=Paper=
{{Paper
|id=Vol-2924/paper8
|storemode=property
|title=Complex scheduling of measurement and calculation systems functioning (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2924/paper8.pdf
|volume=Vol-2924
|authors=Boris Sokolov,Valerii Zakharov,Aleksey Krylov
}}
==Complex scheduling of measurement and calculation systems functioning (short paper)==
https://ceur-ws.org/Vol-2924/paper8.pdf
Complex Scheduling of Measurement and Calculation
Systems Functioning
Boris Sokolova, Valerii Zakharova, Aleksey Krylova
a
St. Petersburg Federal Research Center of the Russian Academy of Sciences (SPC RAS), 39, 14th line V.O.,
St.Petersburg, 199178, Russia
Abstract
The article suggests a polymodel description of cyber-physical systems (CFS) functioning,
that represent multifunctional hardware and software complexes aimed at reception
(transmission), storage, processing and forming of controlling actions both for the service
objects (SO), conducting a given set of target tasks that are not included into CFS, as well
as at ensuring their own reliable operation. Within the subject field, related to scientific
device engineering, these models and relevant algorithms applying them, have a big
scientific and practical value, as due to optimization of the measuring and computing
operations (MCO), they allow to generally increase efficiency of using precise
instrumental complexes in the specified environmental conditions. The developed
polymodel description is based on the original dynamic interpretation of relevant
processes.
Keywords
Cyber-physical systems, measuring and computing operations scheduling, dynamic
models, optimal software control, software tools.
“Smart and Safe Cities”, “smart” defense-
1. Introduction relevant objects etc., such systems can ensure
implementation of technologies for controlled
1 self-organization within traffic management
Currently various classes of cyber-
on the city streets by means of analyzing data
physical systems (CPS) are becoming the
on status and driving direction, received from
major component of digital production and
vehicles; coordinated functioning of
digital economics in general; these systems
production equipment for effective
involve measuring, telecommuncational and
manufacturing of small sets of various items,
control subsystems. [1,2]. Hereafter CPS is
as well as electricity generation by providing
referred to a centralized and/or distributed
workload optimization of thermal electric
hardware and software system, implementing
power stations, nuclear power plants,
physical and infocommunicational procedures
hydroelectric power stations, etc.
of processing, accumulation, storage, search,
In this case the CPS measurement and
protection, dissemination and usage of data
calculation subsystems can be considered as
and information, as well as interacting with
variants of intellectual self-managed
objects of the real world through physical
measurement and calculation systems with a
processes.
number of specific features. In the first
Based on the CPS projects of “Smart
instance these features include the following
Manufacturing”, “Smart Houses”, “Smart
[3]: the number of measurement channels
Energy”, “Smart Transport”, “Smart Life
within one CPS can involve from tens to
Safety System”, “Smart Healthcare System”,
hundreds of units even in the upcoming years;
1
measurement channels can include sensors of
Intelligent Transport Systems. Transport Security - 2021, May
14, St. Petersburg, Russia.
various values, both scalar and tensor,
EMAIL: sokolov_boris@inbox.ru (B. Sokolov); whereby in the territorial aspect the sensors
Valeriov@yandex.ru (V. Zakharov); kralex98@yandex.ru can be placed remotely from each other;
(A. Krylov).
ORCID: 0000-0002-2295-7570 (B. Sokolov); 0000-0002-2086- measurement information is transmitted over
(V. Zakharov); 0000-0003-0087-857X (A. Krylov). long distances through wire and wireless
©� 2021 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0). communication channels.
CEUR Workshop Proceedings (CEUR-WS.org)
Measurement information processing can implementing MCO (which are a subset of OI)
be implemented by means of various can be formulated as follows: it is required to
computational technologies, including cloud find such an admissible control programme for
technologies, at the same time the processing information-computational operations and
must be implemented close to the real time CPS (their functioning scheduling), so that
scale [4]. CPS control subsystems are within its implementation all the operations,
characterized by similar features. that are a part of relevant technological cycles
Creation of economically effective CPS is of SO control, would be conducted timely and
possible only in case the data, information and in the full scale, and the quality of
supporting knowledge, is characterized by informational support to the SO would meet
high confidence, received swiftly and the all the specified requirements. At the same
operational costs are sufficiently small. Due to time, if there are several admissible
limited scope of the article let us consider only programmes for CPS control received, it is
the issue of developing the MCO scheduling required to select the best possible
plan, as the most important and time- (appropriate) programme (comprehensive
consuming stage of the complex scheduling on plan) based on the accepted optimality
CPS functioning [5, 6]. criterion [10, 11].
2. Scheduling problem description 3. Dynamic models for CPS fucntioning
scheduling
Let us assume that there is a set of service
objects (SO): = {A
A , i ∈ N}, forming part of Formalization of the scheduling task, as it
i
some SO group and aimed at solving the joint was described in the introduction, will be
set target task (i.e., monitoring of eco- implemented, applying the dynamic
economic objects condition). To ensure SO interpretation of the process on technical
proper functioning it is required to operations realization, suggested by the
permanently conduct evaluation and correction authors. Based on the problem description of
of navigational data on board of each SO. This CPS scheduling, let us introduce the following
task is implemented by CPS [2, 9]: that models for programme control.
include hardware and software complexes, The dynamic model for programme control
which solve tasks on reception (transmission), of interaction operations (including the
storage, processing and forming of controlling computing operations) in CPS (model Мо).
actions both for the service objects, that are m
M o = u ( o ) (t ) | xi(γo ) = ∑ εij (t ) ⋅ ui(γo j) ; xi(γo ) (t0 ) =0;
not included into CPS, and at ensuring their j =1
si
own reliable operation. m
xi(γo ) (t f ) ai(γo ) ; ∑∑ ui(γo j) ≤ c (jo,1) ;
=
Let us introduce a set of CPS: =i 1 γ= 1
B= {B j , i ∈ M }, M ={1,..., m }. Herewith, due to m sj
∑∑ u ≤ c (o )
iγ j
( o ,2)
i ; ui(γo j) (t ) ∈ {0,1}; (1)
availability of unitized hardware and software j= 1 γ= 1
tools in order to provide informational
ui(γo j) ∑ (ai(αo ) − xi(αo ) ) + ∏ (ai(βo ) − xi(βo ) ) = 0;
interaction on SO and CPS, in case relevant α∈Γ
iγ 1 β ∈Γiγ 2
information is available, each of the listed = i, j 1,..., m; i= ≠ j; γ 1,...,si } ,
elements of SO and CPS is capable to a certain
with xi(γo ) — the variable, characterizing the
extent conduct functions of any other element,
based on the emerging situation. state of IO implementation ( Dγ(i ) , Dα(i ) , Dβ(i ) );
To ensure convenience of further aγ( o ) , ai(αo ) , ai(βo ) — the specified volumes of
representation we introduce the generalized set
of interacting objects (IO) operations implementation; ui(γo )j (t ) — control
=B { Bl , l , i, j ∈ =
M N = M {1,..., m}} . Let us
action; ui(γo )j (t ) = 1 , if operation Dγ(i ) is
also review a set of operations for interaction implemented, and in the opposite case
(OI) =D (i ) { Dγ(i) , γ ∈ Φ}=
, Φ {1,..., si }. ui(γo )j (t ) = 0 ; Γi γ1 , Γi γ 2 — a set of numbers of
interaction operations, conducted with object
All considered, at the informative level the
Bi , immediately preceding and technologically
task on scheduling of CPS functioning for
related to operation Dγ(i ) applying logic difference of the model (2) from the ones
operations «AND», «OR» respectively; previously proposed is that the operations on
c (jo ,1) , ci( o ,2) — are defined constants, CPS state parameters measurement, through
restrictions over control actions ui(γe )j are
characterizing the hardware restrictions, ,
related to CPS functioning in general; εij (t ) — directly connected to MCO, implemented by
the known matrix time function, whereby the CPS, specified in the model Мо. This allows to
spatitemporal restrictions are set, related to research the task on scheduling MCO
procedures of data collecting, transmitting and
interaction of objects Bi (or Bk ) with B j , this
processing, and the tasks on scheduling
function receives the value 1, if Bi gets into measurements of the controlled objects
the defined zone of interaction B j ; 0 — in the parameters from unified system positions.
opposite case. Quality evaluation of CPS MCO
The dynamic model for controlling programme control processes (or, in other
interaction operations (including computation words, quality of MCO operational
operations) in CPS (model Мe). scheduling) can be conducted using various
=Me {= (e)
u (t ) | x (g)
F (t )x ;
т
i
(g)
i
(e)
(g)
i
objective functions. Let us introduce some of
them:
= (i )
y (t ) d (t )x
j j i +ξ ; j 1 m si
tf
m
m d jd т
(2) =J1( o ) ∑∑ {[ai(γo ) − xi(γo ) (t f )]2 + ∑ ∫ ηiγ (τ)ui(γo )j (τ)d τ}, i ≠ j; (3)
− Z i Fi − Fi т Z i − ∑ ∑ ui(γe )j
Zi = 2 =i 1 γ= 1
j
; =j 1 t0
j= 1 γ∈Γ i σ 2
j
J 2( e ) = bγT K i (t f )bγ ;
}
i ≠ j; i, j ∈ M ; 0 ≤ ui(γe )j ≤ c (jeγ) ui(γo )j ,
tf
(4)
m m
∑∑ ∑ ∫ u γ (τ )dτ , j ≠ i, (5)
(g)
with x i — state vector of OS Bi ; Fi(t) — is =J 3( e ) (e)
i j
=i 1 =j 1 γ∈D (i )
t0
the specified matrix, characterizing the
dynamic of variable change (computed with ηiγ (τ) — known monotone functions of
parameters), describing OS state (i.e., their time, that are selected taking into
spatial position or aircraft systems state§); ξ(je ) consideration the given scheduled time frames
— uncorrelated errors of SO parameters of the start (finish) of implementing OS of
measurements, that are conducted by CPS MCO with CPS Bi . The indicator (3) is
technical means B j ; it is supposed that introduced in case it is necessary to evaluate
measurement errors comply with the normal depth of boundary conditions fulfillment, as
distributive law with zero mathematical well as the value of total fine for not
expectation and dispersion equal to σ2j ; implementing the operations specified
scheduled time frames. For OS, where we
Dγ(i ) ∈ D (i ) ; ui(γe )j (t ) — control action, defining consider instrumental complexes, aimed at
intensity of SO measuring parameters y (ji ) (t ) solving tasks on monitoring specified
(i.e. distance to SO, temperature and humidity environmental objects (SEO) state, the
aboard SO), that are conducted in the remote operations, related to evaluation of their
mode with technical means of CPS B j ; ci(γe ) — position, that therefore allow to define SEO
position, have the special significance.
specified values, characterizing technological Thereby the value of quality indicator (4)
capabilities of means B j while implementing characterizes the determination accuracy of χ
operation Dγ(i ) ; Z i — matrix, reciprocal to –й component of vector xi( g ) (
correlation matrix K i (t ) of errors in evaluating
bχ = 0 0...1...0 0 —
T
specified intermediate
state vector OS Bi ; Γi — a set of interaction
vector, which defines the required element
operations, conducted by CPS with OS Bi ; with number χ in the correlation matrix K i (t )
d j (t ) — given vector, that defines ). Objective function of type (5) allows to
specifications of measuring tool equation provide quantitative evaluation for CPS
technical implementation of CPS B j ; K i 0 — resources consumption while implementing
value K i at the start time t = t0 ; σ2γ i — operations Dγ(i ) , related to OS state changes.
specified determination accuracy χ -й of the Further, let us provide formal problem
statement on scheduling MCO, implemented
state vector component xi( g ) (t ) OS. The major
by CPS. It is required to find such admissible
control, that answers the required limitations
and transfers the dynamic system from the
specified initial state into the specified final
state. In case there are several such control
actions (complex plans), it is required to select
the best possible (optimal) among them,
ensuring that components of the generalized
vector take extreme values.
Previously the works [12,13] demonstrated,
how it is possible to narrow down the task on
scheduling operations and distributing
resources in complex technical objects to two-
point boundary value problem, applying
Boltyansky’s method of local sections. In this
case the task on MCO scheduling is Figure 1: The results on heuristic and optimal
formulated as task on searching for optimal scheduling of MCO, implemented by CPS
programme control, that ensures required
determination accuracy of CPS and OS Application of this approach allows to
position within minimum time frames (or with reduce the amount of unprocessed
minimum power consumption from MCO informational flows by 20%; eliminate
implementation) [14]. Traditionally, the tasks unbalanced resources consumption; reduce
of this class (tasks of scheduling theory) are interruptions of scheduled time in operation
solved applying the method of mathematical implementation by 17%; increase the
programming [5,11,15]. The suggested usage generalized quality indicator by 19%.
of methods for theory of optimal control in Moreover, additional researches of
order to solve tasks of the scheduling theory processes on implementing measuring
allows to improve the quality of scheduling operations, related to evaluation of various
results (including increase of efficiency on factors influence on the mentioned factors,
plans development, reduction in energy were held. The graphs (Fig. 2, Fig. 3) show,
consumption within its implementation, etc.) that for each OS with a new interaction session
[5, 16]. with CPS the accuracy of measurement of its
position parameters increases.
4. Results analysis on solving scheduling of
measuring and computing operations in
CPS
The search for a MCO complex plan is
implemented in two stages. At the first stage in
order to initialize the generalized procedure for
measuring and computing operations
optimization there was an admissible heuristic
plan synthesized. In order to implement it the
well-known FIFO algorithm (“first in, first
out”) was used. At the second stage the multi- Figure 2: The graph of coordinate measurement
step procedure for solving the two-point errors change, depending on the service session for
boundary value problem was conducted, to various OS
which the initial nonclassical task on calculus
of variations was narrowed. The results of two
stages implementation are shown in Fig. 1.
Within the second group of experiments the
parameters of measuring tool disperison were
sequentially reduced by half (Fig. 4). The
graph shows that the influence of measuring
tool dispersion parameters in a lesser extent
affects the results of measurements
optimization.
Figure 3: The graphs for coordinate measuring
errors change, depending on the interaction session
for a selected OS
In order to evaluate the influence of
changing various parameters on measurement
accuracy 2 groups of experiments were
conducted, within which the coefficients, that
are referred to errors cross-correlation matrix Figure 5: Graph of the conducted experiments
and measuring instrument dispersion were results with change in CPS measuring tool
changed. dispersion parameters
In the first group experiments were In all the conducted experiments identical
sequentially held with changing coefficients, consistency of measurement quality
included into correlation errors matrix. In each improvement with each new session of OS
of the experiments the coefficients of errors interaction with CPS is observed.
correlations were sequentially reduced over all
parameters. The experiments results are shown 5. Conclusion
in Fig. 4.
The article provides a polymodel description
and results of solving task on planning MCO
of CPS. The main features and differences
between the suggested models are that within
dynamic interpretation of MCO, included into
CPS technological cycle, processes
implementation, the dimension of the solved
scheduling tasks and strength of association in
scheduling algorithm are notably reduced. This
dimension is defined within solving
scheduling task at each time point by a number
Figure 4: Graphs of coordinate measurement errors of independent tracks in the general network
change, depending on the interaction session for a graph, implemented by CPS, by current
selected OS spatiotemporal, technical, technological
The graph (Fig. 4.) shows, that reduction of restrictions.
coefficients in the errors correlation matrix The studies on the developed models
leads to improvements in the measurement features and characteristics showed, that by
quality. means of CPS operation rational (optimal)
The results show, that after optimization scheduling, firstly, the general capacity of CPS
process the gained amount of measuring increases and, secondly, CPS resource
information is received within shorter period consumption for MCO implementation
of time. It should be also mentioned that, reduces, and as well time lags in CPS control
provided there are the largest values in the paths reduce, thirdly, there is a reduction of
correlation matrix of measuring tool errors, the peak informational loads within sudden
largest improvement in measuring quality is changes of CPS structure. Moreover, based on
observed as a result of optimization. dynamic description of CPS functioning
processes, it is possible to explicitly connect [8] V. Kupriyanovsky, D. Namiot, S. Sinyagov,
its elements and subsystems control Cyber-phisical systems as a base for digital
technology with results of target application of economy. International Journal of Open
instrument complexes, implementing data on Information Technologies (2016) 18-24.
[9] W. Shijie, Z. Yingfeng, Z. A credit-based
SEO reception, processing and analysis, as
dynamical evaluation method for the smart
well as with characteristics of CPS hardware configuration of manufacturing services under
and software complexes. MCO complex Industrial Internet of Things. J Intell Manuf
scheduling offers interesting prospects on 32, (2021) 1091–1115.
forming justified requirements to CPS
characteristics. In [17] information is provided [10] V. V. Zakharov, Dynamic interpretation of
about multiple ways to apply the suggested formal description and solution of the
approach in practice in order to solve tasks of problem of complex object modernization.
scheduling theory, emerging in various subject Journal of Instrument Engineering. (2019)
fields (space technology, shipbuilding, state 914-920. doi: 10.17586/0021-3454-2019-62-
10-914-920
administration, etc.).
[11] R. Csalodi, Z. Süle, S. Jaskó, T. Holczinger, J.
Abonyi, Industry 4.0-Driven Development of
6. Acknowledgements Optimization Algorithms: A Systematic
Overview. Complexity, (2021) 1-22.
The research described in this paper is [12] L.S. Pontryagin, V.G. Boltyanskiy, R.V.
partially supported by the Russian Foundation Gamkrelidze, E.F. Mishchenko, The
Mathematical Theory of Optimal Processes.
for Basic Research (19–08–00989, 20-08-
Oxford. Pergamon Press (1964).
01046), state research 0073–2019–0004. [13] V. N. Kalinin, B. V. Sokolov, A dynamic
model and an optimal scheduling algorithm
References for activities with bans of interrupts.
Automation and Remote Control (1987) 88–
[1] A. A. Teilans, A. V. Romanovs, Y. A. 94.
Merkuryev, P. P. Dorogovs, A. Y. Kleins, and [14] E.B. Lee, L. Markus. Foundations of optimal
S. A. Potryasaev, Assessment of Cyber control theory, 1967.
Physical System Risks with Domain Specific [15] V.S. Tanayev, V.V. Shkurba, Introduction to
Modelling and Simulation, SPIIRAS Scheduling Theory, 1975.
Proceedings (2018) 115-139. [16] M.Yu. Okhtilev, B.V. Sokolov, R.M.
doi:10.15622/sp.59.5 Yusupov. Intellektual'nye tekhnologii
[2] W. Wolf, Cyber-physical Systems. Computer, monitoringa i upravleniya strukturnoy
(2009) 88-89. doi: 10.1109/MC.2009.81. dinamikoy slozhnykh tekhnicheskikh
[3] D. Ivanov, B.V. Sokolov, A. Dolgui. ob"ektov (Intellectual Technologies of
Introduction to Scheduling in Industry 4.0 and Monitoring and Management of Structural
Cloud Manufacturing Systems. In: Sokolov Dynamics of Complex Technical objects)
B., Ivanov D., Dolgui A. (eds) Scheduling in (2006).
Industry 4.0 and Cloud Manufacturing. [17] Laboratory of Information Technologies in
International Series in Operations Research & System Analysis and Modeling,
Management Science, (2020). http://www.litsam.ru, last accessed
https://doi.org/10.1007/978-3-030-43177-8_1 2021/06/06.
[4] Li Da Xu, Eric L. Xu & Ling Li Industry 4.0:
state of the art and future trends, International
Journal of Production Research (2018) 2941-
2962. doi:10.1080/00207543.2018.1444806
[5] D. F. Rossit, F. M. Tohmé, M. Frutos.
Industry 4.0: Smart Scheduling, International
Journal of Production Research, 57(12),
(2019) 3802-3813.
[6] R. M. Yusupov, A. A. Musae. Efficiency of
Information Systems and Technologies:
Features of Estimation. SPIIRAS
Proceedings. 2, (2017) 5-34.
[7] R.L. Ackoff, The art of problem solving,
1978.