A node work scheduling method for rechargeable wireless sensor networks based on information freshness

Abstract

The present invention relates to a method for scheduling the work of a rechargeable wireless sensor network node based on information freshness. The method belongs to the field of wireless communication technology. A wireless sensor network model is established in which each node in the network is equipped with a single limited capacity rechargeable battery, and the relationship between the remaining battery energy and the average information age of the network is theoretically analyzed using the random hybrid system method. Based on the analysis results of this theory, a full charging strategy that can obtain a smaller average network information age is proposed; then, in view of the problem that the charging speed of the node battery is a finite value, a wireless sensor network model in which the node is equipped with dual limited capacity rechargeable batteries is proposed, and the average information age optimization problem of the network is established. The Lyapunov drift plus penalty method is used to simplify the optimization problem, and a node scheduling algorithm based on information freshness is proposed. The present invention can effectively reduce the average information age of the system, improve the real-time performance of receiving information, and has practical application value.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications and relates to a method for scheduling work of chargeable wireless sensor network nodes based on information freshness. Background Art

[0002] In the past decade, wireless sensor networks (WSNs) have developed rapidly in many application areas such as environmental monitoring, military applications, industrial automation, healthcare, and smart cities. A wireless sensor network is composed of a large number of wireless sensor nodes with communication, computing, and storage capabilities, which are randomly deployed in the monitoring area and form a multi-hop self-organizing network system through wireless communication. Its purpose is to collaboratively sense, collect, and process information in the network area, and transmit the corresponding information to the observer.

[0003] However, the network life of wireless sensor networks is limited by the battery capacity of sensor nodes. Energy limitations lead to a short life of wireless sensor networks. Replacing sensor nodes when the energy is exhausted is not only a tedious task, but a large number of discarded batteries is also very harmful to the environment. In recent years, many studies have been conducted to extend the network life, which can be divided into two basic categories, namely energy saving and energy supply. The former includes cross-layer resource allocation, clustering and routing, data aggregation, sleep scheduling, and mobile data collection. Although energy saving significantly improves the network life, it cannot ensure that the network operates permanently because sensor nodes will eventually exhaust their limited battery energy and cannot continue to work. Energy supply methods such as renewable energy harvesting (REH) and wireless power transmission (WPT) can restore the energy of the batteries in sensor nodes (regularly or on demand) so that the network can operate permanently. Energy supply has led to the development of wireless recharging sensor networks (WRSN) equipped with rechargeable lithium-ion batteries and energy harvesting modules. Different from traditional wireless sensor networks, rechargeable wireless sensor networks can obtain renewable energy (wind energy, solar energy, etc.) from the surrounding environment or charge batteries through wireless chargers to achieve sustainable operation.

[0004] On the other hand, in wireless sensor networks for real-time applications, sensor nodes need to perceive the surrounding physical environment and monitor the system status in real time, so as to provide timely, fresh and effective information for intelligent decision-making and control. Unlike the information carried by traditional broadband services, most wireless sensor networks transmit short data packets carrying updated information of sensor nodes. This information may be the instantaneous acceleration and position of the vehicle, or the ambient temperature, soil moisture, and the status of the network control or decision-making system. Similar to the age of a person, after the data is generated, as time passes in one direction, the obsolescence of the data information also increases in one direction and continues to "age". In order to give users a good perception experience, the information should be used as soon as possible after it is generated to ensure that the information used is as fresh as possible. If the destination obtains outdated information, it will lead to invalid decisions and erroneous control, and even bring about systemic disasters. Traditional network performance indicators, such as throughput and latency, cannot effectively characterize the freshness of information in the system. To this end, Sanjit Kaul and Roy Yates proposed a new network performance metric, Age of Information (AoI), at the 2011 INFOCOM conference to measure the freshness of information.

[0005] As a key performance indicator, AoI is defined as the length of time it takes for a data packet to be successfully received from the time it is generated at the source to the time it is successfully received at the destination. Compared with traditional latency metrics, AoI characterizes the freshness of state information from the perspective of the destination, measures the time difference in obtaining information at the destination, and takes into account the latency and successful reception time of each data packet.

[0006] In a wireless sensor network, each time a sink node receives a new data packet, it will update its status based on the timestamp of the data packet. Outdated data packets cannot accurately describe the current status and lose their value. Therefore, ensuring the freshness of data packets is of great significance. It is extremely important to study the node working strategy of wireless sensor networks from the perspective of information freshness. Since the working state of nodes in wireless sensor networks is restricted by factors such as their channel state, transmission power, and battery energy state, the problem of information freshness has become more and more complicated. Therefore, designing a suitable node working strategy for rechargeable wireless sensor networks to ensure the instant delivery of data packets and thus reduce the average information age of the system has become an important issue that needs to be solved. Summary of the invention

[0007] The present invention provides a method for scheduling the work of a rechargeable wireless sensor network node based on information freshness, so as to reduce the average information age of the rechargeable wireless sensor network system. By scheduling each node in the wireless sensor network, it is achieved that the nodes can complete communication tasks normally and obtain a lower average information age.

[0008] The technical solution adopted by the present invention comprises the following steps:

[0009] Step 0: Before scheduling, first determine whether each node in the network is equipped with dual limited capacity rechargeable batteries. If not, proceed to step 1-1; if yes, proceed to step 2-1;

[0010] Step 1-1: Construct a wireless sensor network system model consisting of a group of K nodes and a sink node, where each node is equipped with a single finite capacity battery. The node sends the collected data packets containing time-sensitive information to the sink node. The sink node processes the received data packets and extracts the time-sensitive information. It is assumed that the node is idle in the current time slot and the node battery is not empty. The newly arrived data packet containing state information will be processed immediately and sent to the sink node. If any of the above conditions are not met when the data packet arrives, the data packet will be ignored and discarded. The data packet being served will not be preempted, and no data packet will be retained in the queue. In the system considered, the data packet containing the state update arrives at the node based on the Poisson point process of rate λ. It is assumed that the node sends the data packet to the sink node at the service rate μ. It is assumed that the node uses energy from a finite capacity battery to serve the collected data packets. The energy unit is discrete and standardized, so the service of the data packet consumes one unit of energy when it is completed. The battery capacity of the node is represented by B units;

[0011] Step 1-2: The full charging strategy can be described as: only when the energy in the node battery is exhausted, will it be replenished through energy collection or charging device, and no new data packets will be processed before the battery is fully charged. Under the full charging strategy, the network can get a smaller average AoI. In order to verify the effectiveness of the full charging strategy, the Stochastic Hybrid Systems (SHS) technology is used to analyze one of the nodes, and the expression of the node average AoI is derived as follows:

[0012]

[0013] Step 2-1:

[0014] Aiming at the problem that the battery needs a certain charging time to be fully charged in the single-battery system model, the system model is improved to construct a wireless sensor network system model consisting of a group of K nodes and a sink node, in which each node is equipped with dual batteries. In one battery cycle, battery 1 is used as a charging battery to collect energy, and battery 2 is used as a power supply battery to provide energy for the node to send data packets. The two batteries are alternated in the next battery cycle. The sink node is interested in time-sensitive information from nodes that measure physical phenomena. Each node transmits time-sensitive information to the sink node in the form of an updated status data packet. Each status data packet contains the measurement value of the monitored process and a timestamp indicating the generation time. It is assumed that the node will decide whether to send a data packet or switch batteries at the beginning of each time slot t based on the current state.

[0015] Assume that each node is equipped with two batteries with the same capacity, both B max , the energy in the ith battery of node k at time slot t is denoted as B k,i (t), i = {1, 2}, the total energy in node k is expressed as B k (t), satisfying:

[0016]

[0017] Assume that k,i (t), i∈{1,2} represents the battery allocation of node k in time slot t. k,i (t)∈{0,1}, if ρ k,i (t) = 1, which means that battery i is used as a power supply battery to provide energy for the node to send data packets in time slot t; otherwise, it means that battery i is used as a rechargeable battery to replenish energy in time slot t. In each time slot, only one battery is powered. Therefore:

[0018]

[0019] Assumptions k (t) represents the transmission action of node k in time slot t, that is, indicates that the node sends a data packet containing time-sensitive information to the sink node, and Indicates that the node does not send a data packet in the current time slot, assuming that the sampling time (i.e., the time required to obtain the data packet) is negligible;

[0020] Node k will decide to send a packet at the beginning of time slot t only if the node has enough energy to ensure that the packet can be successfully transmitted in time slot t. Therefore, if node k sends a packet in time slot t (i.e., s k (t) = 1), the data packet will be successfully transmitted during time slot t. To this end, the following constraints are used:

[0021]

[0022] where β represents the size of the state packet in bits. This constraint ensures that when node k sends a packet at the beginning of time slot t (i.e., s k (t) = 1), the achievable rate of node k in time slot t is r k (t) = β, which can ensure that the data packet is transmitted during time slot t.

[0023] Assume that the node adopts the Harvest-Store-Use (HSU) strategy, which means that the node can only use the energy in the power supply battery. The energy collected in the current time slot is stored in the rechargeable battery and can only be used in the subsequent time slot. The energy change in the node can be expressed as:

[0024]

[0025] in, represents the energy collected by the rechargeable battery of node k in time slot t, represents the energy consumed by the battery of node k at time slot t (if a data packet is sent at time slot t).

[0026] In order to ensure that the node has enough energy to send the status data packet in time, a long-term average battery energy constraint within time T is defined to avoid the situation where the node collects fresh status data packets but cannot transmit them to the sink node due to insufficient energy. This constraint can be written as:

[0027]

[0028] Where δ is the defined battery energy threshold.

[0029] The time between the latest data packet successfully received by the sink node in the network and the last time the data packet was successfully received is taken as the information age, the information age function is constructed, and the average information age is calculated; the information age function of the node can be expressed as: △ = tu(t), t refers to the current time slot, u(t) is the timestamp of the latest data packet received by the sink node before time slot t. When the sink node successfully receives the data packet of sensor node k in time slot t, the information age of the new data packet generated by sensor node k at the beginning of time slot t+1 is 1. On the contrary, if the data packet of node k is not successfully received, the information age of the data packet on node k increases by 1. At time slot t+1, the information age of the data packet on sensor node k can be expressed as:

[0030]

[0031] Therefore, the average information age of node k at time T is:

[0032]

[0033] For ease of handling, we simplify it by using the expected time mean of the information age:

[0034]

[0035] Step 2-2:

[0036] Based on the goal of minimizing the total average information age, the transmission actions of nodes in each time slot are jointly optimized under the node battery energy constraint. k (t)} k∈K , battery distribution {ρ k,i (t)} k∈K,i∈{1,2} To establish an optimization problem, the optimization problem is formulated as:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] Among them, inequality C1 is the battery energy constraint; inequality C2 limits the node energy to not exceed the maximum battery capacity; C3 limits the energy consumed by the node to send a data packet in a time slot to not exceed the available energy of the node's battery in the current time slot; C4 is the feasible value of the node battery allocation; C5 limits that only one battery is powered in each time slot; C6 is the feasible value of the node transmission action.

[0045] Step 2-3:

[0046] Since the objective function and constraints of the optimization problem involve long-term averages and are difficult to solve, the virtual queue plus penalty drift method in Lyapunov optimization theory is used to solve this problem. According to the drift additive method, the battery energy constraint C1 is implemented by converting it into a queue stability constraint. For each inequality constraint C1, virtual queues are associated in such a way that the stability of these virtual queues implies the feasibility of the battery energy constraint C1.

[0047] make represents the virtual queue associated with the battery energy constraint C1. The virtual queue is updated in each time slot as:

[0048]

[0049] The concept of strong stability is used here. If the following conditions are met, the virtual queue is strongly stable:

[0050]

[0051] Strong stability of the virtual queue means that the battery energy constraint C1 is satisfied.

[0052] The Lyapunov function is defined as:

[0053]

[0054] The Lyapunov function measures network congestion: if the Lyapunov function is small, then all queues are small, and if the Lyapunov function is large, then at least one queue is large. Therefore, by minimizing the expected change in the Lyapunov function from one time slot to the next, the queues It can be stable.

[0055] Lyapunov drift is defined as the expected change of the Lyapunov function over a time slot and is expressed as:

[0056]

[0057] According to the drift plus penalty minimization method, a scheduling strategy that minimizes the objective function with constraints C1-C6 is obtained by solving the following problem:

[0058]

[0059] stC1-C6

[0060] Among them, the parameter V ≥ 0 is used to adjust the emphasis on the objective function (i.e., the total average AoI). By changing the value of V, an ideal trade-off can be obtained between the size of the queue backlog and the objective function value.

[0061] Due to the existence of max{·} function in the virtual queue evolution, Lyapunov drift It becomes difficult to solve. Therefore, following the standard procedure of the drift plus penalty method, an upper bound on the drift part is provided, which is easy to use in the optimization process, and the penalty part (i.e., the original objective function) remains unchanged. It should be pointed out that when the upper bound is used to replace the Lyapunov drift, we can get:

[0062] (1) By minimizing the upper bound of Lyapunov drift, the above logic of stabilizing the virtual queue still holds;

[0063] (2) The asymptotic optimality (V→∞) of the proposed dynamic scheduling algorithm remains unchanged.

[0064] Replacing the Lyapunov drift part with the upper bound, the objective function can be rewritten as:

[0065]

[0066] in, In all time slots are all constants. In a specific time slot is fixed. Ignoring irrelevant terms, the optimization problem can be approximated as:

[0067]

[0068] stC2-C6(18b)

[0069] Step 2-4: By solving the optimal solution of the approximate optimization problem in each time slot, a node scheduling algorithm based on Lyapunov optimization is obtained. In the node scheduling algorithm, whether the node sends a data packet at the beginning of the time slot depends on whether the energy required to send the current data packet is less than the energy stored in the node. If the required energy is less than the energy in the current node power supply battery, the node sends the data packet to the aggregation node; if the required energy is greater than the energy in the current power supply battery, but the rechargeable battery has sufficient energy, the node needs to switch the battery first and then send the data packet to the aggregation node; if the required energy is greater than the energy stored in the current node, the currently arriving data packet will be discarded.

[0070] Step 3: Under the above node work scheduling method, the system can obtain a lower average information age.

[0071] The beneficial effects of the present invention are:

[0072] In many emerging wireless communication technology applications, it is urgent to ensure the timeliness and freshness of sensor data collection. Rechargeable wireless sensor networks can work completely on captured energy, which greatly broadens their application areas. Due to the mutual coupling between the charging process and the communication process of sensor nodes, their working state is restricted by multiple factors such as channel state, transmission power and battery energy state. The present invention uses information age as a metric to evaluate the timeliness of state information update, and proposes a full charging strategy for wireless sensor networks with nodes equipped with a single limited capacity rechargeable battery; for wireless sensor network systems with nodes equipped with dual limited capacity rechargeable batteries, a node work scheduling algorithm is proposed by introducing Lyapunov optimization theory to minimize the total average information age. Due to the instability and random fluctuations of energy acquisition from the environment and the random fading of the wireless channel, it is necessary to dynamically control the working state of the node to efficiently utilize the collected energy and channel resources. The node full charging strategy and node work scheduling algorithm proposed in the present invention solve this problem. The present invention has broad application prospects in many fields, such as being applicable to the periodic collection and real-time monitoring of node perception information within the communication radius, and combined with the communication protocol, partial avoidance of communication conflicts can be achieved. In addition, the use of extremely low-power wireless rechargeable nodes in human neurology research can achieve low-power detection of neural signals. Since the nodes in the rechargeable wireless sensor network do not need a battery power module, they can be permanently embedded in the monitoring structure to collect data on the temperature, movement, stress, etc. of the structure. In terms of human movement, the sensors configured in the rechargeable wireless sensor network nodes have extremely low power consumption, which can facilitate the real-time collection of movement status information, and also have broad application prospects in occasions such as movement recognition and daily activity monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a specific flow chart of the work scheduling method of the rechargeable wireless sensor network node based on information freshness proposed by the present invention;

[0074] Figure 2 It is a schematic diagram of the system model of the single battery part of the node work scheduling method proposed by the present invention;

[0075] Figure 3 is the SHS discrete state Markov chain diagram of Example 1;

[0076] Figure 4 It is a comparison diagram of information age between the full charging strategy and other charging strategies in a single battery system in the node work scheduling method proposed by the present invention under different system parameters;

[0077] Figure 5 It is a schematic diagram of the system model of the dual-battery part of the node work scheduling method proposed by the present invention;

[0078] Figure 6 It is a comparison diagram of the total system information age of the node scheduling algorithm in the dual-battery system in the node work scheduling method proposed in the present invention and the single-battery system at different V values;

[0079] Figure 7 It is a comparison diagram of the total information age of the system of the node scheduling algorithm in the dual battery system in the node work scheduling method proposed in the present invention under different battery energy thresholds δ. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0081] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0082] The specific process of the rechargeable wireless sensor network node work scheduling method based on information freshness proposed in the present invention is shown in Figure 1 .

[0083] Embodiment 1:

[0084] A rechargeable wireless sensor network system model is constructed, which consists of a group of K nodes and a sink node, where each node is equipped with a single limited capacity battery, such as Figure 2 shown.

[0085] This example analyzes the average AoI of one of the nodes. In the system under consideration, packets containing status updates arrive at the node based on a Poisson point process with rate λ. It is assumed that the node sends packets to the sink node at a service rate μ. It is assumed that the node uses the energy of a finite capacity battery to serve the collected packets. The energy unit is discrete and standardized, so the service of the packet consumes one unit of energy when completed. The battery capacity of the node is represented by B units. The packet containing the status update will be processed immediately if and only if the node is idle in the current time slot and the node battery is not empty. If any of the above conditions are not met when the packet arrives at the node, the packet will be ignored and discarded. The packets in service will not be preempted, and no packets will be retained in the queue. The random processes related to the generation and service time of the packets are assumed to be independent.

[0086] The full charging strategy can be described as follows: only when the energy in the battery is exhausted after the node processes the current data packet, will it replenish energy through energy harvesting or through a charging device at a charging rate η, and will not process new data packets until the battery is fully charged.

[0087] The SHS method is used to calculate the average AoI under the full charging strategy, which is expressed as a function of several system parameters, including the packet arrival rate λ, the service rate μ, the battery charging rate η, and the node battery capacity B. For the system, the discrete state is represented by q(t)∈Q={0,1,...,2B}, the state index is q(t), and each state is associated with a tuple (i,j), where i∈{1,0} represents the number of energy units in the node battery and j∈{0,1} represents the number of packets being processed. The continuous state is given by x(t)=[x0(t)x1(t)], where x0(t) represents the size of the AoI of the sink node, and its value should be △(t); x1(t) represents how much the AoI of the sink node will become after successfully receiving a data packet. The Markov chain of the discrete state q(t) is as follows Figure 3 The corresponding SHS transformation is shown in Table 1.

[0088] Table 1 The corresponding Markov chain state transition table, 1≤m≤B-1

[0089]

[0090] In SHS, a state transition corresponds to a change in the discrete state q(t) and produces a jump in the continuous state x(t). Assume a binary matrix A l Define the discrete state transition l in x(t), x'=xA l . The transformation l is interpreted as follows:

[0091] l = 0: The data packet arrives at the node at a rate of λ. Since the data packet has not yet arrived at the sink node, the AoI of the sink node is not affected, so x'0 = x0. The data packet arriving at this time is fresh, and its information age is 0. Therefore, x'1 = 0. l = 2m is similar to l = 0.

[0092] l = 1: packets are processed at the node at a rate μ and sent to the sink node. Obviously, due to this state transition, the AoI at the sink node is reset to the age of the packet just processed. Therefore, x'0 = x1. Since the packet at the node has been sent to the sink node, the node is empty at this time, so x'1 = 0. l = 2m + 1 is similar to l = 1.

[0093] l = 2B: The battery is charged at a rate of η. Since battery charging does not affect the AoI at the sink node, x'0 = x0. In addition, since there is no data packet at the node at this time, x'1 = 0.

[0094] The evolution of the continuous state x(t) depends on the discrete state q(t). Specifically, when q(t) = q, we have:

[0095]

[0096] That is, in all discrete states, x0(t) increases at unit rate with time t. However, only in the state In the example, x1(t) increases at a unit rate because there are packets at the node.

[0097] A basic assumption in using SHS to analyze AoI is that the Markov chain q(t) is ergodic, otherwise the average AoI analysis is meaningless. Under this assumption, the state probability vector π(t) = [π0(t),…,π n (t)] always uniquely converges to

[0098] The equilibrium equation is:

[0099]

[0100]

[0101] Therefore, substituting the parameters in Table 1 into the equilibrium equations (20) and (21), we have:

[0102]

[0103]

[0104]

[0105] If the discrete-state Markov chain q(t) is stationary and ergodic, there must be a nonnegative solution So that:

[0106]

[0107] Therefore, the calculated result Substituting equation (19) into equation (23), we have:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] In the SHS method, the expression of average AoI is:

[0114]

[0115] Substituting (24a)-(24e) into formula (25), we can obtain the average AoI of nodes under the full charging strategy:

[0116]

[0117] In order to measure the technical effect of the full charging strategy of the present invention, MATLAB software was used to perform simulation analysis under several sets of different system parameters, and the method was compared with other charging strategies (reference Abd-Elmagid, MA, Dhillon, HS: Closed-form characterization of the MGF of AoI in energy harvesting status update systems. IEEE Transactions on Information Theory 68(6), 3896–3919(2022)) to evaluate the effectiveness of the method.

[0118] like Figure 4As shown in the figure, the curve marked with a circle corresponds to the average AoI under the full charging strategy, while the curve marked with a star corresponds to the average AoI under other charging strategies. When η is small, the average AoI under the full charging strategy is significantly smaller than the average AoI under other charging strategies. When η increases, the average AoI under the two charging strategies gradually approach, but the average AoI under the full charging strategy is still smaller. The simulation results can be explained as follows: under the full charging strategy, the node makes more full use of the battery, so a smaller average AoI can be obtained. The results show that the choice of charging strategy is the key to reducing the average AoI, and the full charging strategy is the best strategy to reduce the average AoI when the node is equipped with a single battery with limited capacity.

[0119] Embodiment 2:

[0120] This embodiment considers a wireless sensor network consisting of a group of K nodes and a receiver, such as Figure 5 Each node is equipped with dual batteries, that is, in one battery cycle, battery 1 collects energy for charging, and battery 2 provides energy for the node to send updates, and the two are alternated in the next battery cycle.

[0121] The sink node is interested in time-sensitive information from nodes that measure physical phenomena. Each node transmits time-sensitive information to the sink node in the form of a status packet, each of which contains the measurement value of the monitored process and a timestamp indicating the time of generation. It is assumed that the node decides whether to send a packet or switch batteries at the beginning of each time slot t based on the current state;

[0122] In the node scheduling algorithm, whether the node sends a data packet at the beginning of the time slot depends on whether the energy required to send the current data packet is less than the energy stored in the node. If the required energy is less than the energy in the current node power supply battery, the node sends the data packet to the aggregation node; if the required energy is greater than the energy in the current power supply battery, but the rechargeable battery has sufficient energy, the node needs to switch batteries first and then send the data packet to the aggregation node; if the required energy is greater than the energy stored in the current node, the currently arriving data packet will be discarded.

[0123] Assume that each node is equipped with two batteries with the same capacity, both B max The energy in the ith battery of node k at time slot t is denoted as B k,i (t), i = {1, 2}, the total energy in node k is expressed as B k (t), satisfying:

[0124]

[0125] Assume that k,i(t), i∈{1,2} represents the battery allocation of node k in time slot t. k,i (t)∈{0,1}, if ρ k,i (t) = 1, which means that battery i is used as a power supply battery to provide energy for the node to send data packets in time slot t; otherwise, it means that battery i is used as a rechargeable battery to replenish energy in time slot t. There is only one battery in each time slot, so:

[0126]

[0127] Assumptions k (t) represents the transmission action of node k in time slot t, that is, indicates that the node sends a data packet containing time-sensitive information to the sink node, and Indicates that the node does not send a data packet in the current time slot. Assume that the sampling time (i.e., the time required to obtain a data packet) is negligible.

[0128] Node k will decide to send a packet at the beginning of time slot t only if the node has enough energy to ensure that the packet can be successfully transmitted in time slot t. Therefore, if node k sends a packet in time slot t (i.e., s k (t) = 1), the data packet will be successfully transmitted during time slot t. To this end, the following constraints are used:

[0129]

[0130] where β represents the size of the state packet in bits. This constraint ensures that when node k sends a packet at the beginning of time slot t (i.e., s k (t) = 1), the achievable rate of node k in time slot t is r k (t) = β, which can ensure that the data packet is transmitted during time slot t.

[0131] Assume that the node adopts the Harvest-Store-Use (HSU) strategy, which means that the node can only use the energy in the power supply battery. The energy collected in the current time slot is stored in the rechargeable battery and can only be used in the subsequent time slot. The energy change in the node can be expressed as:

[0132]

[0133] in, represents the energy collected by the rechargeable battery of node k in time slot t, represents the energy consumed by the battery of node k at time slot t (if a data packet is sent at time slot t).

[0134] In order to ensure that the node has enough energy to send the status data packet in time, a long-term average battery energy constraint is defined to avoid the situation where the node collects fresh status data packets but cannot transmit them to the sink node due to insufficient energy. The constraint can be written as:

[0135]

[0136] Where δ is the defined battery energy threshold.

[0137] The time between the latest data packet successfully received by the sink node in the network and the last time the data packet was successfully received is taken as the information age, the information age function is constructed, and the average information age is calculated. The information age function of the node can be expressed as: △ = tu(t), t refers to the current time slot, u(t) is the timestamp of the latest data packet received by the sink node before time slot t. When the sink node successfully receives the data packet of sensor node k in time slot t, the information age of the new data packet generated by sensor node k at the beginning of time slot t+1 is 1. On the contrary, if the data packet of node k is not successfully received, the information age of the data packet on node k increases by 1. At time slot t+1, the information age of the data packet on sensor node k can be expressed as:

[0138]

[0139] Therefore, the average information age of node k at time T is:

[0140]

[0141] For ease of handling, we simplify it by using the expected time mean of the information age:

[0142]

[0143] With the goal of minimizing the average information age, the transmission actions of nodes in each time slot are jointly optimized under the node battery energy constraint. k (t)} k∈K , battery distribution {ρ k,i (t)} k∈K,i∈{1,2} To establish an optimization problem, the optimization problem is formulated as:

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] Among them, inequality C1 is the battery energy constraint; inequality C2 limits the node energy to not exceed the maximum battery capacity; C3 limits the energy consumed by the node to send a data packet in a time slot to not exceed the available energy of the node's battery in the current time slot; C4 is the feasible value of the node battery allocation; C5 limits that only one battery is powered in each time slot; C6 is the feasible value of the node transmission action.

[0152] Since the objective function and constraints of the optimization problem involve long-term averages and are difficult to solve, the virtual queue plus penalty drift method in Lyapunov optimization theory is used to solve this problem. According to the drift additive method, the battery energy constraint C1 is implemented by converting it into a queue stability constraint. For each inequality constraint C1, virtual queues are associated in such a way that the stability of these virtual queues implies the feasibility of the battery energy constraint C1.

[0153] make represents the virtual queue associated with the battery energy constraint C1. The virtual queue is updated in each time slot as:

[0154]

[0155] The concept of strong stability is used here. If the following conditions are met, the virtual queue is strongly stable:

[0156]

[0157] Strong stability of the virtual queue means that the battery energy constraint C1 is satisfied.

[0158] The Lyapunov function is defined as:

[0159]

[0160] The Lyapunov function measures network congestion: if the Lyapunov function is small, then all queues are small, and if the Lyapunov function is large, then at least one queue is large. Therefore, by minimizing the expected change in the Lyapunov function from one time slot to the next, the queues Can be stable.

[0161] Lyapunov drift is defined as the expected change of the Lyapunov function over a time slot and can be expressed as:

[0162]

[0163] According to the drift plus penalty minimization method, a scheduling strategy that minimizes the objective function with constraints C1-C6 is obtained by solving the following problem:

[0164]

[0165] stC1-C6

[0166] Among them, the parameter V ≥ 0 is used to adjust the emphasis on the objective function (i.e., the total average AoI). Therefore, by changing the value of V, an ideal trade-off can be obtained between the size of the queue backlog and the objective function value.

[0167] Due to the existence of max{·} function in the virtual queue evolution, Lyapunov drift It becomes difficult to solve. Therefore, following the standard procedure of the drift plus penalty method, an upper bound on the drift part is provided, which is easy to use in the optimization process, and the penalty part (i.e., the original objective function) remains unchanged. It should be pointed out that when the upper bound is used to replace the Lyapunov drift, we can get:

[0168] (1) By minimizing the upper bound of Lyapunov drift, the above logic of stabilizing the virtual queue still holds;

[0169] (2) The asymptotic optimality (V→∞) of the proposed dynamic scheduling algorithm remains unchanged.

[0170] In order to obtain the Lyapunov drift The upper bound of , using the following inequality, for any λ≥0,σ≥0,ψ≥0, is:

[0171] (max[λ-σ+ψ,0]) 2 ≤λ 2 +σ 2 +ψ 2 +2λ(ψ-σ) (15)

[0172] According to the above inequality and the update formula of the virtual queue, The upper bounds of are:

[0173]

[0174] The objective function can be rewritten as:

[0175]

[0176] in, In all time slots are all constants. In a specific time slot is fixed. Ignoring irrelevant terms, the optimization problem can be approximated as:

[0177]

[0178] stC2-C6(18b)

[0179] By solving the optimal solution of the approximated optimization problem in each time slot, the node scheduling algorithm based on Lyapunov optimization is obtained. Table 2 gives the pseudo code of the node scheduling algorithm.

[0180] Table 2 Pseudocode of the node scheduling algorithm based on Lyapunov optimization Algorithm Node scheduling algorithm

[0181]

[0182] In order to measure the technical effect of the system of the present invention equipped with dual batteries at the node, a simulation analysis was performed using MATLAB software assuming that the number of nodes K = 10. Figure 7 As shown. It can be seen that with the increase of V value, the total average AoI of the dual-battery system decreases, because the V value represents the importance of the objective function (i.e., AoI minimization). And by comparing the total average AoI of the multi-node single-battery system with the dual-battery system, it is also verified that the dual-battery system is superior to the single-battery system in reducing the system average AoI.

[0183] Figure 7 The total average AoI of the dual-battery system under different node energy thresholds is given. The simulation results show that as the energy threshold δ decreases, the total average AoI of the system will also decrease, because a decrease in the energy threshold means that the battery is more fully utilized.

[0184] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0185] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for scheduling work of rechargeable wireless sensor network nodes based on information freshness, characterized in that: The following steps are included: Step 0: Before scheduling, first determine whether each node in the network is equipped with dual limited capacity rechargeable batteries. If not, start step 1-1; if yes, start step 2-1; Step 1-1: Construct a wireless sensor network system model consisting of a group of K nodes and a sink node, where each node is equipped with a single finite capacity battery. The node sends the collected data packets containing time-sensitive information to the sink node. The sink node processes the received data packets and extracts the time-sensitive information. It is assumed that the node is idle in the current time slot and the node battery is not empty. The newly arrived data packet containing state information will be immediately processed and sent to the sink node. If any of the above conditions are not met when the data packet arrives, the data packet will be ignored and discarded. The data packet being served will not be preempted, and no data packet will be retained in the queue. In the system considered, the data packet containing the state update arrives at the node based on the Poisson point process of rate λ. It is assumed that the node sends the data packet to the sink node at the service rate μ. It is assumed that the node uses energy from a finite capacity battery to serve the collected data packets. The energy unit is discrete and standardized, so the service of the data packet consumes one unit of energy when it is completed. The battery capacity of the node is represented by B units; Step 1-2: Full charging strategy: Only when the energy of the node battery is exhausted, it will be replenished by energy collection or by a charging device at a charging rate η, and no new data packets will be processed before the battery is fully charged. An analysis is carried out on one of the nodes, and the expression of the node average AoI is derived as follows: Step 2-1: Construct a wireless sensor network system model consisting of a group of K nodes and a sink node, where each node is equipped with dual batteries; take the time between the time when the latest data packet is received by the sink node and the time when the previous data packet is successfully received as the information age, construct the information age function, and calculate the average information age of the system; Step 2-2: Based on the goal of minimizing the average information age, under the node battery energy constraint, the communication transmission actions {s k (t)} k∈K and battery allocation {ρ k,i (t)} k∈K,i∈{1,2} To set up an optimization problem, s k (t) represents the transmission action of node k in time slot t, ρ k,i (t) represents the battery allocation of node k in time slot t; Step 2-3: Construct Lyapunov drift plus penalty function and transform the optimization problem; Step 2-4: Solve the optimal solution of each time slot optimization problem to obtain a node scheduling algorithm based on Lyapunov optimization; Step 3: Under the above node work scheduling method, the system can obtain a lower average information age.

2. According to claim 1, a method for scheduling work of a rechargeable wireless sensor network node based on information freshness is characterized in that: In step 1-2, for a node in the system, the random hybrid system (SHS) technology is used to analyze the average information age of the node under the full charging strategy in the single battery model.

3. The method for scheduling work of a rechargeable wireless sensor network node based on information freshness according to claim 1, characterized in that: In the node equipped with dual batteries in step 2-1, the rate at which the battery collects energy is a finite value, and it takes a certain amount of time for the battery to be fully charged. In the previous battery cycle, node battery 1 collects energy as a rechargeable battery, and node battery 2 provides energy to the node as a power supply battery to send data packets. In the next battery cycle, the two are alternating. The dual-battery model can well solve the problem of timely replenishment of node battery energy, thereby further reducing the average information age. The sink node is interested in time-sensitive information from nodes that measure physical phenomena. Each node transmits time-sensitive information to the sink node in the form of an updated status data packet. Each status data packet contains the measurement value of the monitored process and a timestamp indicating the generation time. It is assumed that the node will decide whether to send a data packet or switch batteries at the beginning of each time slot t based on the current state. Assume that each node is equipped with two batteries with the same capacity, both B max , the energy in the ith battery of node k at time slot t is denoted as B k,i (t), i = {1, 2}, the total energy in node k is expressed as B k (t), satisfying: Assume that k,i (t), i∈{1,2} represents the battery allocation of node k in time slot t, ρ k,i (t)∈{0,1}, if ρ k,i (t) = 1, which means that battery i is used as a power supply battery to provide energy for the node to send data packets in time slot t; otherwise, it means that battery i is used as a rechargeable battery to replenish energy in time slot t. In each time slot, only one battery is powered. Therefore: Assumptions k (t) represents the transmission action of node k in time slot t, that is, indicates that the node sends a data packet containing time-sensitive information to the sink node, and Indicates that the node does not send a data packet in the current time slot, assuming that the sampling time (i.e., the time required to obtain the data packet) is negligible; Node k will decide to send a packet at the beginning of time slot t only if the node has enough energy to ensure that the packet can be successfully transmitted in time slot t. Therefore, if node k sends a packet in time slot t (i.e., s k (t) = 1), the data packet can be successfully transmitted during time slot t. To this end, the following constraints are used: Where β represents the size of the state packet in bits. This constraint ensures that when node k sends a packet at the beginning of time slot t, i.e., s k (t) = 1, the achievable rate of node k in time slot t is r k (t) = β, which can ensure that the data packet is transmitted during time slot t; Assuming that the node adopts the collect-store-use HSU strategy, which means that the node can only use the energy in the power supply battery, the energy collected in the current time slot is stored in the rechargeable battery and can only be used in the subsequent time slots. The energy change in the node can be expressed as: in, represents the energy collected by the rechargeable battery of node k in time slot t, represents the energy consumed by the battery of node k in time slot t if a data packet is sent in time slot t; In order to ensure that the node has enough energy to send the status data packet in time, a long-term average battery energy constraint within time T is defined to avoid the situation where the node collects fresh status data packets but cannot transmit them to the sink node due to insufficient energy. This constraint can be written as: Where δ is the defined battery energy threshold; The time between the latest data packet successfully received by the sink node in the network and the last time the data packet was successfully received is taken as the information age, the information age function is constructed, and the average information age is calculated; the information age function of the node can be expressed as: △ = tu(t), t refers to the current time slot, u(t) is the timestamp of the latest data packet received by the sink node before time slot t, when the sink node successfully receives the data packet of sensor node k in time slot t, then the information age of the new data packet generated by sensor node k at the beginning of time slot t+1 is 1, on the contrary, if the data packet of node k is not successfully received, the information age of the data packet on node k increases by 1, and at time slot t+1, the information age of the data packet on sensor node k can be expressed as: Therefore, the average information age of node k at time T is: For ease of handling, we simplify it by using the expected time mean of the information age:

4. According to claim 1, a method for scheduling work of a rechargeable wireless sensor network node based on information freshness is characterized in that: In step 2-2, the optimization problem is formulated as: Among them, inequality C1 is the battery energy constraint; inequality C2 limits the node energy to not exceed the maximum battery capacity; C3 limits the energy consumed by the node to send a data packet in a time slot to not exceed the available energy of the node's battery in the current time slot; C4 is the feasible value of the node battery allocation; C5 limits that only one battery is powered in each time slot; C6 is the feasible value of the node transmission action.

5. The method for scheduling work of a rechargeable wireless sensor network node based on information freshness according to claim 4 is characterized in that: In step 2-3, the battery energy constraint C1 is implemented by converting it into a queue stability constraint according to the drift additive method, and for each inequality constraint C1, the virtual queues are associated in such a way that the stability of these virtual queues implies the feasibility of the battery energy constraint C1; make represents the virtual queue associated with the battery energy constraint C1, which is updated in each time slot as: The concept of strong stability is used here. If the following conditions are met, the virtual queue is strongly stable: Strong stability of the virtual queue means satisfying the battery energy constraint C1; The Lyapunov function is defined as: The Lyapunov function measures network congestion: if the Lyapunov function is small, then all queues are small, and if the Lyapunov function is large, then at least one queue is large, so by minimizing the expected change in the Lyapunov function from one time slot to the next, the queues It can be stable; Lyapunov drift is defined as the expected change of the Lyapunov function over a time slot and is expressed as: According to the drift plus penalty minimization method, a scheduling strategy that minimizes the objective function with constraints C1-C6 is obtained by solving the following problem: stC1-C6 The parameter V ≥ 0 is used to adjust the emphasis on the objective function, that is, the total average AoI. By changing the value of V, an ideal trade-off can be obtained between the size of the queue backlog and the objective function value. Due to the existence of max{·} function in the virtual queue evolution, Lyapunov drift It becomes difficult to solve, so we follow the standard procedure of the drift plus penalty method to provide an upper bound on the drift part that is easy to use in the optimization process. The penalty part, that is, the original objective function, remains unchanged. It should be pointed out that when the upper bound is used to replace the Lyapunov drift, we can get: (1) By minimizing the upper bound of Lyapunov drift, the logic of stabilizing the virtual queue still holds; (2) The asymptotic optimality V→∞ of the proposed dynamic scheduling algorithm remains unchanged. Replacing the Lyapunov drift part with the upper bound, the objective function can be rewritten as: in, In all time slots are constants, In a specific time slot is fixed, and irrelevant items are ignored. The optimization problem can be approximated as: stC2-C6.

6. The method for scheduling work of a rechargeable wireless sensor network node based on information freshness according to claim 1, characterized in that: In the node scheduling algorithm in steps 2-4, whether the node sends a data packet at the beginning of the time slot depends on whether the energy required to send the current data packet is less than the energy stored in the node. If the required energy is less than the energy in the current node power supply battery, the node sends the data packet to the aggregation node; if the required energy is greater than the energy in the current power supply battery, but the rechargeable battery has sufficient energy, the node needs to switch batteries first and then send the data packet to the aggregation node; if the required energy is greater than the energy stored in the current node, the currently arriving data packet will be discarded.

Images