=Paper=
{{Paper
|id=Vol-2859/paper19
|storemode=property
|title=Adaptive Management of the Order in Which Resources are Provided to Cloud Users
|pdfUrl=https://ceur-ws.org/Vol-2859/paper19.pdf
|volume=Vol-2859
|authors=Aleksandr Matov
|dblpUrl=https://dblp.org/rec/conf/its2/Matov20
}}
==Adaptive Management of the Order in Which Resources are Provided to Cloud Users==
https://ceur-ws.org/Vol-2859/paper19.pdf
220
Adaptive management of the order in which resources
are provided to cloud users
© Aleksandr Matov
Institute for information recording of NAS of Ukraine, Kyiv, Ukraine
Abstract. The review considers the issues of further development of the princi-
ples of creating adaptive infrastructures of cloud computing, capable of dynami-
cally adapting to user requirements and current features and changes in operating
conditions. Methods and analytical conditions for adapting the provision of re-
sources to users of cloud computing have been developed. These conditions pro-
vide an opportunity to develop technology (mechanisms and algorithms) for the
use of adaptive discipline (order) of providing computing resources to users. In
turn, this allows you to meet the time requirements of different users to obtain
timely computational results or make the most efficient use of available cloud
computing resources. . This is relevant for real-time systems and, above all, for
special information systems built using private clouds, and can be critical with
limited computing resources of cloud computing.
Analytical (formulaic) conditions of adaptation are developed on the basis of
the corresponding indicators of efficiency and mathematical models of cloud cal-
culations. The stochastic nature of the main factors and the need to quantify mass
processes based on probability theory determines the use of the analytical model
of cloud computing as a multi-threaded and multi-priority queuing system with
queues with mixed service discipline. The model takes into account probable fail-
ures and various features and has arbitrary distribution laws for some probable
processes. The model allows to calculate the time characteristic - the response
time of the system in terms of features of operation and failures of cloud compu-
ting.
Keywords: cloud computing, mathematical model, discipline of computing re-
sources provision, mixed service discipline, absolute and relative priorities,
time characteristics, response time, efficiency of cloud computing.
1 Introduction
Creating adaptive infrastructures that are able to adapt to changing operating conditions
and maintain systems in optimal, and sometimes just in working order, is an important
direction in the development of modern global information and analytical systems using
cloud computing (СС) technologies. For such adaptation, a dynamic adaptive mixed
discipline of providing computing resources to users of СС is proposed [1,3].
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
221
Consider two practical problems of dynamic adaptation of a mixed discipline of re-
source provision with relative-absolute priorities. One of the main indicators of the ef-
fectiveness of СС are indicators based on the assessment of the temporal characteristics
of these systems and which must be maintained at a given level. Such indicators can be
set by agreement between the supplier and user of СС and are especially important for
systems primarily for special information systems based on private clouds. Due to the
random nature of the computational process, there are additional delays in information
processing, the permissible limitations for the time of its stay in the СС are violated,
which negatively affects the effectiveness of solving target tasks of users.
To ensure the required efficiency of СС in such situations, it is necessary to maintain
the time characteristics of the system at a given level. Given the shortage of computing
resources, this is possible only by increasing the efficiency of the computing process,
in particular, by adapting the discipline of service.
Along with this, there is the problem of the most efficient use of available computing
resources at any time during the operation of the management of СС. This problem can
also be solved by adapting the discipline of service.
2 Indicators of resource efficiency for users of cloud computing
The aim of the work is to develop methods and analytical conditions, adaptation of the
provision of computing resources to users of СС to ensure the time characteristics of
information and analytical systems and optimize the use of resources of СС.
As an indicator of the effectiveness of СС we take the average total cost (fine) of re-
sponse time СС, time delay in the queue, waiting time in queues and time to provide
resources, ie stay in the СС as in the queuing system (QMS)) on applications (require-
ments) of users.nTo do this, use the known functionality [3]:
C ( S ) i i vi( s )
i 1 ,
from what (we have M N
C ) ( m , n ) ( m , n ) v ( ) ( m , n )
m 1n 1 , (1)
where
i - cost (fine) per unit of response time of СС (delays, stay in СС) of applications
of the i-th stream;
i - intensity of the i-th stream of applications;
vi(S )
- the average response time of СС applications of the i-th stream;
n - is the number of types of applications;
s - is a parameter that characterizes the method of organizing the computational
process;
222
v( ) (m, n)(m 1, M , n 1, N m )
- the average response time of СС applications
(m, n) -th stream;
(m, n) - the unit cost of response time СС (delay in HO) applications (m, n) -th
stream;
(m, n) - intensity (m, n) -flow.
This efficiency indicator is based on the assumption that the results of the use of
resources by the user are depreciated in proportion to the time of their delay in the СС,
ie stay in the СС as in the QMS. Then the purposes of adaptation of the mixed discipline
of service will be either satisfaction of requirements of timely stay (m, n) of applications
in the system set by admissible values of this time, or minimization of functional (1).
These goals are achieved by finding the appropriate optimal breakdowns into relative
and absolute priorities, ie the problems of adaptation of a mixed service discipline with
a relative-absolute priority are optimization problems, the general formulation of which
is discussed above.
Since the above objectives of adapting a mixed service discipline can be achieved
with several different breakdowns of application flows into groups of absolute priority,
it is necessary to introduce an additional restriction on the choice of breakdown.
The presence of absolute priority in HO requires some technological losses of re-
sources, which are proportional to the number of groups (levels) of absolute priority. In
this regard, it is necessary to consider the optimal breakdown, which ensures the
achievement of adaptation goals with a minimum number of groups of absolute priority
M.
Then the(considered problems of adaptation of the mixed discipline of service can
v ) (m, n) v Д (m, n) 0
be formally set as follows:
M min ; (2)
( ) 0
C min
M min . (3)
It is not possible to solve the problems of finding the optimal breakdown (2) and (3)
using known analytical optimization methods. The only way to solve these problems is
a heuristic approach, which has no formal justification, but is based only on the specif-
ics of problems (mathematical models) and related understandings.
From expressions (1) - (3) it follows that the achievement of the goals of adaptation
of the mixed service discipline is associated with the need to assess the value of the
average response time of СС (stay in СС) applications (m, n) -type v (m, n) on re-
sources. Therefore, there is a need to synthesize a mathematical model of СС with a
mixed discipline of providing computing resources (maintenance).
223
3 Cloud infrastructure model class
Development of mathematical models of cloud computing or information systems
created using clouds is an important area for identifying and improving their character-
istics [2…10]. Cloud computing is an object with a high level of uncertainty in the
operation process. Here, the external uncertainty of the flow of requests for computing
resources (СR) (environment) is complemented by the internal uncertainty of the СС
(object), which is associated with the presence or absence of the necessary СR, acci-
dental failures of the СС system, as well as the need to provide certain time character-
istics for many clients. . This determines the need for the introduction of adaptation into
the functioning of the СС.
In addition, the introduction of adaptation into the process of functioning of СС is
associated with the need to maintain the system in optimal and sometimes simply op-
erational condition, regardless of the many external and internal factors that remove СС
from the required target state.
Cloud computing (CС) is an object with a high level of uncertainty in the functioning
process, the main factors of which are [1]:
-probability of the flow of requests for computing resources (СR);
-the presence of the necessary PR and the randomness of the time of their use by
customers;
-accidental failures of the infrastructure of СС and the time of their elimination;
-the need to provide certain time characteristics for a number of customers, for ex-
ample, the response time of СС;
-the need for optimal use of СR depending on the cost of delay time ordered by
customers, the results of calculations and operating conditions;
-the need to introduce adaptation into the process of operation of the СС in order to
provide certain time characteristics for a number of customers and the optimal use of
СR.
The stochastic nature of the main factors and the need to quantify mass processes
based on probability theory determines the use of queuing theory. Then it is possible
and expedient to use the technology of dynamic adaptive mixed discipline of providing
PR (service) to users of СС as mechanisms of adaptation of СС [1].
Analytical models for subtraction of time characteristics in the conditions of features
of functioning of СС with use of mixed discipline of service with absolutely - relative
priorities and the account of failures are offered. Models are based on works [2, 3].
4 Mathematical description of multi-threaded and multi-
priority model of cloud infrastructure operation with queues
with mixed service discipline and failure adaptation.
Let the input of the CC system, in which the discipline of service with a relatively
absolute priority is implemented, arrive N Poisson flows of applications of intensity
(m, n) (m 1, M , n 1, N m ) . These flows are aligned with N priorities [2].
224
The duration of the maintenance of applications of priority (m, n) is a random vari-
B (t )
able with a distribution function m, n , the first b (m, n) and the second
b ( 2) (m, n)
start point.
An application of priority (m, n) whose service is interrupted by applications from
groups with 1, m 1, numbers is returned to the queue. Updating its service is possible
either after servicing all interrupted applications (maintenance discipline A), or after
servicing all interrupted applications and all applications for accumulated flows, the m
(m,1), (m, n 1)
group with numbers (discipline of service upgrade B) .
The serving device (CC) fails in accordance with the Poisson law with the 0 pa-
rameter. The period of recovery of the device is a random variable that has an arbitrary
b b2
distribution law Во(t) with the first 0 and second 0 initial moments.
During the restoration of the service device, requests of some streams in the queue
are accepted, while others are not accepted. This condition is given by the matrix-row
n , i 1, N n 1
of coefficients i , , and in the case if requests of the i stream are accepted
ni 0
in the queue, and if requests are denied.
Adaptation to bounce will be that in the period of recovery device incoming appli-
cations can either accumulate in the queue (discipline replenishment queue I), or re-
ceive a refusal and leave the system (discipline replenishment queue II).
Failure of the servicing device can occur both during its free state and during service
of the application. In the latter case, the renewal of the service is carried out either from
the interrupted application, if there are no applications interrupting its service, (the dis-
cipline of the renewal of service C), or from applications of the senior relative priority
of the corresponding group, if any (discipline of renewal of service D).
In case of repeated receipt of the servicing device, the interrupted application shall
be maintained from the place where it was interrupted. Within one priority, applications
are served in the order of receipt.
The combination of service updating disciplines and queue replenishment allows
you to consider independent models of different types of systems that have the proper
designation. Different features of functioning consist of various combinations of disci-
plines A, B, C, D, I and II.
R KrM N
Let CC be in stationary mode, which M condition is for systems of type I,
RM (m, n)
R 1 m1n 1
and for systems of type II - M . Here - total loading of the
( (m, n) (m, n)b( m, n)
device applications ( - loading of the device (m, n) - applica-
K 1 /(1 0 ) ( 0b0
tions), and r - the system readiness coefficient ( 0 - loading the
device with refusals).
v (m, n)
It is necessary to determine the average time spent in the system of applica-
tions of each (m, n) -priority, ie, the response time of the system CC.
225
5 Definition of time characteristics of a model of a system of
type AS-I.
To determine the average time of applications in the system (time response systems)
type AS-I use the known direct method [3].
Let some application (j, k) be a priority in the system. The average duration of this
application in the system v (j, k) consists of the average waiting time in the queue w (j,
k) and the average service time b (j, k):
v( j, k ) w( j, k ) b( j, k )
.
The average waiting time in the queue w (j, k) consists of the average waiting time
before service and the average standby time in the interrupted state u (j, k):
w( j , k ) wН ( j , k ) u ( j, k )
.
The last term in this formula is due to the interruptions in the maintenance of the
1, j 1
application (j, k) -priority of applications from groups and denials, that is:
u ( j , k ) u З ( j , k ) u0 ( j , k )
.
Average time from the beginning of service (j, k) - application to completion is the
average full time of service:
( j , k ) b ( j , k ) u ( j , k )
. (4)
Let's start with the calculation u (j, k), for which we apply the approach described in
[2].
b( j , k ) j 1
During the service j 1 N(j,
m
k) -supply on average will occur interruptions
j 1 (m, n)
where m 1n 1 the intensity of the total flow of interrupted applica-
tions.
As a result of these interruptions (j, k), the application returns to the queue and waits
b( j , k ) R j 1
for the termination of service interruptions that will continue in average
units of time j 1 N m
R j 1 (m, n)b(m, n)
where m1n 1 . (5)
1, j 1
During this time, applications from groups will be received, which will lead
b( j, k ) R 2j 1
to an increase in waiting time (j, k) - applications for value . In addition, the
service of these applications will be accompanied by additional accumulation of appli-
cations of the same priorities, requiring service before (j, k) -payment. This process is
endless, with supplements to the waiting time (j, k) -positions form a declining geomet-
R 1
ric progression with a denominator j 1 . The sum of members of such geometric
progression is the mean time of all service interruptions (j, k) -request:
226
R j 1
Т (1) b( j , k )
1 R j 1
. (6)
(1)
In the mean time Т , the device will fail
Т (1) 0
, resulting in it will be restored
Т (1) 0b0 Т (1) 0
within units of time. Since in the system type AS-I during the period
of recovery the device again receives applications that continue to accumulate in the
queue, then after the device is restored, the average waiting time (j, k) -supply in the
interrupted R jincrease
state will 1 by R 2j 1
Т (2) Т (1) 0 b( j , k ) 0
1 R j 1 (1 R j 1 ) 2
. (7)
During this time there may be a refusal of the device, the restoration of which will
be accompanied by the accumulation of new applications served before (j, k) -pay-
ments, etc.
1, j 1
The total time of all applications service interruptions (j, k) -priority of ap-
u З ( j , k ) Т Т Т ()
(1) ( 2)
plication groups, taking into account device refusals
. This expression represents the sum of two infinitely decreasing geometric progres-
sions. After calculating the sum of the members of each of them and compiling the
results, we get: R j 1
u З ( j , k ) b( j , k )
K r R j 1
. (8)
Similarly, the average waiting time (j, k) is determined in the interrupted state due
u ( j, k )
to device refusals 0 . The only difference is the beginning of reasoning. During
b( j , k )0
the service (j, k) -supply, the device will fail on average, which will result in
b( j , k ) 0
its restoration within units of time. Taking into account the possibility of
accumulation in the period of device renewal and priority service of applications with
1, j 1
absolute priority fromR j 1 group, the average waiting time (j, k) -payments will in-
b( j , k ) 0
1 R j 1
crease by .
During this time, the device can again be denied, R j 1which additionally increases the
b( j , k ) 02
1 R j 1
waiting time (j, k) - request for value etc.
In the final analysis,uwe( jget: K r 0
, k ) b( j , k )
0
K r R j 1
. (9)
Then the total average waiting time K
R j 1(j, 0
k)r -request in the interrupted state:
u ( j , k ) b( j , k )
K r R j 1
, (10)
and the total average service time (j, k) -request:
227
1
( j , k ) b ( j , k )
K r R j 1
. (11)
w ( j, k )
Now calculate Н . Before (j, k) -request entered the system for the first time,
the following should be done:
1) the device is restored
1, j
2) an application has been served from or groups of submissions of the served
j 1, M
application from the groups;
2, j 1, j 1
3) service requests from groups interrupted by applications from
groups;
1, j
4) service requests from groups interrupted by denials of the device;
(1,1), ( j , k )
5) existing requests for streams with numbers are served;
(1,1), ( j , k 1)
6) service
wН requests
( j , k ) flowed with numbers received during the waiting
0 ( j, k ) ( j, k ) 0 ( j, k )
time (j, k) -request,
j 1N m taking into accountk device refusals.
wН (m, n) (m, n) wН ( j , n) ( j , n)
For the average
m 1n 1 duration of these events, n 1 we write the equation:
R j ,k 1 K r 0
[ 0 z Н ( j , k )] z Н ( j, k )
K r R j ,k 1 K r R j ,k 1
. (12)
Here
0 K r 00 - average time for updating the device in the presence (j, k) -position:
K r 0 0 b0( 2) / 2b0
- probability
j N m of recovery of the device [2], ;
( j , k ) ( m, n)(m, n)
m1n1 - average time for the maintenance of the applica-
tion by the device
(m, n) b(2) (m, n) / 2b(m, n) ;
j N min the presence (j, k) -request:
Rm1
( j, k ) (m, n)(m, n)
m 2 n 1 K r Rm 1 - average time to receive applications
K m1
1, j 1 : (m, n)
2, j K r Rm1
from groups interrupted by applications from groups -
probability of staying in queue (m, n) - applications, interrupted by applications from
1, m 1 groups. This probability is determined by the formula (8), taking into account
the intensity
(m, n) of the flow (m, n) -payments;
228
j Nm
K r 0
0 ( j, k ) (m, n)(m, n)
m1n 1 K r Rm1 - average time of subscription of appli-
1, j
cationsKfrom groups interrupted by device refusals
r 0 (m, n)
K r Rm1
- the probability that the queue has (m, n)-applications, inter-
rupted by the denial of the device. This probability is determined on the basis of (9)
with account
(m, n) ;
z Н ( j, k )
- average waiting time (j, k) - application, equal to the sum of the consid-
ered components
0 ;
j 1 N mwithout accounting
k 1
R j ,k 1 (m, n) ( j , n)
m1n 1 n 1 .
Note that in each queue there can be jnoN mmore than one application interrupted by
1 1
wН ( j , kwith
applications
K r2 0 or0 denial.
) absolute priority
K r R j ,k from equation
After simple transformations m 1n 1 K r R
(12) m obtain
we 1 the following recurrence
relation: j 1 N m
(m, n)(m, n) wН (m, n) (m, n)
m 1n 1
k 1
wН ( j , n) ( j , n)
n 1 (13)
j 1 N m k
R j ,k (m, n) ( j , n)
where m1n 1 n 1 .
To obtain a formula for explicit determination, we analyze the relation (13) for
"pure" service disciplines with a relative and absolute priority.
For the discipline of service with a relative N1 priority we receive:
K r3 0 0 (1, n) (1, n)
n 1
wН (1,1)
- for the first flow K r [ K r (1,1)] ,
N1
K r3 0 0 (1, n) (1, n)
n 1
wН (1,2)
- for the second flow. [ K r (1,1)] [ K r (1,1) (1,2)] .
These formulas allow us to assume a general solution in the form:
229
N1
K r3 0 0 (1, n)(1, n)
n 1
wН (1, k )
( K r R1,k 1 )( K r R1,k )
, (14)
k 1 k
R1,k 1 (1, n), R1,k (1, n)
Where n1 n1 .
(M N , Nm 1
For the discipline of service with absolute priority for all
m 1, M )
of the expression (13) we obtain:
• for the flow
K 3 of
the first
(1group
,1) (1,1)
wН (1,1) r 0 0
K r [ K r (1,1)] ;
• for the flow
K 3of
the
second group
(1,1) (1,1) (2,1)(2,1)
wН (2,1) r 0 0
[ K r (1,1)][ K r (1,1) (2,1)] .
Then on the basis of these equalities wej get the general expression:
K r3 0 0 (m,1) (m,1)
wН ( j ,1) m 1
( K r R j 1,1 )( K r R j ,1 )
(15)
where j j
R j 1,1 (m,1), R j ,1 (m,1)
m1 m1 .
Analyzing the expression (14) and (15), it is easy to assume the general form of the
w ( j, k )
formula for determining Н for a jmixed
N m discipline of service:
K r3 0 0 (m, n) (m, n)
wН ( j , k ) m1n 1
( K r R j ,k 1 )( K r R j ,k )
(16)
Substituting formula (16) in (13) and making simple transformations, we can verify
the validity of this assumption.
By expressions (11) and (16) we calculate the required average time of stay (j, k) -
request v (j, k) in the AS-I system
Similarly, as for the system type AC-I, formulas can be derived for determining the
temporal characteristics for the remaining systems type AC-II, BD-I, BD-II.
230
6 Methods and analytical conditions for adapting the provision
of resources to users of СС
Adaptation of the mixed service discipline with the СС model is to find the optimal
( 0 )
breakdown of application flows by groups (levels) of absolute priority , ie such a
{N m }m 1, M )
set of numbers at which the temporal characteristics of the СС model
would provide0 equality according to(problem (2):
opt{N1, N2,, NM / ) (m, n) Д (m, n), Ф, М min}
, (17)
and in accordance with problem (3) equality:
0 opt{N1, N 2 ,, N M / C ( ) min, Ф, М min} . (18)
Since the number of application streams N is finite, the problem of finding the opti-
mal breakdown
0 can be solved by a complete search of all possible breakdowns and
choosing from them one that satisfies equations (17) and (18). However, this path for
real-time СС is unacceptable, because the number of all possible breakdowns
Ф 2 N 1 at large N is large and the implementation of the method of complete search
requires significant time. Therefore, there is a need to develop such methods of adap-
tation that allow to obtain the optimal breakdown as a result of considering a limited
number of grouping options.
To find the breakdown
0 that provides equality (17), a method is proposed, the
essence of which is to alternate the requirements for the time of stay of applications in
the system, starting with the first stream, by sequentially forming first the first, then the
second, etc. groups of absolute priority. The adaptation process begins with a break-
down that corresponds to the discipline of service with a "pure" relative priority (M =
1, N1 = N). In this regard, the first of the breakdowns, in which the purpose of adapta-
tion is fulfilled, is characterized by the minimum possible number of groups of absolute
priority M, ie is optimal.
To find a breakdown
0 that satisfies equality (18), a method of adaptation is pro-
posed, the essence of which is the purposeful formation of groups of absolute priority,
starting with the latter, based on the analysis of the sign of increment of the average
( )
total cost of applications in the system C . When forming the next group, the flow
requests of the formed groups are excluded from consideration, because they do not
affect the average time spent in the flow request system of the previous groups of ab-
solute priority. The process of adaptation in this case begins with a breakdown that
corresponds to the discipline of service with a "pure" absolute priority (M = N, Nm =
1), which also provides a minimum number of groups M in fulfilling the goal of adap-
tation.
( )
Let's define C . Assume that the previous q-breakdown has the form
N1 N 2 Nl 1 1, Nl 2 N j P l 1,
where P is the number of application
streams considered at the stage of formation of the next group with number j. When
231
j 1
P N Nm
numbering groups from the latter m1 . The following
breakdown dif-
fers from the q-breakdown in that the application streams of the last two groups are
N N 2 N l 1, N l 1 N j P l
combined into one 1 .
When C
( q, )
the transition from q-breakdown to
breakdown is defined as fol-
lows: N
C ( q , ) C ( ) C ( q ) i i i( q , )
i 1 (19)
i(q, ) i( ) i(q) , i 1, N
where .
From formula (19) it follows that the
breakdown is considered better compared
( q, )
to the q-breakdown, if C 0 . In this case C ( q, ) 0 , the q-breakdown is pre-
ferred. The expression C
( q , )
0 means that the breakdown by the criterion of
the average total cost of applications in the system is not worse than the q-breakdown,
but provides fewer groups of absolute priority M.i
C ( q, ) K r3 0 0 r r
Let's calculate bi on an example of system r 1 of type AC-I for which on the basis
, i 1, l ;
of expressions
(11) and (16) it is possible to write
K R i 1 ( K r R i 1 )( K r R i ) down:
i( ) r P
K r3 0 0 r r
bi
r 1 i l 1, P .
,
K r R l ( K r R i 1 )( K r R i )
(20)
0 , breakdown,
i 1, l ;
In the transition
from q-breakdown
P
to the increase in the average
( q, )
residence time ofapplicationsinthe r rsystem i
( q , ) r l 2
i , i l 1;
( K r Rl )( K r Rl 1 )
bi l 1
( K R )( K R ) , i l 2, P .
r l r l 1
(21)
( q, )
Then write the increase C in the form
P
232
C ( q , ) l 1l 1 l(q1, ) i i i( q , )
i l 2
l 1 P 2 i
i bi( 2) b l 1
2 ( K r Rl )( K r Rl 1 i l 2 2 b
,
) l 1 1 i i
(22)
i D[ti ] / bi
where - is the coefficient of variation of the service time of the ap-
D[t ]
plications of the i-th stream ( i - variance of the service time). At indicative law
service of applications of the i-th stream i
1 , and at deterministic service - i 0
.
Analysis of expression (22) shows that the feasibility of the transition from q-break-
down to
breakdown is determined
P by
the sign of2 the
input::
C l i bi( 2 ) l 1 i
bl 1 1 bi 2
il 2 i . (23)
It follows from this equality:
Cl 0
1) if for all l 0, N 2 , the optimal is the discipline of service with a
"pure" relative priority;
Cl 0
2) when for all l the optimal is the discipline of service with "pure" absolute
priority;
Cl 0 or Cl 0
3) in the case of not all l optimal is a mixed discipline of
service.
Thus, to determine the feasibility of the transition from q-breakdown to
break-
Cl
down, it is sufficient by formula (23) to calculate and analyze the result. Changing
Cl 0
the breakdown is appropriate if .
Conclusions
1. Further development of the principles of creating adaptive infrastructures of cloud
computing, able to dynamically adapt to user requirements and current features and
changes in operating conditions. This scientific direction remains relevant and requires
further research.
2. Cloud data centers are objects with a high level of randomness of the operation
process, the main factors of which are: the probability of the flow of requests for com-
puting resources; availability of necessary resources and randomness of time of their
use by consumers; randomness of infrastructure failures and time of their elimination.
Due to the random nature of the computational process there are additional delays in
processing information, violate the permissible restrictions on the time of its stay in the
system (at the time of system response), which negatively affects the effectiveness of
solving target tasks of users. This is relevant for real-time systems and, above all, for
special information systems built using private clouds, and can be critical with limited
computing resources.
233
3. It is possible to get rid of or reduce the impact of favorable phenomena on the
functioning by introducing adaptation into the process of functioning of the infrastruc-
ture. In addition, the introduction of adaptation is associated with the need to maintain
the СС in the optimal (efficient use of resources), and sometimes just a working condi-
tion, regardless of the many factors that bring the data center infrastructure out of the
required target state. The purpose of adaptation can be to maximize revenue from cus-
tomer service, eliminate system overload and maintain it in a stationary mode of oper-
ation.
4. The problem of adaptation can be solved by using the adaptive discipline (order)
of providing computing resources to users. Unforeseen and uncontrolled changes in the
environment and system inevitably change the optimal setting of the discipline, if such
was implemented in the system. Therefore, systematic adjustments (adaptation) of the
discipline are inevitable if you want to maintain the system in the optimal mode, re-
gardless of changes in the environment and system. For adaptation, a dynamic adaptive
mixed discipline with absolute relative priorities of providing computing resources to
users of cloud computing was used, one of the options for creating the technology of
which was considered by the author in [1,4]. The adaptation of the discipline consists
of an optimal change in the number and position of the boundaries that divide the flow
of user requests for resources into groups of absolute priority, within which the relative
priority, ie in changing the number of groups and the number of flows in groups.
5. The development of analytical conditions for the adaptation of the provision of
resources to users of cloud computing is performed on the basis of the analytical model.
Analytical conditions allow to develop mechanisms and algorithms of adaptation of
СС. These mechanisms and algorithms take into account the physical properties of СС,
such as instantaneous elasticity (dynamic migration, allocation and release of resources
for rapid scaling according to needs) and measurement services (management and op-
timization of resources using measurement tools). The moment of activation of the ad-
aptation algorithm is determined by the control system of the СС in case of violation of
acceptable limits on response time, change of controlled parameters of the system (for
example, its total load) or system efficiency indicator above the limit values.
6. The stochastic nature of the main factors and the need to quantify mass processes
based on probability theory determines the use of the analytical model of cloud com-
puting as a multi-threaded and multi-priority queuing system with a mixed service dis-
cipline. The model takes into account probable failures and various features and has
arbitrary distribution laws for some probable processes. Then as a mechanism of adap-
tation of СС it is possible and expedient to use the technology of dynamic adaptive
mixed discipline of providing resources to users of СС.
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