=Paper=
{{Paper
|id=Vol-2590/paper14
|storemode=property
|title=Estimation of Energy Costs for Priority Maintenance of Mobile Devices of the Ubiquitous Sensor Network
|pdfUrl=https://ceur-ws.org/Vol-2590/paper14.pdf
|volume=Vol-2590
|authors=Tatyana Astakhova,Mikhail Kolbanev,Alexey Shamin
|dblpUrl=https://dblp.org/rec/conf/micsecs/AstakhovaKS19
}}
==Estimation of Energy Costs for Priority Maintenance of Mobile Devices of the Ubiquitous Sensor Network==
https://ceur-ws.org/Vol-2590/paper14.pdf
Estimation of Energy Costs for Priority
Maintenance of Mobile Devices of the
Ubiquitous Sensor Network
Tatyana Astakhova1[0000−0002−7032−0697] , Mikhail
2[0000−0003−4825−6972]
Kolbanev , and Aleksey Shamin1[0000−0001−7690−8718]
1
Nizhny Novgorod State University of Engineering and Economics, Oktyabrskaya
Str. 22a, 606340 Knyaginino, Russia ctn af@mail.ru, ngiei-spo@mail.ru
2
St. Petersburg State Electrotechnical University “LETI”, Professor Popov Str. 5,
197376 St. Petersburg, Russia mokolbanev@mail.ru
Abstract. The object of study is the ubiquitous sensor network of mo-
bile devices. The energy consumption model for servicing in the discipline
of relative priorities is the subject of research. The purpose of this work
is to build a model of priority service for mobile devices, in accordance
with which, those sensor nodes that are located near the base station
receive a relative priority in service. With this approach, it is likely that
the remote sensor devices during the polling of the nearest ones will also
enter the priority service area, which, in turn, will reduce energy con-
sumption when transferring a data block from some mobile sensor device
to the base station. To build the model, it is necessary to use a compre-
hensive technique: the first part of the model allows us to estimate the
probability-time characteristics of the process of delivery of information
data blocks from sensor devices to the base station; the second part of
the model is designed to estimate the total energy consumption of sensor
devices. It is assumed that at each moment of time, the sensor devices
are distributed on the sensor field in accordance with the Poisson law.
A numerical calculation and analysis of the influence of spatial and time
characteristics on the energy consumption of mobile sensor devices of a
ubiquitous sensor network is carried out.
Keywords: Distribution density · Energy costs · Energy efficiency ·
Poisson field of points · Probability-energy characteristics · Sensor de-
vices · Ubiquitous sensor network
1 Introduction
One of the most popular and widespread methods of collecting and transmitting
data is ubiquitous sensor networks [1–7]. The ubiquitous sensor network is a
Copyright ⃝c for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
2 T. Astakhova et al.
network of intelligent sensors, including mobile sensor devices, which can change
their location within the sensor field. If the sensor field is equipped with one
base station, then the sensor devices during the movement can be either closer
to it or further.
An important characteristic of ubiquitous sensor networks is the amount of
power consumption by self-powered sensor nodes. [8–11]. It is advisable to receive
information in the form of data blocks at those moments when they are closer
to the base station [12, 13].
A significant part of energy costs is associated with the information interac-
tion of sensor devices with a base station. Moreover, the closer the sensor device
is to the base station, the less energy it spends when transmitting an information
block [14].
Consider the following algorithm for the interaction of sensor devices with a
base station. Assume that the process of transmitting data from sensor devices
consists of two stages. First, the mobile touch device informs the base station
with a short message that it is ready to transmit data. Then, on command from
the base station, it transmits the generated block. The base station knows in
which part of the sensor field each sensor device is located.
On the other hand, the bandwidth of the base station is usually such that in
order to receive information from sensor devices, it cannot wait for a particular
device to get close enough to it. At the same time, in each polling cycle of sensor
devices, the base station should interact with all devices, and not just those in
the immediate vicinity.
Therefore, the base station can use the service discipline with relative prior-
ities. A higher first priority will be given to mobile sensor devices located in the
near part of the sensor field.
Purpose of work is building a model of priority service for mobile devices,
in accordance with which, those sensor nodes that are located near the base
station receive a relative priority in service. With this approach, it is likely that
the remote sensor devices during the polling of the nearest ones will also enter
the priority service area, which, in turn, will reduce energy consumption when
transferring a data block from some mobile sensor device to the base station.
The object of study is the ubiquitous sensor network of mobile devices. The
subject is the model of energy consumption in servicing in the discipline of
relative priorities.
Tasks to be solved:
1. Analysis of data acquisition modes of sensor devices within the cluster.
2. Construction of a mathematical model that establishes the dependence of
energy consumption on the distribution function of sensor devices across the
sensor field.
3. Conducting numerical experiments of the constructed model.
A very general approach to the formation of the process of separation of
time resources of the base station (“processor separation mode” according to
Kleinrock) between the interrogated sensor devices forming a cluster is proposed.
Estimation of Energy Costs for Priority Maintenance of Devices of the USN 3
It is based on a model for moving sensor devices in the space of a sensor field;
assigning higher relative priorities to those sensor devices that require less energy
to deliver data.
2 Methods
To build a model, it is necessary to solve several interrelated tasks. The proposed
model consists of two parts. The first part of the model allows us to estimate the
probabilistic-time characteristics of the process of delivery of information data
blocks from sensor devices to the base station. For this, queuing models M/G/1
with relative priorities are used. The desired probability of aging information
generated by sensor devices is estimated by the method described in the arti-
cle [15], based on the Laplace-Stieltjes transform of the residence time for each
of the relative priorities.
The second part of the model is designed to estimate the total energy con-
sumption of sensor devices. For this, the approach developed in the works is
used [16–18].
At the same time, it is assumed that at each moment of time, the sensor
devices are located on the sensor field in accordance with the Poisson law.
2.1 Priority mode of data collection from sensor devices of some
cluster
Suppose that sensor devices receive service priorities depending on the distance
from the base station (see. Fig 1).
Algorithm for the interaction of sensor devices with a base station.
1. Informing the base station from the mobile sensor device with a short mes-
sage about the readiness to transmit data.
2. Command transmission from the base station of the formed block.
For the queuing model M/G/1, the input flux for service to the system is
a Poisson flow, in the system there is a single-channel serving device and an
arbitrary distribution of the service time. The input Poisson flux has an intensity
of λ. The service device is represented by an k-th order Erlang flow generator
– in the form of a Markov chain sequence with some intensity of transitions
between states.
The flow of applications is formed by packages that need to be transferred
(serviced), service is the transmission of a packet. The residence time of an
application in the system consists of the waiting time in the device buffer and
the mediocre service time (packet transmission, data block).
Relative priorities play a role in the selection of applications from the queue.
At the time of selection, the priorities of applications that are pending are com-
pared, and service is provided to the application with the highest priority (with
increasing number, priority decreases, that is, the highest priority is the first).
4 T. Astakhova et al.
Fig. 1: Possible types of separation of the sensor field.
If in the process of servicing an application claims with higher priorities ar-
rive, the servicing of the current application is not interrupted, and the received
applications are sent to the queue.
Under the conditions described in [15], the following expressions are valid for
the probability-time characteristics of the service process.
The main characteristics of this system are the Pollachek-Khinchin formulas.
The average delivery time for the M/G/1 system is determined by the access
control protocols for the control elements to the transmission medium and log-
ical channel control and the parameters of the physical layer and transmission
medium:
s(1 − ρ)g(esT )
ωhd (s) = (1)
s + λ(g(esT ) − 1)
where λ – input flow rate, ρ – flow loading, T – time parameter, g(esT ) – Laplace-
Stieltjes transform of the service interval distribution function.
The Laplace-Stieltjes transform of the time distribution function th (s) of the
service delivery process in response to the transmission of a data block with
relative priority h is expressed as
th (s) = ωhproc (s)βh (s)ωhd (s) (2)
Estimation of Energy Costs for Priority Maintenance of Devices of the USN 5
where ωhproc (s) and βh (s) are the Laplace-Stieltjes transform, respectively, of
the distribution function of the waiting time for the start of processing and the
processing time of a data block with priority h.
For ωhproc (s) expressions are
∑
(1 − ρ)Gh (s) + j:hj >h λj [1 − βj (Gh (s))]
proc
ωh (s) = ∑ (3)
s − j:hj =h λj [1 − βj (Gh (s))]
∑
Gh (s) = s + λj [1 − βj (G(s))] (4)
j:hj 0), etc.
The number of inner rings is n = R−r δ , R > r > 0, δ > 0.
If δ is a sufficiently small quantity, then we can assume that the distance to
all points of the Poisson field that are inside the i-th inner ring is
ri = r + i · δ
In order to determine the average number of points of the Poisson field that
are inside the i-th ring, it is necessary to know its inner and outer radius. The
following formulas are valid for it:
li = r + (i − 1) · δ, Li = li + δ
The area of the i-th ring is
Si = πδ((2i − 1)δ + 2r)
6 T. Astakhova et al.
By the Poisson formula, the average number of points that are located in the i
-th inner ring is
Ni = Si · ν
where Si is the area of the i-th ring, ν is the distribution density of mobile sensor
devices.
The probability that the n-th mobile sensor device is in a circle of radius r
( )
n Γ (n) − Γ n, π r2 ν
Fcirc (r) = P (R < r) =
Γ (n)
∫ ∞ −t z−1 ∫ ∞ −t a−1
where Γ (z) = 0 e t dt, Γ (a, z) = z e t dt.
The probability that the moving unit will be in the ring is calculated by the
formula: ( ) ( )
2
Γ n, π (r + δ) ν − Γ n, π r2 ν
n
Fring (r) =
Γ (n)
The average energy spent on the transmission of a data block by a sensor device
will be calculated as:
ē = P̄tr · τ (6)
where P̄tr – is the average power [W] required for transmission.
Examples of realistic distance forecasts are considered on the basis of a two-
beam model of propagation of radio waves according to the formula of Friis (Ha-
rald Friis) [19–22]. Due to the fact that the problem being solved, presented in
this article, is devoted to the study of the interaction of sensor devices operating
on agricultural land, we assume that transmission occurs in a homogeneous en-
vironment in the absence of obstacles, reflections, interference, and other factors
affecting the distribution and reception signal (which is more typical of urban
buildings). According to the equation for transmission, the power Ptr with a
known degree of approximation can be converted to the circle radius – r [m],
within which a sensor device can be selected for transit of the data block:
16Pr π 2 r2 f 2
Ptr =
Ctr Cr c2
where Ctr is the gain of the transmitting antenna, Cr is the gain of the receiving
antenna, Ptr is the radio signal power at the transmitting antenna [W], Pr is the
power of the radio signal at the received antenna [W], r is the distance between
the antennas of the mobile sensor devices of the ubiquitous sensor network in
meters, c is the speed of light, f is signal flow frequency.
It follows from the Friis formula that reducing the distance between two
mobile sensor devices by 2 times reduces the energy consumption for transmitting
a data block from one to another by 4 times.
Suppose that the average energy consumption of the network is all the average
energy consumption for all points located within a given area.
The average energy spent on transmitting one data block to the base station
from a sensor device located inside a circle of radius r is denoted by:
ēc = P̄circ · τc (7)
Estimation of Energy Costs for Priority Maintenance of Devices of the USN 7
The average energy spent on transmitting one data block to the base station
from a sensor device located inside the i-th ring will be found as:
ēiring = P̄circ
i
· τi (8)
The total energy will be calculated as follows:
∑
ē = ēc + ēiring (9)
i
The average number of sensor devices polled per cycle can be expressed as
∑
N = Nc + Ni (10)
i
where Nc is the number of devices in a circle of radius r, Ni is the number of
sensor devices in the i-th ring, i = 1, n + 1.
To get the average power needed to transfer a data block from one sensor
device located in the inner circle (P̄circ ) or in the ring (P̄ring ) of base station, it
is necessary to calculate the power according to the Friis formula with average
values of the distances from the sensor device to the base station for the circle
and ring, respectively.
3 Results
Consider the case when the sensor field is divided into two parts: around the
base station (circle of radius r) and the ring (external radius r + δ, where δ > 0)
(Fig. 2(A)), and suppose that the sensor devices can move closer to the base
station, for example, in a circle of radius r − σ, σ ≥ 0 (Fig. 2(B)).
Fig. 2: Sensor field with mobile smart things.
8 T. Astakhova et al.
The average energy spent transmitting one data block to the base station
from a sensor device inside a circle of radius r:
16Pr π 2 r2 f 2
ēc = τ (11)
Ct rCr c2
The average energy spent transmitting one block of data from a sensor device
inside a large circle of radius r + δ:
16Pr π 2 (r + δ)2 f 2
ēR = τ (12)
Ct rCr c2
The average energy spent transmitting one data block to the base station from
a sensor device inside the ring:
( )2
4Pr π 2 r + 2δ f 2
ēring = τ (13)
Ct rCr c2
The total energy spent on the transfer of one data block to the base station from
all devices inside a large circle:
16π 3 Pr
ēR̃ = (r + δ)4 f 2 ντ (14)
Ct rCr c2
Then the total energy excluding the transition:
4π 3 Pr ( 4 )
ēc+ring = 2
δ + 6δ 3 r + 12δ 2 r2 + 8δr3 + 4r4 f 2 ντ (15)
Ct rCr c
When setting priority service, we strive to read information from sensor devices
that enter the inner circle. The probability of this event will be denoted as Frc .
Then the proportion of things in the inner circle will increase according to the
proposed probability.
Introduce a priority survey of things that are in a certain area. At the be-
ginning of the polling cycle, data is received from sensor devices that are inside
a circle of radius r, and only then from devices that are in the ring.
∑Ncirc i
The duration of one polling cycle is ζ. By ζcirc = i=1 ζcirc we denote
the time spent polling devices from the inner circle. During this time, ζcirc with
probability Frc the sensor device from the ring will move inside the small circle.
This means that the average number of points in a circle of radius r will increase
by this probability times the average number of points in the ring, i.e. Frc ·
Sring · ν.Therefore, the average number of touch devices polled per cycle can be
expressed as
Ñcirc = Ncirc + Fcr · Nring
Such situations arise quite often in agriculture, for example, when grazing cows
in a pasture.
Estimation of Energy Costs for Priority Maintenance of Devices of the USN 9
The total energy, taking into account the transition from a larger ring to a
small ring of width σ with a speed of movement v [m/s] during t and a probability
of transition Fcr :
4π 3 Pr (( 3 ) )
ēF = 2
δA − σ(σ + 2r)(A2 + 4r2 ) · (1 − Frc ) + 4r2 (r + σ)2 f 2 ντ
Ct rCr c
(16)
where A = σ + 2r, σ = vt.
Using the above expressions, we performed a numerical calculation and an-
alyzed the influence of the parameters of an ubiquitous sensor network on the
power consumption of the radio signal at the transmitting antenna of the sensor
device. The calculations were carried out with the following initial data: speed of
light c = 3 · 108 m/s, density ν = 0.33 m12 , gain Ctr = 1, Cr = 1, radio frequency
f = 13.56·106 Hz, speed of movement of sensor devices v = 1 m / s, transference
time t = 1 s, large ring width δ = 50 m, small circle radius r = 10..50 m, data
block transmission time τ = 1·10−3 s. The receiver sensitivity limit is -110 dBm,
which corresponds to Pr = 10−14 W.
The effect of the speed of movement of sensor devices along the sensor field
on energy consumption is shown in the figure 3.
Fig. 3: Energy dependence on sensor speed.
10 T. Astakhova et al.
The figure 4 shows the difference in energy consumption in two cases: without
taking into account the movements of the sensor devices (Fig. 1(A)), and the
case when the discipline with relative priorities is used (Fig. 1(B)).
Fig. 4: Top score for energy consumption.
Energy consumption depending on changes in the radius of the small inner
circle and the probability of transition is presented in Fig. 5.
Energy consumption depending on the radius of the inner circle at different
values of the probability of transition of the sensor devices from the large circle
closer to the base station (case C in Fig. 1) is shown in Fig. 6.
The resulting model made it possible to estimate energy consumption when
using priority service discipline.
4 Conclusion
In this work we obtained probability distribution function for random power
values of the radiating antenna of the sensor device, which provides a stable
transmission of information. An assessment of the influence of spatial parameters
of an ubiquitous sensor network on its total energy consumption is proposed.
Under certain laws of motion of these sensor devices in the sensor space, the
proposed model will significantly reduce the energy consumption necessary for
the interaction of mobile sensor devices.
Estimation of Energy Costs for Priority Maintenance of Devices of the USN 11
Fig. 5: Dependence of energy consumption on radius of small circle and
probability of movement of sensor devices.
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