, if the trigger generation strategy is a state-triggered generation strategy, the reset mapping matrix includes: The status update data packet completes the service corresponding to the third reset mapping matrix. The second reset mapping matrix corresponding to the change of the sensor's operating state from the on state to the off state. The fourth reset mapping matrix corresponding to the change of the sensor's operating state from off to on. .

[0020] Optionally, the information age vector balance equation corresponding to the state-triggered generation strategy is expressed as:

[0021] in, This refers to the information age vector corresponding to the eight discrete states of the state-triggered generation strategy. The outflow rates of the eight discrete states, including the state-triggered generation strategy. ,matrix The age growth rate of the eight discrete states, including the state-triggered generation strategy. The steady-state probabilities of eight discrete states, including the state-triggered generation strategy, are represented in a matrix. The inflow rate of eight discrete states, including the state-triggered generation strategy, is represented by a matrix. Including the first The reset mapping matrix, the third reset mapping matrix, and the fourth reset mapping matrix, the matrix and the matrix They are respectively:

[0022] .

[0023] Optionally, if the trigger generation strategy is a dual-trigger generation strategy, the reset mapping matrix includes: The status update data packet completes the first reset mapping matrix corresponding to the service. The second reset mapping matrix corresponding to the change of the sensor's operating state from the on state to the off state. The fourth reset mapping matrix corresponding to the change of the sensor's operating state from off to on. .

[0024] Optionally, the information age vector balance equation corresponding to the dual-trigger generation strategy is expressed as:

[0025] in, Let be the information age vector corresponding to the four discrete states of the dual-trigger generation strategy. ,matrix The age growth rate of the four discrete states including the dual-trigger generation strategy. The steady-state probabilities of the four discrete states including the dual-trigger generation strategy, matrix The inflow rate matrix of the four discrete states including the dual-trigger generation strategy. It includes a first reset mapping matrix, a second reset mapping matrix, and a third reset mapping matrix, the matrix and the matrix They are respectively:

[0026] .

[0027] Second, embodiments of the present invention provide an information age analysis device based on service interruption, the device comprising: The system construction module is used to build a dual-queue state update system; the dual-queue state update system includes: two sensors and a monitor, the two sensors are used to monitor the same physical process and generate state update data packets, and the monitor is used to receive the state update data packets; The parameter definition module is used to define the on / off state transition rate and service rate of each sensor. The on / off state transition rate is the rate at which each sensor changes between the on and off states, and the service rate is the rate at which the state update data packets of each sensor are successfully transmitted and the service is completed. The steady-state probability calculation module is used to calculate the steady-state probability of the two sensors being in multiple discrete states based on the discrete state transition rules of the two sensors, the switch state transition rate, and the service rate, for multiple trigger generation strategies. The multiple discrete states correspond to multiple combinations of the two sensors' operating states. Each trigger generation strategy is used to indicate the triggering method for the two sensors to send the state update data packet to the monitor. The information age calculation module is used to calculate the information age vector under each trigger generation strategy based on the steady-state probability of the various discrete states, the switching state transition rate and the service rate, and to determine the average information age from the information age vector; The generation strategy determination module is used to determine the target trigger generation strategy for the two sensors based on the average information age under the multiple trigger generation strategies.

[0028] Third, embodiments of the present invention also provide an electronic device, including a processor, a memory, and a communication bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor communicates with the memory through the communication bus, and the processor executes the machine-readable instructions to implement the method described in any of the above embodiments.

[0029] Fourth, embodiments of the present invention also provide a storage medium storing a computer program, wherein the computer program is executed by a processor to perform any of the methods described above.

[0030] The beneficial effects of this invention are: The information age analysis method based on service interruption provided by this invention constructs a dual-queue state update system model that takes service interruption into account, designs various trigger generation strategies, analyzes the average information age of the system, and effectively improves the performance of the dual-queue state update system by analyzing the impact of service interruption on information freshness, ensuring more stable state updates and more timely information between sensors and monitoring terminals.

[0031] By defining the switching state transition rate and service rate of each sensor, the inevitable service interruption process of the sensor in actual operation is modeled as a controllable random process. This modeling method can truly reflect the intermittent working state of the sensor caused by factors such as power fluctuations, signal interference, and equipment aging, providing input parameters that conform to physical reality for the subsequent accurate analysis of information age.

[0032] By comparing the average information age under various strategies, a clear basis for selecting target strategies can be provided for practical IoT systems. Designers can select the optimal triggering generation strategy based on the information freshness requirements of the monitoring task, combined with the sensor's interruption characteristics and service capabilities, thereby maximizing system performance with limited resources and improving the accuracy and reliability of real-time monitoring. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 A flowchart illustrating the information age analysis method provided in this embodiment of the invention. Figure 1 ; Figure 2 A system architecture diagram provided for embodiments of the present invention; Figure 3 A flowchart illustrating the information age analysis method provided in this embodiment of the invention. Figure 2 ; Figure 4 A schematic diagram of a Markov chain in a random hybrid system provided in an embodiment of the present invention. Figure 1 ; Figure 5 A schematic diagram of a Markov chain in a random hybrid system provided in an embodiment of the present invention. Figure 2 ; Figure 6 A flowchart illustrating the information age analysis method provided in this embodiment of the invention. Figure 3 ; Figure 7The graph shows the average information age as a function of service rate under the three strategies. Figure 8 shows the average information age as... A graph showing the functional relationship of the ratio change; Figure 9 A schematic diagram of the structure of the service interruption information age analysis device provided in an embodiment of the present invention; Figure 10 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0036] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified and changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0037] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual images, and should not be construed as limiting the invention. It is understandable that some well-known structures and their descriptions may be omitted in the drawings for those skilled in the art.

[0038] Figure 1 A flowchart illustrating the information age analysis method provided in this embodiment of the invention. Figure 1 ,like Figure 1 As shown, the method may include: Step 101: Construct a dual-queue state update system. The dual-queue state update system includes two sensors and one monitor. The two sensors are used to monitor the same physical process and generate state update data packets, and the monitor is used to receive the state update data packets.

[0039] In this embodiment, the dual-queue state update system can also be referred to as a remote monitoring system. Figure 2 The system architecture diagram provided for the embodiments of the present invention is as follows: Figure 2As shown, the dual-queue state update system includes two sensors (sensor 1 and sensor 2) and a monitor.

[0040] Two sensors operate in parallel, observing the same physical process and generating state update data packets, which are then transmitted to a shared monitor. Upon receiving the state update data packet, the monitor updates its own state to maintain the freshness of the stored information. Simultaneously, it sends an error-free acknowledgment signal (ACK) to the sensor that sent the state update data packet. The ACK signal is assumed to be instantaneous and error-free. Upon receiving the ACK signal, the sensor determines that the corresponding data packet service is complete and uses the received state update data packet to update the physical process state information, thereby achieving real-time state monitoring.

[0041] Step 102: Define the on / off state transition rate and service rate for each sensor. The on / off state transition rate is the rate at which each sensor changes between the on and off states. The service rate is the rate at which each sensor's state update data packet is successfully transmitted and serviced.

[0042] In this embodiment, the random service interruption process of each sensor is modeled as a switching process. Since sensors are susceptible to random interruptions caused by battery depletion, hardware failures, and preemption by high-priority tasks during actual operation, service interruptions are inevitable. The service process of each sensor is adjusted by an on-off process to simulate potential service interruptions. The switching process includes an on state and a off state. In the on state, the sensor can normally perform data packet generation, processing, and transmission operations; in the off state, the sensor suspends all data packet-related operations.

[0043] Among them, sensors i ( The service rate of ) follows the parameter. The exponential distribution, in isomorphic scenarios Adjust as needed in heterogeneous scenarios , The value satisfies the following condition when the total service rate is fixed. constant.

[0044] The switch state transition rate includes the on state transition rate and the off state transition rate, and the duration of the sensor's on state. T on Obtain the parameter as The exponential distribution has a probability density function of: Duration of the off state T off Obtain the parameter as The exponential distribution has a probability density function of: , Here, represents the transition rate parameter from the open state to the closed state. Here, is the transition rate parameter from the closed state to the open state, and is the transition rate from the closed state to the open state. In this embodiment, the ratio of these two parameters can be adjusted. Simulate service interruptions of varying intensities.

[0045] Step 103: For multiple trigger generation strategies, calculate the steady-state probability of the two sensors in multiple discrete states based on the discrete state transition rules, switch state transition rate and service rate of the two sensors. Multiple discrete states correspond to multiple combinations of working states of the two sensors. Each trigger generation strategy is used to indicate the triggering method for the two sensors to send state update data packets to the monitor.

[0046] In this embodiment, a free-generation (GAW) triggered generation strategy is constructed, where the data source can actively decide when to perform the sampling process and generate relevant data packets. By constructing multiple different types of triggered generation strategies, corresponding to different data packet update mechanisms, and adapting to different service interruption scenarios, the system performance under different mechanisms can be comprehensively compared and analyzed, providing a clear basis for information age analysis. Different triggered generation strategies can be characterized by different events that trigger sampling operations.

[0047] Based on the type of trigger generation strategy, the two sensors are divided and combined into various working states to obtain a variety of discrete states that match the trigger generation strategy, such as a combination of the on and off states of the two sensors, or a combination of the on, off, idle, and busy states of the two sensors.

[0048] Discrete state transition rules are used to indicate the rules for transitioning from one discrete state to other discrete states. According to the discrete state transition rules, the first discrete state after the transition for each discrete state (i.e., which discrete states each discrete state can transition to) and the second discrete state before the transition for each discrete state (i.e., which discrete states can transition to each discrete state) can be determined.

[0049] Based on the service rate of transition from each discrete state to the first discrete state, the switching state transition rate, and the service rate of transition from the second discrete state to each discrete state, as well as the switching state transition rate, calculate the steady-state probability of each sensor in each discrete state. Steady-state probability is used to indicate the probability that a sensor is stably in each discrete state.

[0050] For example, based on the discrete state transition rules and transition rates, a Markov chain equilibrium equation is established, and combined with the normalization condition, the steady-state probability vector of the discrete state is solved. , The total number of discrete states can be expressed by the following formula:

[0051] Where Q is the set of discrete states. To start from discrete state q The set of all events that trigger the event. To reach discrete state q The collection of all events, It is "the first" l The transition rate of "event-like events", including discrete states q Service rate for transition to the first discrete state, switch state transition rate, and second discrete state to discrete state transition rate q Service transfer rate, switch state transfer rate To pass the event l Transition to each discrete state q The steady-state probability of the second discrete state.

[0052] Step 104: Based on the steady-state probability, switching state transition rate and service rate of various discrete states, calculate the information age vector under each trigger generation strategy, and determine the average information age from the information age vector.

[0053] In this embodiment, based on the steady-state probability, switching state transition rate, and service rate of multiple discrete states under each trigger generation strategy, an information age vector balance equation for multiple discrete states is constructed. One side of the information age vector balance equation consists of the switching state rate or service rate of each discrete state transitioning to the first discrete state and the information age unknown of each discrete state. The other side consists of the steady-state probability of each discrete state, the switching state transition rate or service rate of the second discrete state transitioning to each discrete state, and the information age unknown of the second discrete state.

[0054] The balance equations of information age vectors for multiple discrete states are solved to determine the information age vector under each triggering generation strategy. The information age vector under each triggering generation strategy includes information age vectors under multiple discrete states. The information age vector of each discrete state is used to indicate the continuous evolution of the corresponding age information under each discrete state. The first element of the information age vectors of multiple discrete states under each triggering generation strategy is accumulated to obtain the average information age under each triggering generation strategy.

[0055] Step 105: Determine the target trigger generation strategy for the two sensors based on the average information age under various trigger generation strategies.

[0056] In this embodiment, the freshness requirements of information vary in different IoT scenarios. By obtaining the service rate and switch state transition rate of the sensors in the actual scenario, this scheme calculates the average information age under various trigger generation strategies, and selects the trigger generation strategy that meets the scenario requirements as the target trigger generation strategy, so that the freshness of the data monitored and transmitted by the two sensors meets the requirements.

[0057] In one possible implementation, the multiple trigger generation strategies include at least: The delivery-triggered generation strategy instructs each sensor to generate a new state update data packet immediately after the previous state update data packet is successfully sent.

[0058] The state-triggered generation strategy is used to instruct each sensor to generate a new state update data packet when it switches from the off state to the on state.

[0059] The dual-trigger generation strategy is used to indicate that a new state update data packet is generated when either the delivery-triggered generation strategy or the state-triggered generation strategy occurs.

[0060] In this embodiment, the delivery-triggered generation strategy (DeT), the state-triggered generation strategy (ST), and the dual-triggered generation strategy (DuT) adopt a source-end preemptive parallel mechanism. When the service of sending a state update data packet to the monitor by any sensor is completed, the monitor will simultaneously synchronize the physical process state information to the two sensors. The other sensor determines the generation timestamp of the newly received state update data packet based on the physical process state information. If its generation timestamp is later than the timestamp of the data packet that the other sensor is currently generating, it means that this data packet is an outdated data packet, and it is directly discarded. The state update data packet is directly regenerated according to the trigger generation strategy, or a new state update data packet is generated when the sensor switches from the off state to the on state.

[0061] Among them, outdated data packets refer to data packets whose generation timestamp is earlier than the generation timestamp of the currently being processed data packet, and which have not been acknowledged by the monitor. The probability density of a data packet successfully being sent to the monitor and thus completing the service is as follows: The probability of completing the service satisfies That is, the longer the data packet is sent (t), the greater the probability that the data packet will complete the service.

[0062] The state-triggered generation strategy includes idle state management logic. When any sensor's state update data packet completes its service, all sensors immediately enter an idle state, ceasing data packet sampling until any sensor's service state switches from off to on, triggering sampling to generate a new state update data packet. Simultaneously, the new state update data packet also triggers source-side preemption; any updates currently being served will be replaced by the new state update data packet. The trigger condition for a sensor to switch from idle to busy state is that the service state is on, with a switching probability... For, that is, the duration of the off state. T off The larger the value, the longer the shutdown time, and the greater the probability that the sensor will switch from an idle state to a busy state. The rate at which the sensor switches from a busy state to an idle state is its own service rate. , Switching probability .

[0063] The dual-trigger generation strategy combines the delivery-triggered generation strategy and the state-triggered generation strategy. Its execution mechanism includes the following rules: a parallel transmission mechanism with preemption at the system source end, and the generation of data packets is triggered by either of two events, namely the delivery trigger event of "any data packet service completed" or the state trigger event of "any sensor service state switching from off to on". When a new data packet is triggered, the system performs generation trigger preemption, and the new data packet will preempt the outdated data packet that is being served.

[0064] In one possible implementation, Figure 3 A flowchart illustrating the information age analysis method provided in this embodiment of the invention. Figure 2 ,like Figure 3 As shown, step 103 above, for various trigger generation strategies, calculates the steady-state probability of two sensors in various discrete states based on the discrete state transition rules, switching state transition rates, and service rates of the two sensors. This process may include: Step 201: Based on the discrete state transition rules, switch state transition rates, and service rates of the two sensors, construct a diagonal matrix and an off-diagonal matrix. The diagonal elements of the diagonal matrix represent the total outflow rate of each discrete state transitioning to other discrete states, and the elements of the off-diagonal matrix represent the inflow rate of other discrete states transitioning to each discrete state.

[0065] Step 202: Construct the balance equations of Markov chains for various discrete states based on the diagonal and off-diagonal matrices.

[0066] Step 203: Solve the Markov chain equilibrium equations to determine the steady-state probabilities of various discrete states.

[0067] In this embodiment, the total outflow rate for each discrete state is determined based on the service rate of transitioning from each discrete state to the first discrete state, the on state transition rate, and the off state transition rate. A diagonal matrix is ​​then constructed based on the total outflow rates of multiple discrete states. .

[0068] Based on the service rate, open state transition rate, or closed state transition rate of the transition from the second discrete state j to each discrete state i, the inflow rate of the transition from the second discrete state j to each discrete state i is determined. Based on the inflow rates of multiple discrete states, a non-diagonal matrix S is constructed, whose matrix elements... Characterizes the inflow rate of the transition from the second discrete state j to each discrete state i.

[0069] For example, the equilibrium equations of a Markov chain can be expressed as:

[0070] in, .

[0071] By solving the simultaneous equilibrium equations of Markov chains under various discrete states, the steady-state probabilities of these discrete states can be determined. .

[0072] In one possible implementation, the trigger generation strategy corresponds to four discrete states.

[0073] In this embodiment, the discrete state set Q is divided based on the combination of two sensor service states, that is, all possible combinations are divided into the following four discrete states according to the two service states of "on" or "off", Q={0,1,2,3}: q=0: Both sensor services are enabled, and the system is processing a status update data packet.

[0074] q=1: The service of sensor 1 is on, the service of sensor 2 is off, and the system is processing a status update data packet.

[0075] q=2: The service of sensor 2 is on, the service of sensor 1 is off, and the system is processing a status update data packet.

[0076] q=3: The services of both sensors are in a closed state, and the service of the current data packet is blocked.

[0077] Figure 4 A schematic diagram of a Markov chain in a random hybrid system provided in an embodiment of the present invention. Figure 1 ,like Figure 4As shown, under the DeT and DuT strategies, taking the state of two sensors with q=0 as an example, the service rate of the two sensors completing the service is: When two sensors transition from the state q=0 to q=1, the transition rate of sensor 2 to the on state is: The two sensors transition from the state q=0 to q=2. The transition rate of sensor 1 to the on state is... Then the total outflow rate in the discrete state q=0 is Similarly, the total outflow rate in the discrete state q=1 is The total outflow rate in the discrete state q=2 is The total outflow rate in the discrete state q=3 is Then, under the DeT and DuT policies, the diagonal matrix The four diagonal elements are: , , , .

[0078] Taking the discrete state q=0 as an example, the service rate (outflow rate) for completing the service is: The inflow rates for the transition from discrete states q=1, q=2, and q=3 to q=0 are respectively , 0, and the same applies to other discrete states. Therefore, under the DeT and DuT policies, the off-diagonal matrix... The expression is:

[0079] The balance equations of the Markov chain under the DeT and DuT policies can be expressed as:

[0080] in, .

[0081] Specifically, the Markov chain equilibrium equation is expressed as:

[0082] in, and For the service rate of the two sensors, To enable state transition rate, To disable state transition rate, , , and These are the steady-state probabilities for the four discrete states.

[0083] In one possible implementation, the trigger generation strategy corresponds to eight discrete states.

[0084] In this embodiment, considering that the sensor is not always in a busy state, the discrete states under the ST strategy are divided into 8 categories, namely Q={0,1,2,3,4,5,6,7}, as follows: q=0: Both sensors are in the enabled state and both are busy. The system is processing a status update data packet.

[0085] q=1: Both sensors are in the enabled state, the current data packet service has been completed, and both sensors are in the idle state.

[0086] q=2: Sensor 1 is in the on state, Sensor 2 is in the off state, both sensors are busy, and the system is processing a status update data packet.

[0087] q=3: Sensor 1 is in the on state, Sensor 2 is in the off state, the current data packet service has been completed, and all sensors are in the idle state.

[0088] q=4: Sensor 1 is in a closed state, Sensor 2 is in a busy state, and the system is processing a status update data packet.

[0089] q=5: The service status of sensor 1 is off, the service status of sensor 2 is on, the current data packet service has been completed, and all sensors are in an idle state.

[0090] q=6: The service status of both sensors is off, and the service of the current data packet is blocked.

[0091] q=7: Both sensors are in a closed state and are in an idle state.

[0092] Figure 5 A schematic diagram of a Markov chain in a random hybrid system provided in an embodiment of the present invention. Figure 2 ,like Figure 5 As shown, under the ST strategy, the switching transition between idle and busy states also needs to be considered, including the rate at which the sensor transitions from idle to busy. The rate at which one transitions from busy to idle is or .

[0093] Taking the state of q=0 as an example, the total outflow rate transitioning to discrete states q=1, 2, and 4 is: diagonal matrix under ST strategy The eight diagonal elements are: , , , , , , , .

[0094] The inflow rates from discrete states q=0, 1, 2, 3, 4, 5, 6, 7 to discrete state q=0 are 0, ... , , , 0, 0, and the same applies to other discrete states. Therefore, under the ST strategy, the off-diagonal matrix... The expression is:

[0095] The equilibrium equation of the Markov chain under the ST strategy can be expressed as:

[0096] in, .

[0097] Specifically, the Markov chain equilibrium equation is expressed as:

[0098] in, , , , , , , and These are the steady-state probabilities for eight discrete states.

[0099] In one possible implementation, Figure 6 A flowchart illustrating the information age analysis method provided in this embodiment of the invention. Figure 3 ,like Figure 6 As shown, step 104 above, which calculates the information age vector for each triggering generation strategy based on the steady-state probability, switching state transition rate, and service rate of various discrete states, and determines the average information age from the information age vector, may include: Step 301: Based on the steady-state probability of each discrete state, the outflow rate of each discrete state to other discrete states, the age growth rate of each discrete state, the inflow rate of other discrete states to each discrete state, and the reset mapping matrix of each triggering generation strategy, construct the information age vector balance equation. The reset mapping matrix is ​​used to indicate the age change matrix when transitioning from other discrete states to each discrete state.

[0100] In this embodiment, the service rate for transitioning from each discrete state to the first discrete state is determined according to... , or and the start state transition rate Or the state transition rate is turned off The rate of age increase for each discrete state Steady-state probability under each discrete state The service rate of transition from the second discrete state to each discrete state , or and the start state transition rate Or the state transition rate is turned off Construct an information age vector balance equation. Wherein, For the continuous state of information age It increases at a rate that increases with time.

[0101] Example, continuous state based on information age Based on the evolutionary rules and reset mapping matrix, establish an information age-related vector:

[0102] Among them, continuous state Characterizing age-related processes in a continuous state , The age of the monitor's instantaneous information. To update the information age of the data packet based on the current state in the sensor, a continuous state evolution rule is defined for each discrete state. and All grow at a unit rate, that is , For indicator functions, when The value is 1 if the condition is met, and 0 otherwise. Information age-related vector. It converges to a non-negative limit, namely the information age vector. Information age vector The following information age vector balance equation is satisfied:

[0103] Wherein, the continuous state during discrete state transition is defined. Reset mapping matrix Characterizing continuous states from arrive The update rules.

[0104] S302. Solve the information age vector balance equation to obtain the information age vector under each triggering generation strategy. The information age vector includes: the expected value of the instantaneous information age in the monitor under various discrete states and the expected value of the information age of the current state update data packet in the sensor.

[0105] In this embodiment, the information age vector is determined by simultaneously solving the information age balance equations for multiple discrete states under each trigger generation strategy. Each discrete state's information age vector contains the instantaneous information age in the monitor. Expected value Information about age in the current state update data packets from sensors Expected value .

[0106] S303. Determine the average information age based on the expected instantaneous information age of multiple discrete states under each triggering generation strategy.

[0107] In this embodiment, the average information age under each trigger generation strategy is calculated based on the expected instantaneous information age of all discrete states in the information age vector under each trigger generation strategy.

[0108] For example, the expression for average information age can be represented as:

[0109] in, For the relevant vector Chinese correspondence The amount.

[0110] In one possible implementation, if the triggering generation strategy is a delivery-triggered generation strategy, resetting the mapping matrix includes: The status update data packet completes the first reset mapping matrix corresponding to the service. The second reset mapping matrix corresponding to the sensor's operating state switching .

[0111] In this embodiment, the delivery-triggered generation strategy is used to generate a new data packet after the previous data packet is completed. Therefore, when the state update data packet completes its service, it is based on the first reset mapping matrix. The monitor's instantaneous information age is updated to the information age of the current data packet, that is... The information age of the current data packet is reset to 0, that is... .

[0112] When the sensor service state changes, it is based on the second reset mapping matrix. The monitor's instantaneous information age and the information age of the current data packet remain unchanged, that is... , .

[0113] Furthermore, the information age vector balance equation corresponding to the delivery-triggered generation strategy is expressed as:

[0114] in, The information age vectors corresponding to the four discrete states that trigger the generation strategy for delivery. Outflow rates for four discrete states, including delivery-triggered generation strategies. ,matrix The age growth rate of four discrete states, including delivery-triggered generation strategies. Steady-state probabilities of four discrete states including a delivery-triggered generation strategy, matrix The inflow rate matrix of four discrete states including the delivery-triggered generation strategy. Includes a first reset mapping matrix and a second reset mapping matrix, the matrix sum matrix They are respectively:

[0115]

[0116] in, for The first order matrix, its second order matrix All row elements are 1, and all other row elements are 0.

[0117] In one possible implementation, if the triggering generation strategy is a state-triggered generation strategy, resetting the mapping matrix includes: The third reset mapping matrix corresponding to the status update data packet completion service The second reset mapping matrix corresponding to the change of the sensor's operating state from on to off. The fourth reset mapping matrix corresponding to the sensor's operating state changing from off to on. .

[0118] In this embodiment, the state-triggered generation strategy is used to generate new state update data packets when the sensor's service state changes. Therefore, when the state update data packet completes its service, it is processed according to the third reset mapping matrix. The monitor's instantaneous information age is updated to the information age of the current data packet, that is... The information age of the current data packet remains unchanged, that is .

[0119] When the sensor service status changes from on to off, according to the second reset mapping matrix The monitor's instantaneous information age and the information age of the current data packet remain unchanged, that is... , .

[0120] When the sensor service status changes from off to on, according to the fourth reset mapping matrix The age of the monitor's instantaneous information remains unchanged, that is The information age of the current data packet is reset to 0, that is... .

[0121] Furthermore, the information age vector balance equation corresponding to the state-triggered generation strategy is expressed as:

[0122] in, This represents the information age vector corresponding to the eight discrete states of the state-triggered generation strategy. The outflow rates of eight discrete states, including those generated by a state-triggered strategy. ,matrix The age growth rate of eight discrete states, including those generated by a state-triggered strategy. Steady-state probabilities of eight discrete states including a state-triggered generation strategy, matrix The inflow rate matrix of eight discrete states including a state-triggered generation strategy. Including the Reset mapping matrix, third reset mapping matrix, and fourth reset mapping matrix, matrix sum matrix They are respectively:

[0123]

[0124] In one possible implementation, if the trigger generation strategy is a dual-trigger generation strategy, resetting the mapping matrix includes: The status update data packet completes the first reset mapping matrix corresponding to the service. The second reset mapping matrix corresponding to the change of the sensor's operating state from on to off. The fourth reset mapping matrix corresponding to the sensor's operating state changing from off to on. .

[0125] In this embodiment, the dual-trigger generation strategy is used to generate a new state update data packet when the previous data packet is completed or when the sensor's service state changes. Therefore, when the state update data packet completes its service, it is based on the first reset mapping matrix. The monitor's instantaneous information age is updated to the information age of the current data packet, that is... The information age of the current data packet is reset to 0, that is... .

[0126] When the sensor service status changes from on to off, according to the second reset mapping matrix The monitor's instantaneous information age and the information age of the current data packet remain unchanged, that is... , .

[0127] When the sensor service status changes from off to on, according to the fourth reset mapping matrix The age of the monitor's instantaneous information remains unchanged, that is The information age of the current data packet is reset to 0, that is... .

[0128] Furthermore, the information age vector balance equation corresponding to the dual-trigger generation strategy is expressed as:

[0129] in, This represents the information age vector corresponding to the four discrete states of the dual-trigger generation strategy. ,matrix Age growth rate of four discrete states including a dual-trigger generation strategy. Steady-state probabilities of four discrete states including a dual-trigger generation strategy, matrix Inflow rates of four discrete states including a dual-trigger generation strategy, matrix It includes a first reset mapping matrix, a second reset mapping matrix, and a third reset mapping matrix. sum matrix They are respectively:

[0130]

[0131] Furthermore, in homogeneous server scenarios After processing the information age vector balance equation, the closed-form analytical expression of the average information age for the three update generation strategies is as follows: The closed-form analytical expression for the average information age of the DeT strategy is:

[0132] The closed-form analytical expression for the average information age of the ST strategy is:

[0133] The closed-form analytical expression for the average information age of the DuT strategy is:

[0134] The information age analysis method based on service interruption provided in the above embodiments constructs a dual-queue state update system model that considers service interruption, designs multiple trigger generation strategies, analyzes the average information age of the system, and effectively improves the performance of the dual-queue state update system by analyzing the impact of service interruption on information freshness, ensuring more stable state updates and more timely information between sensors and monitoring terminals.

[0135] By defining the switching state transition rate and service rate of each sensor, the inevitable service interruption process of the sensor in actual operation is modeled as a controllable random process. This modeling method can truly reflect the intermittent working state of the sensor caused by factors such as power fluctuations, signal interference, and equipment aging, providing input parameters that conform to physical reality for the subsequent accurate analysis of information age.

[0136] By comparing the average information age under various strategies, a clear basis for selecting target strategies can be provided for practical IoT systems. Designers can select the optimal triggering generation strategy based on the information freshness requirements of the monitoring task, combined with the sensor's interruption characteristics and service capabilities, thereby maximizing system performance with limited resources and improving the accuracy and reliability of real-time monitoring.

[0137] To verify the correctness of the method of the present invention and to explore the influence of system parameters on information age performance, two sets of simulation experiments were designed and carried out, and the corresponding results are shown below.

[0138] Figure 7 The graph shows the average information age as a function of service rate under the three strategies, such as... Figure 7As shown, the simulation results agree well with the analysis results, verifying the correctness of the theoretical derivation. Furthermore, it can be noted that the longer the off state lasts, the lower the switching frequency between on and off states, thus amplifying the impact of service interruption on information age. When the off time is longer than the on time, the ST strategy, especially under low service rate conditions, shows a more significant advantage over the DeT strategy. This is because in the ST strategy, the sensor can immediately generate new data packets when it detects the service state changing from off to on, preempting the currently ongoing service. The DeT strategy, however, cannot compensate for the loss of information freshness caused by a long off state in a timely manner. Compared to the ST strategy, the average information age advantage of the DeT strategy gradually becomes apparent in the high service rate range. This phenomenon can be explained by the fact that the rapid transmission of updates reduces the impact of service interruption on system performance. In addition, it was observed that the DuT strategy outperforms both the DeT and ST strategies in achieving a lower average information age.

[0139] Figure 8 shows the average information age as... The functional relationship of the ratio change is shown in Figure 8(a), with the ratio fixed. As shown in Figure 8(b), fixed It is important to note that, The proportion of abnormal runtime is represented, thus reflecting the impact of service shutdown. It can be observed that the performance under the three strategies exhibits significantly different trends. As shown in Figure 8(a), the average information age under the DeT and DuT strategies increases with... The average information age increases with the increase of the ST strategy, while the average information age increases with the increase of the ST strategy. The increase first drops rapidly, then gradually rises. This is because... The initial increase in the frequency of switching between on and off states highlighted the advantages of the ST strategy and effectively reduced the average information age. However, with As the number of services continues to grow and the activation period shortens, the number of successful updates per service cycle decreases. In this situation, the impact of service interruptions becomes increasingly significant, leading to a slow increase in the average information age. Furthermore, when the proportion of on / off duration... When the data size is small, the DeT strategy is superior to the ST strategy, but inferior to the DuT strategy. This can be explained by the fact that DeT continuously samples and transmits update packets during a longer on period, thus maintaining a high level of information freshness.

[0140] However, the DuT strategy leverages its state-triggered generation mechanism to reduce information staleness caused by service interruptions, thus achieving better average information age performance. As the open period duration shortens, the ST strategy outperforms the DeT strategy because its state-triggered mechanism effectively compensates for information aging caused by prolonged shutdown. Furthermore, the age performance under the DuT strategy gradually degrades to the same level as the ST strategy because the relatively short open time is insufficient for data packets to complete service. This indicates that with a shorter open period, better information age can be achieved directly without feedback, relying solely on server state to regulate update generation.

[0141] Conversely, Figure 8(b) shows a different phenomenon: as the impact of service interruption gradually intensifies, i.e. the duration of the shutdown period increases, in the dual-queue update system, more reliance on monitoring feedback to control update generation is crucial for achieving better average information age performance.

[0142] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments can be accomplished by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Furthermore, any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory.

[0143] Based on the above method embodiments, this invention provides an information age analysis device based on service interruption. Figure 9 A schematic diagram of the structure of the service interruption information age analysis device provided in an embodiment of the present invention is shown below. Figure 9 As shown, the device may include: System building module 401 is used to build a dual-queue state update system. The dual-queue state update system includes: two sensors and one monitor. The two sensors are used to monitor the same physical process and generate state update data packets, and the monitor is used to receive state update data packets. The parameter definition module 402 is used to define the switch state transition rate and service rate for each sensor. The switch state transition rate is the rate at which each sensor changes between the on and off states, and the service rate is the rate at which the state update data packet of each sensor is successfully transmitted and serviced. The steady-state probability calculation module 403 is used to calculate the steady-state probability of two sensors in multiple discrete states based on the discrete state transition rules, switch state transition rate and service rate of the two sensors for multiple trigger generation strategies. The multiple discrete states correspond to multiple combinations of working states of the two sensors. Each trigger generation strategy is used to indicate the triggering method for the two sensors to send state update data packets to the monitor. The information age calculation module 404 is used to calculate the information age vector under each triggering generation strategy based on the steady-state probability, switching state transition rate and service rate of various discrete states, and to determine the average information age from the information age vector. The generation strategy determination module 405 is used to determine the target trigger generation strategy of the two sensors based on the average information age under multiple trigger generation strategies.

[0144] In one possible implementation, embodiments of the present invention also provide an electronic device. Figure 10 A schematic diagram of an electronic device provided in an embodiment of the present invention, such as... Figure 10 As shown, the electronic device may include a processor 501, a memory 502, and a communication bus 503. The memory 502 stores machine-readable instructions that can be executed by the processor 501. When the electronic device is running, the processor 501 communicates with the memory 502 through the communication bus 503, and the processor 501 executes the machine-readable instructions to implement the method of the above embodiment.

[0145] In one possible implementation, the present invention also provides a storage medium storing a computer program, which is executed by a processor to perform the methods described above.

[0146] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of information age analysis based on service interruption, characterized in that, The method includes: A dual-queue state update system is constructed; the dual-queue state update system includes: two sensors and a monitor, the two sensors are used to monitor the same physical process and generate state update data packets, and the monitor is used to receive the state update data packets; Define the on / off state transition rate and service rate for each sensor, wherein the on / off state transition rate is the rate at which each sensor changes between an on and off state, and the service rate is the rate at which the state update data packet for each sensor is successfully transmitted and serviced. For multiple trigger generation strategies, based on the discrete state transition rules of the two sensors, the switch state transition rate, and the service rate, the steady-state probability of the two sensors being in multiple discrete states is calculated. The multiple discrete states correspond to multiple combinations of the working states of the two sensors. Each trigger generation strategy is used to indicate the triggering method for the two sensors to send the state update data packet to the monitor. Based on the steady-state probabilities of the various discrete states, the switching state transition rate, and the service rate, calculate the information age vector under each trigger generation strategy, and determine the average information age from the information age vector; Based on the average information age under the various trigger generation strategies, the target trigger generation strategy for the two sensors is determined.

2. The method of claim 1, wherein, The step of calculating the steady-state probability of the two sensors being in multiple discrete states based on the discrete state transition rules of the two sensors, the switching state transition rate, and the service rate includes: Based on the discrete state transition rules of the two sensors, the switching state transition rate, and the service rate, a diagonal matrix and an off-diagonal matrix are constructed. The diagonal elements of the diagonal matrix represent the total outflow rate of each discrete state transitioning to other discrete states, and the elements of the off-diagonal matrix represent the inflow rate of other discrete states transitioning to each discrete state. Based on the diagonal matrix and the off-diagonal matrix, construct the Markov chain balance equations for the various discrete states; Solve the Markov chain equilibrium equations to determine the steady-state probabilities of the various discrete states.

3. The method of claim 2, wherein, If the triggering generation strategy corresponds to four discrete states, the Markov chain balance equation is expressed as: wherein, and are the service rates of the two sensors, are the on state transition rates, are the off state transition rates, , , and are the steady state probabilities of the four discrete states, respectively. If the triggering generation strategy corresponds to eight discrete states, the Markov chain balance equation is expressed as: where, , , , , , , and are the steady-state probabilities of the eight discrete states, respectively.

4. The method of claim 1, wherein, The step of calculating the information age vector under each trigger generation strategy based on the steady-state probabilities of the various discrete states, the switching state transition rate, and the service rate, and determining the average information age from the information age vector, includes: Based on the steady-state probability of each discrete state, the outflow rate of each discrete state to other discrete states, the age growth rate of each discrete state, the inflow rate of other discrete states to each discrete state, and the reset mapping matrix of each triggering generation strategy, an information age vector balance equation is constructed. The reset mapping matrix is ​​used to indicate the age change matrix when transitioning from other discrete states to each discrete state. Solve the information age vector balance equation to obtain the information age vector under each trigger generation strategy. The information age vector includes: the expected value of the instantaneous information age in the monitor under the various discrete states and the expected value of the information age of the current state update data packet in the sensor. The average information age is determined based on the expected instantaneous information age of multiple discrete states under each trigger generation strategy.

5. The method of claim 4, wherein, If the trigger generation strategy is a delivery trigger generation strategy, the reset mapping matrix includes: The state update data packet completes the first reset mapping matrix corresponding to the service The second reset mapping matrix corresponding to the working state switching of the sensor .

6. The method of claim 5, wherein, The information age vector balance equation corresponding to the delivery trigger generation strategy is expressed as: wherein a vector of information ages corresponding to the four discrete states of the delivery trigger generation policy, an outflow rate comprising the four discrete states of the delivery trigger generation policy, a matrix a matrix of steady state probabilities comprising the four discrete states of the delivery trigger generation policy, a matrix of inflow rates comprising the four discrete states of the delivery trigger generation policy, comprising the first reset mapping matrix and the second reset mapping matrix, the matrix and the matrix are respectively: wherein is a a matrix whose first row elements are all 1 and the remaining row elements are all 0.

7. The method of claim 4, wherein, If the trigger generation strategy is a state-triggered generation strategy, the reset mapping matrix includes: The status update data packet completes the service corresponding to the third reset mapping matrix. The second reset mapping matrix corresponding to the change of the sensor's operating state from the on state to the off state. The fourth reset mapping matrix corresponding to the change of the sensor's working state from the off state to the on state. .

8. The method according to claim 7, characterized in that, The information age vector balance equation corresponding to the state-triggered generation strategy is expressed as: in, This refers to the information age vector corresponding to the eight discrete states of the state-triggered generation strategy. The outflow rates of the eight discrete states, including the state-triggered generation strategy. ,matrix The age growth rate of the eight discrete states, including the state-triggered generation strategy. The steady-state probabilities of eight discrete states, including the state-triggered generation strategy, are represented in a matrix. The inflow rate of eight discrete states, including the state-triggered generation strategy, is represented by a matrix. Including the first The reset mapping matrix, the third reset mapping matrix, and the fourth reset mapping matrix, the matrix and the matrix They are respectively: 。 9. The method according to claim 4, characterized in that, If the trigger generation strategy is a dual-trigger generation strategy, the reset mapping matrix includes: The status update data packet completes the first reset mapping matrix corresponding to the service. The second reset mapping matrix corresponding to the change of the sensor's operating state from the on state to the off state. The fourth reset mapping matrix corresponding to the change of the sensor's working state from the off state to the on state. .

10. The method according to claim 9, characterized in that, The information age vector balance equation corresponding to the dual-trigger generation strategy is expressed as: in, Let be the information age vector corresponding to the four discrete states of the dual-trigger generation strategy. ,matrix The age growth rate of the four discrete states including the dual-trigger generation strategy. The steady-state probabilities of the four discrete states including the dual-trigger generation strategy, matrix The inflow rate matrix of the four discrete states including the dual-trigger generation strategy. It includes a first reset mapping matrix, a second reset mapping matrix, and a third reset mapping matrix, the matrix and the matrix They are respectively: 。

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