We consider a wireless sensor network (BSS), which provides data exchange between sensor devices (SU) with autonomous power, randomly distributed in three-dimensional space of agricultural land. It is shown that the lack of centralized power supply for the sensor device poses speci c challenges for developers of wireless sensor networks related to the need to increase the operating time of sensor devices without replacing or recharging the battery and to reduce the power consumption of each sensor device and (or) all network devices in total. In this regard, there is an urgent task of assessing the probability-energy characteristics of wireless sensor networks and each individual device. An analysis is made of the features of the energy consumption process of wireless sensor networks in agricultural applications, indicators are selected to evaluate the energy consumption characteristics, and models and methods for evaluating the characteristics of sensor devices are proposed that take into account the spatial, temporal and energy characteristics of the sensor network, such as the geometric size and density of the sensor eld , frequency range of interaction, strategy for selecting a relaying touch device when forming Vania message transmission route to the base station.Are given are given of the dependence of the probabilistic-energetic characteristics of sensor devices on the listed parameters. The presented models and methods can be used to solve a wide range of problems arising in the development of protocols for the operation of wireless sensor networks.
Among the information systems of the third platform of information, providing a
transition to a digital economy, is the Internet of things.By de nition, [
One of the most important subject areas of the Internet of things is agriculture, the digital transformation of which involves the creation of platform solutions aimed at: { intellectual management of agricultural land; { work with data on the state of soils, plants and ecosystems; { collection of data on garden agribusinesses; { closed farm management; { use in livestock complexes, etc.
The implementation of any of these digital platforms involves the use of a large number of sensor devices that must be distributed in the space of agricultural land, measure the physical characteristics of agricultural environments, form sensor networks and transmit the collected information in real time to data processing and storage centers for complex analysis and adoption management decisions.
The systemic properties of the Internet of things depend mainly on the properties of wireless sensor networks, which, using identi cation technologies, sensors, wireless communications and autonomous power supply, provide data exchange between a large number of sensor devices, distributed and possibly moving in some space. Each of the sensor devices provides a measurement of the physical parameters of the adjacent part of the general environment and has an information image located in cloud structures. Thus, collectively, sensor devices allow the formation of dynamically changing big data on the state of various macro objects, an example of which with regard to agriculture can be a eld, greenhouse, farm or garden.
The recommendations [
The lack of centralized power supply to the terminals poses speci c challenges for developers of wireless sensor networks related to the need to increase the operating time of sensor devices without replacing or recharging the battery, and for this to reduce the power consumption of each sensor device and (or) all network devices in total.
The energy consumer in the sensor device is a group of sensors, a data
processing subsystem, a communication subsystem and a radio transmitter [
In this regard, there is an urgent task of assessing the probability-energy characteristics of wireless sensor networks and each individual device. Such assessments are necessary for making decisions in the process of network selforganization in accordance with the changing external and internal functioning conditions.
The purpose of this study is to develop models for assessing the probabilistic and energetic characteristics of sensor devices in the three-dimensional space of agricultural land, which take into account the complex in uence on the energy consumption of spatial and probabilistic-temporal characteristics of wireless sensor networks, as well as algorithms for selecting relay sensors in the formation of message transmission routes to the base station.
To achieve this goal, the following tasks were solved: { analysis of the features of the energy consumption process of wireless sensor networks in agricultural applications; { selection of indicators for assessing the energy consumption characteristics of sensor devices in three-dimensional space and the development of models for evaluating these indicators; { numerical analysis of energy consumption of wireless sensor networks. 2
An integral component of the IT infrastructure of the digital economy are wired
and wireless communication networks [
Time characteristics set a measure for comparing the sequence and frequency (speed) of events that change the state of data in the process of information exchange between network elements. These include the intensities of the occurrence of certain events, the load serviced by certain network elements, the times of data distribution through communication channels, waiting times for the start of service, and other random variables.
Energy characteristics, in turn, set a measure for assessing the e orts that must be made to ensure the movement of information objects, such as messages, signal bits or data blocks, in space and time in the process of information exchange. An example of such characteristics are: { the amount of energy consumed per one data block or unit of information services; { the amount of carbon emissions in terms of one server or group of users; { the ratio of energy consumption of information equipment and engineering systems that support its work; { power consumption per 1 square. m. area of technical premises; { transaction value in kilowatt hours or carbon emissions, etc.
Wired and wireless networks di er from each other in terms of the need for spatial, temporal and energy resources and, accordingly, the target indicators for their use. The development goal of wired communication networks are: { in the eld of spatial characteristics - an increase in the number of users by increasing the coverage area of hierarchically organized and stationary stations and network nodes; { in the eld of temporal characteristics - an increase in network bandwidth and processing speeds of service data (metadata) to reduce delays and blockages in the transmission of messages; { in the eld of energy characteristics - ensuring uninterrupted power supply due to redundancy of power supply systems and energy storage directly in stations and nodes of communication networks.
Unlike wired networks, the need for the resources of the Internet of things is signi cantly a ected by the speci c properties of wireless sensor networks and their terminals, which include: { a wide range of geometric sizes from fractions of meters to kilometers, and the ability to scale; { autonomy of each sensor device, which has its own power and operates according to its own algorithm; { a wide variety of sensors that carry out complex measurements of the most diverse parameters of space; { the ability to self-organize in case of a random change in the number and location of interacting sensors due to their failures, transition to sleep mode, mobility, etc.; { use of radio signal transmission technologies. { a wide range of data transfer rates and acceptable response times to events, etc
These features determine the composition and target values of the characteristics of wireless networks. The main spatial characteristic is the size of the sensor eld. In contrast to the coverage area of infrastructure networks, the sensor eld can: { accommodate thousands of devices, including nanodevices requiring integrated management; { be both two-dimensional (agricultural eld), and three-dimensional (either a farm or a greenhouse).change linear dimensions, which depend on random movements of devices.
All other spatial characteristics depend on the area or volume of the sensor eld and the number of connected devices. The mathematical model of the sensor eld is a random eld of points - a collection of points that are randomly distributed in space. Field density is the average number of points per unit area (volume). Dense and superdense sensory elds are distinguished. A uniform eld is a eld whose density is a constant.
In many applications, the sensor eld can be described by the Poisson eld of points, which has the following properties: { the probability of the appearance of one or another number of points in any area of the plane (space) does not depend on how many points fell in any areas that do not intersect with this one; { the probability of falling into the elementary region of two or more points is negligible compared to the probability of a single point.
The number of points of the Poisson eld falling in any region of space having volume S is distributed according to Poisson's law:
am Pm =
e a; a = S m! where a{the expectation of the number of points in the selected area S; ,{ distribution density of sensor devices in volume.
The distance between the nearest points of the Poisson eld is a random
variable r> 0, which in volume is determined by the following distribution functions
F1(r) and probability density f1(r) [
F1(r) = 1 f1(r) = 4 e 43 r3 r2e 43 r3 r1 = where () is the gamma function.
For the distribution function Fn(r) and density fn(r) of the probability of the distance to the n-th remoteness of a point of a Poisson eld on the plane, the formulas are valid:
Fn(r) = n; 43
f1(r) = 31 ne 34 r3 r3 n 14n n n (n) (6) (7) The average distance to the n-th smart thing is calculated by the formula: rn = p333 p32 2 p3 3p
The requirements for the probabilistic-temporal characteristics of wireless networks also di er signi cantly from the requirements for wired networks. One of the main di erences is the time requirements for data delivery by wireless sensor networks, which can vary widely. If in wired networks of the NGN standard a single maximum allowable delay of 100 ms is established for data transfer between any network elements, then the requirements for delays on the Internet of things completely depend on the type of physical processes taking place in the subject area of the wireless network and recorded by sensors of sensor devices.
For example, in agricultural applications, sensors measuring soil temperature can be polled once every few days, and the permissible time for their reaction to the polling signal can be measured in seconds. Very di erent latency requirements are imposed on networks that measure animal health. Only a reduction in delay of up to 10 ms allows veterinary applications to change the traditional animal treatment model. At the same time, devices worn by animals can both monitor the course of treatment, evaluate the e ect of medications, record changes in physical indicators, the course of rehabilitation, and a ect the state of the animal with the help of special actuators.
For NGN networks, in which the timely delivery of a data packet from a
source to a receiver is the main design task, a large number of models have been
developed for assessing the probability-time characteristics and optimization
according to relevant criteria [
The fundamental di erence between sensor devices and wired network
terminals is associated with autonomous power supply. For this reason, the lifetime
of sensor networks depends on the duration of the energy sources of each device,
and energy saving is an important priority for developers of wireless networks
[
Analysis of a typical energy pro le of sensor devices, taking into account
the phases of data collection, processing, reception and transmission, and sleep,
shows the following [
Systemic methods of energy saving are focused on the rational construction
of the physical environment and algorithms for the interaction of devices with
each other and other network elements. The basis of decisions at this stage of
development should be based on the following premises [
Perhaps the in uence of errors should be reduced by increasing the level of emitted signals or correcting errors by upper-level protocols; { data compression is one of the e ective mechanisms for reducing energy consumption by smart things, due to the reduction in the number of emitted signs.
The energy consumed by sensor devices substantially depends on both spatial and temporal characteristics of sensor networks.
Spatial characteristics a ect the power consumption of sensor devices, since
increasing the distance between interacting devices requires increasing the signal
power at the transmitting antenna in accordance with the Friis formula [
Cper Cpr Where Eper, Epr is the signal power at the antennas of the transmitter and receiver, respectively [W], Cper, Cpr is the gain of transmit and receive antennas, vc is the speed of light, f is the frequency transmission range ' = vfc is the wavelength.
The Friis formula allows one to obtain estimates for the admissible distance between interacting devices: r =
' 4 pEpr
pCperCprEper You can use this formula if you know: (8) (9) { the smallest acceptable signal level at the receiving antenna, depending on the sensitivity of the radio and the level of interference; { signal level at the transmitting antenna, which determines the energy consumption of sensor devices; { the conditions for the propagation of radio signals in the amount of agricultural land, usually characterized by the absence of dense buildings.
Thus, the power spent on signal transmission directly depends on the size of the sensor eld and on the density of the devices placed in it.
Temporal characteristics a ect energy consumption through the intensity of occurrence and duration t periods of activity of devices during which certain radio signals are emitted.
The energy e spent on the transmission of one data block by a touch device can be estimated by the formula: in which the spatial characteristics determine the power value Eper, and the temporal ones determine the duration t. 3
We consider methods for assessing the characteristics of sensor networks, which are basic for solving all other problems. At the forefront is the assessment of the energy consumption of sensor devices for di erent strategies for delivering data from the sensor device to the head node of the cluster or to the base station in the volume of the sensor eld (Fig. 1).
In a eld, a garden, greenhouses, a farm, and other objects, sensors must
monitor the state of soil, air, animals, climatic parameters, and technology, recording
a huge number of various parameters [
In all cases, for the formation of a smart agricultural object, it is necessary
to organize a network of a large number of sensor devices with autonomous
power. To reduce the labor costs associated with replacing electric batteries,
energy-saving modes of operation of sensors should be provided, therefore, the
development of a model for evaluating the appropriate characteristics for the
three-dimensional space of agricultural land is relevant and of practical
importance [
The power consumption of devices and the network as a whole depends on the relay method. Geo-positioning allows you to determine the distance to each sensor device in the network.
The transmission of a data block directly to the base station without relaying is a special case of the methods considered.
Building models to estimate the average distances to all neighbors will allow you to nd the average distance to an arbitrary sensor device.
The required signal power at the transmitting antenna, assuming that the radio signal power at the receiving antenna is constant, is a random variable and depends on the distance between the interacting devices.
Therefore, the average power at the transmitter according to the Friis formula
takes the form [
Where Eper is the average power of the radio signal at the transmitting antenna [W], Epr is the constant power of the radio signal at the receiving antenna [W], Cper is the gain of the transmitting antenna, Cpr is the gain of the receiving antenna.
The total transmission time of the data block from the touch device to the
base station depends on the number of hop and is determined by the expression
[
Let us that the number of hopes in the direction of increasing to the nearest integer: e1 = The average energy spent on the transfer unit of the sensor device: The nal expression for calculating the average energy spent on transmitting a data block to the nearest object: e1 =
Figure 3 shows the dependence of energy consumption on the distribution density of sensor devices in volume.
When relaying through the nearest nodes, an increase in the number of hopes occurs, but the energy is spent on transmission less since the energy consumption is proportional to the square of the distance (Fig. 3).
The spasmodic nature of the functions in Figures 3 and 4 is due to the rounding of the found hop values to the whole.
The data in the tables represents the value of the spatial, temporal and energy characteristics, since the frequency and intensity is a temporal characteristic, and the density is a spatial characteristic. 4
Energy consumption as one of the key issues for wireless sensor networks is
analyzed in publications [
In [
In [
This study analyzes the features of the energy consumption process of wireless sensor networks in agricultural applications. The study allowed us to determine indicators for evaluating the energy consumption characteristics of sensor devices in three-dimensional space and to develop a model for evaluating these indicators.
The developed model for evaluating the characteristics of sensory devices in
the three-dimensional space of smart things di ers from the models considered
in [
A numerical analysis of the energy consumption of wireless sensor networks has been performed. A method and model for a comprehensive assessment of spatial, temporal and energy characteristics are proposed. This method allows you to see how some data depends on others