Engineering, 2013, 5, 1006-1011
Published Online December 2013 (http://www.scirp.org/journal/eng)
http://dx.doi.org/10.4236/eng.2013.512122
Open Access ENG
Adaptive Method of Increase of Package Network Load
Alomar Saleh1, Alomar Mhamad2, V. M. Chuprin3
1Computer Engineering Department, Al-Ahliyyah Amman University, Ardhah, Jordan
2Kyiv National University of Construction and Architecture, Kyiv, Ukraine
3National Aviation University, Kyiv, Ukraine
Received April 22, 2013; revised May 22, 2013; accepted June 1, 2013
Copyright © 2013 Saleh Alomar et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
The method of loading increase of package networks is considered. This method is based on the dynamic redistribution
of the throughput of switch equipment among carrying capacities (bandwidths) of its ports. Redistribution is fulfilled
synchronously with the pulsations of packet streams, which move over the entrances of these ports. In the complement
of switch equipment, it entered the adaptive mechanism of automatic real time redistribution of the throughput of switch
equipment among the bandwidths of ports. This mechanism allows to decrease the quantity of time intervals, when in-
tensities of packet streams are exceeded by the set bandwidths of ports, and, thus to increase the load of equipment by
useful traffic.
Keywords: Bandwidths; Dynamic Redistribution; Throughput; Adaptive Mechanism; Package Networks
1. Introduction
Adaptive control by redistribution of resources of pack-
age networks is a type of dynamic management, and car-
ried out in real time in accordance with the following
principle: to the elements of network, loading on which
presently approaches a critical point, greater part of net-
work resources is selected due to diminishing of part of
resources, which are selected by the under loaded ele-
ments. It is thus considered that the sum of all network
resources during realization of management does not
change and determine the total productivity of the involv-
ed equipment. Under network elements are understood,
foremost, as a node equipment (in particular, package
switches, routers and gateways), and also data links phy-
sically or logically. Under network resources are under-
stood as the throughput of node equipment (package
switches, routers, gateways and their ports) and (or)
bandwidth of the physical (in Hertz) or logical (in a
quantity of protocol data units (PDU), which are passed
for time unit) data links. Terms of the “carrying capacity
of port” and “bandwidth of port” in this work are consid-
ered as synonyms. Under load is understood as an amount
of intensity of streams of package traffic, namely quan-
tity of PDU, which passed on channel or processed node
equipment for time unit. Loading factor of node equip-
ment in the interval of supervision τ is determined by the
relation of average intensity (average speed) of the treat-
ment of PDU, attained on this interval τ, to the through-
put of node equipment. Loading factor of any separate port
is determined by the relation of average intensity (aver-
age speed) of the treatment of PDU on this port to the
carrying capacity (bandwidth) of this port. A typical ex-
ample of using the principle of adaptive management: a
multi-port router (or switch), whose capacity is redis-
tributed between the strips ports in sync with changes in
the intensity of packet streams that are transmitted
through these ports.
A problem consisting of the traffic of modern package
networks has pulsating poorly predictable character. The
term of “pulsation of traffic” means rapid. Sometimes
considerable changes are intensities of streams of proto-
col data units (PDU), what are going on in real time [1].
In the same time, the most known methods of traffic
management in package networks are not used by the
adaptive mechanisms of concordance of productivity of
network equipment (package switches, routers, gateways
and other) with current intensity of traffic in real time [2].
That is to say, the known mechanisms of traffic treatment
do not provide dynamic changes of bandwidths of ports
of switch equipment (SE) and, consequently, can’t quick-
ly change the parameters of tuning synchronously with
the changes of current values of traffic pulsations. Absence
of mechanisms of the dynamic retuning of parameters of

S. ALOMAR ET AL. 1007
SE ports (in particular, bandwidth of ports) results in
appearance of good few of time intervals, when intensi-
ties of PDU streams are exceeded by the set values of
carrying capacities of these ports. As a result, there is a
substantial growth of coefficient losses of PDU. In such
situation, to take possibility of network overload to the
minimum, it is necessary to limit middle speed of PDU
treatment on levels, substantially lower by comparison to
the equipment productivity. So, it is necessary to work
with the low values of network loading factor. For exam-
ple, one of the most effective methods of increasing net-
work load, known under the name “bucket of counters”
[3], due to application of the special mechanisms of pri-
ority treatment and forming of traffic, is allowed in many
cases to avoid the brief overload spades of network, but is
not allowed to provide exploitation of equipment with a
loading factor on levels higher 0.55. Consequently, there
is a ponderable reserve of increase of network load by
useful traffic.
2. General Raising of Task
We will consider simple example of SE, which has three
ports. We will consider that the general throughput of SE,
marked as H, there is a sum of carrying capacities (band-
widths) of its ports :
123
,,hh h
123
H
hh h (1)
We will also consider that a general throughput (1) is a
constant, the choice of which is conditioned vehicle limi-
tations. Intensities of package streams through SE ports
(that, package traffics) will designate accordingly as
, will designate loading factors of ports as
123
, will designate reverse loading factors of ports
accordingly as well as
123
,,nn n
,,kkk
123
,,

 and we will define them
as
3 12
12 3
12
,,
h hh
nn
  
3
n
(2)
Correlations (2) have simple physical maintenance:
they show, as far as carrying capacities of ports of SE
exceed intensities of package streams which served by
them. Direct loading factors of ports are related to the
reverse loading factors the followings correlations:
3 12
12 3
112 23
11
,,
n nn
kk k
hh h
3
1

  (3)
Direct loading factors (3) are shown by the levels of
load of ports and can not be greater, than 1. We will enter
the vector of reverse loading factors of ports in considera-
tion
1
2
3









 (4)
and vector of direct loading factors of ports
1
2
3
k
kk
k





. (5)
Vector form of record of expressions (4) and (5) sim-
plifies the process of design of work of switch equipment
at writing of the calculation programs.
Let current status of ports be characterized the set of
their carrying capacities (that, by the set of their band-
widths), intensities of streams on the entrances of ports
and proper direct and reverse loading factors of its ports.
Let there is a mechanism of dynamic redistribution of
bandwidths of ports in the direction of smoothing of
loading factors of ports (Further this mechanism will be
considered in detail). Then the process of adaptive control
of the dynamic redistribution of bandwidths can be repre-
sented as equalizations of tuning:
-for reverse loading factors;
-for direct loading factors.
k
f
kf





 (6)
Vector records of expressions (6) and (7) comfortably
use for the construction of adaptive algorithm of retuning
of SE in real time, which provide possibility of dynamic
redistribution of carrying capacities of ports in connection
with the possible pulsations of package traffics on these
ports.
A type of right parts of equalizations of tuning will be
represents below. While matters only that, as a result of
“work” of equalizations of tuning (more precisely, as a
result of process of adaptive control, which will be real-
ized software and hardware facilities of SE), values of
loading factors must become the same by the redistribu-
tion of carrying capacities of ports on condition of the
main-tenance of their sum as constant—general unchang-
ing throughput of switch equipment.
Taking into account foregoing will formulate the task
of this research as follows. It is necessary to create the
adaptive mechanism of the automatic redistribution of the
throughput of switch equipment between carrying capaci-
ties (bandwidths) of its ports. This mechanism must pro-
vides possibility of dynamic change in real time of the
bandwidth of ports [4], synchronously with changes pul-
sation intensity of PDU streams, which move over the
entrances of these ports. It is necessary to make optimiza-
tion of work of adaptive mechanism coming from the
condition of maximization of loading factor of switch
equipment at the set value of PDU loss coefficient. Thus
the criterion of optimality must correspond with the con-
dition of equality of loading factors for all ports for the
stable mode, when intensities of streams, which move
over ports, are permanent.
General scheme of work of adaptive redistributive
mechanism. Functioning of adaptive mechanism must be
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S. ALOMAR ET AL.
1008
carried out as follows. In periods of increase of stream
intensity of PDU on some from ports an adjusting me-
chanism must select this port more considerable part
from the general throughput of switch equipment [5].
Thus there must be the proper diminishing of carrying
capacity (bandwidth) of port which diminishing (or con-
stancy) of traffic intensity [6]. Dynamic changes of car-
rying capacities of ports, if they are executed synchro-
nously with the current changes of traffic pulsations (in
accordance with rules, which will be realized the mecha-
nism of the adaptive adjusting), will provide diminishing
of quantity of time intervals, when PDU stream intensi-
ties are exceeded by the set bandwidths of ports, and,
thus, will increase a loading factor.
The structural scheme of adaptive control the band-
widths of ports of Switch Device (SD) is represented on
Figure 1. As visible, the mechanism of automatic control
is plugged in the subsystem of redistributing of carrying
capacities of SD ports. This mechanism is provided by a
management the bandwidths of SD ports so that the gen-
eral throughput of SD was distributed between his ports
in real time synchronously with changes intensity of
PDU streams on SD ports.
Concordantly Figure 1 SD contains n ports, channels
of access to which are conditionally represented as
pointers. The current values of intensities of PDU
streams on each of entrance ports of SD are measured
facilities of measuring block of M. Measuring acts car-
ried out consistently in time with a beforehand certain
intervals. The results of measurements are given on the
regulator of redistribution of carrying capacities of
switch device ports (RRCP). Also on every step of meas-
urements information about the current sizes of band-
widths of all ports F moves on the regulator RRCP
from SD. The measured meanings of bandwidths were
set on the previous step of iterative procedure of adaptive
control. A regulator executes in real time iterative pro-
cedure of smoothing of current values of loading factors
of ports so that the sum of these factors was saved un-
changing. A smoothing algorithm gets out coming from
Figure 1. Scheme of adaptive control the bandwidths of
switch device ports.
the technical conditions of application of equipment. In
any case the fast-acting of the adjusting system must be
concerted with the parameters of pulsations of traffic. On
every step of iterative procedure the count of the found
new values of loading factors in the new values of band-
widths of SD ports is executed. Thus, on the output of
regulator of RRCP the stream of the managing affecting
appears on executive mechanisms of the management
system. These affecting initiate work of mechanism of
redistribution of carrying capacities of ports.
Because of high dynamism and not complete predict-
able of character of changes speed of the real streams
there is possibility of evaluation only of tendencies in
changes speed on short time intervals. It is therefore sug-
gested to use adaptive principle of construction of algo-
rithm of automatic distribution of the throughput of
switch equipment between carrying capacities (band-
widths) of its ports. The accepted law of redistribution
must be represented through the proper differential
equalization of tuning. Equalization of tuning must pro-
vide watching of tendencies in changes intensity of
streams, and also to be a differential. Only the in this case
formulated task in a raising aspect will be rich in content,
reserved and inwardly no conflicting. Obvious useful in-
vestigation of its decision will be an increase of loading
factor to at the set value of PDU losses coefficient.
General scheme of decision of task of adaptive control.
Process of the dynamic redistribution of carrying capacity of
ports at formal level it is possible to represent as differential
equalization of tuning:
f



, (7)
where

—vector of reverse loading factors of ports, аnd
f

—right part of tuning equalization, the type of which
will be specified below. The values of loading factors
must become the same by the redistribution of values of
bandwidth each of ports upon condition of maintenance
of their sum on permanent level. Numeral integration of
tuning equalization on every step of adaptive control can
be executed, for example, in obedience to the method of
Euler:




tht fth

  
 , (8)
where h—step of numeral integration.
On the current step of integration have a new set of
loading factors of ports, the values of which differ from
each other on a less size, what it took place on the previ-
ous step of integration. The new recommended values of
carrying capacities of ports, the sum of which is equal to
the general throughput of switch equipment, corresponds
the new values of loading factors of its ports. A general
conclusion is such: for the decision of task of adaptive
control of the bandwidths of switch equipment ports on
the basis of looking in real time after changes intensity of
package traffic on these ports it is necessary to decide the
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S. ALOMAR ET AL. 1009
task of the dynamic smoothing of loading factors of
switch equipment ports. Thus it comfortably uses some
from the variants of method of the dynamic programming,
which takes into account quality of transient process in
the dynamically guided systems.
Thus, the task of the dynamic tuning of switch equip-
ment is taken to the task of smoothing of loading factors
of its ports. For its practical decision through the method
of the dynamic programming it is necessary to specify
tuning equalization, set an optimizing functional and write
down the proper by it equalization of Bellman. Thus it is
also necessary to set the type of function of Bellman. It
will allow taking the task of the dynamic programming to
the task of the analytical constructing of regulators, the
decision of which, in same queue, is taken to the decision
of equalization of Rikatti. All of it must be carried out
“simultaneously”, as all adopted higher fragments, which
make maintenance of task of the analytical constructing of
regulators, not exist separately, but must exactly corre-
spond each other.
3. Decision of Task t he Method of the
Dynamic Programming
We will consider the task of smoothing of values a few
the variables on condition of maintenance of their sum.
Each of variables physically presents a size, reverse a
loading factor of the proper switch equipment port. That,
the values of loading factors become the same by the re-
distribution of carrying capacities of ports on condition of
maintenance of their sum, equal the throughput of switch
equipment. Let these variables form the vector of Ń. Will
stipulate the conduct of components of vector by tuning
equalization, specify the type of which as follows:
NCu
. (9)
In equalization (9) ù—vector of managing influences,
which is found as a linear function of components of vec-
tor Ń, аnd C—matrix of regulative interconnections, the
quantity of columns in which corresponds the quantity of
ports of switch equipment. The quantity of matrix lines
corresponds the maximally possible number of pairs of
ports, here in every pair the number of even one port dif-
fers from a number in any other pairs of ports. That, iden-
tical pairs are absent in the matrix of C, but all pairs are
made from one great number of ports. The accepted lay-
ing out on pairs establishes regulative connections between
all possible pairs of switch equipment ports. Thus the or-
der of location of pairs in the matrix does not have of value.
For example, will consider Switch Device with three
ports:
1
2
3
n
Nn
n





. (10)
We will appoint the matrix of regulative connections of
C in the following kind:
10 1
11 0
011
C










(11)
Between the first and third port regulative interconnec-
tion, which consists in that part of the throughput of SD is
passed from the third port on first one, will be realized,
that is reflected the proper signs of single elements of
matrix. The second line accordingly reflects the transmis-
sion of part of the throughput of SD from the first port on
third one. The third line reflects the transmission of the
throughput of SD from the second port on third one. As
visible, between three ports (as have three columns of
matrix of C) it is possible in pairs to set three regulative
interconnections that in the construction of matrix repre-
sented three lines. For the reflection of interconnections
between four ports there must be six lines in the matrix of
C, and between five ports are ten lines. We will mark
possibility of ambiguous construction of matrix of C. In
particular, columns and lines can be changed placed. The
transposed record of matrix of C is also possible.
We will find the type of function, suitable for con-
structing of regulator of RRCP (look Figure 1). For this
purpose we will present multiplication of vector (10) and
matrix (11) in a kind


T
123
122 331
10 1
,,11 0
011
,,
NCnn n
nnnnnn








 

. (12)
Multiplication (12) is presented by a transposed vector,
that row-vector. Every component of row-vector is de-
termined a difference between components of vector of Ń.
Further we will appoint the diagonal positively certain
matrix of gravimetric coefficients, taking into account
“weight” of every regulative interconnection:
11
22
33
00
0
00
p
Pp
p





0


n





(13)
And, finally, using a matrix (13), will build the follow-
ing quadratic form:



TT
111 2
1223312223
333 1
22 2
11 1222233331
00
,,0 0
00
.
NCPCN
pn
nnnnnnpn n
pnn
pnnp nnpn n



 




 

(14)
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As visible, expression (14) presents the self-weighted
sum of squares of difference of variables, which con-
stituents vector of Ń. comfortably to use expression (14)
for a search the function of Bellman, and also optimizing
functional, by which it is possible to take the task of the
dynamic programming to the task of the analytical con-
structing of regulators. Expression (14)—it is positively
certain and equals a zero only in the case when all vari-
ables equal a zero.
Will execute forming of optimizing functional taking to
account that it is necessary to provide the set speed of
process of smoothing of variables, and also a periodic (not
shake) character of changes of the guided variables. For
these terms optimizing functional I comfortably to set in a
kind

TTT TT
0
d

I
NCPCNNCQCN uRut 


 
 , (15)
where Ń is vector of the guided variables, T is charac-
ter of operation of transposition of matrix, C is a matrix
of regulative interconnections, P is the - measured
quadratic symmetric not negatively certain matrix of
gravimetric coefficients,
 —it is a positive constant (in-
dex of fading in function of Bellman), Q is the
mm
mm

measured positively certain symmetric matrix of quad-
ratic form (of function of Bellman), ù is a vector of
managing influences, R is the -measured symmet-
ric positively certain matrix of gravimetric coefficients at
managements.
mm
The first member of subinterval expression in a func-
tional (15), as specified already, presents the self-
weighted sum of squares of difference (through the coef-
ficients of matrix of R) of the evened variables, which
constituents vector of Ń. What this sum anymore or than
longer smoothing process, the anymore value of opti-
mizing functional. Therefore minimization of functional
results in smoothing of the guided variables. The second
member in a functional presents the function of Bellman.
On optimum trajectories the Bellman-function decreases
at a speed of not less, than multiplication of it and fading
index  . By the selection of value of  -index, in the con-
ditions of the closed system of adjusting, it is possible to
set the desired speed of process of smoothing of the
guided variables. In practice the index of fading of Bell-
man-function is used for the concordance of speed of
work of mechanism of redistribution of carrying capaci-
ties of SD ports and current dynamics of pulsations of
package traffic, acting on these ports. The third member
of functional (15) determines the “conduct” of regulators,
in particular limits a management and from the formal
point of view locks procedure of determination of opti-
mum management.
Will search the Bellman-function as a quadratic form:
TT
VNCQCN
Taking into account expressions for an optimizing
functional (9) and set Bellman-function (16) equalization
of Bellman will have the following kind:
TTT T
TT
T
0min
uNCPCN NCQCN
VV
uRu NN
DN DN







 




 

. (17)
If to put in equalization (17) expression for tuning
equalization, will get:


TTT TT
TT TTT
0min
uNCPCNNCQCN uRu
uCCQCN NCQCCu
 

 




1
. (18)
By differentiation on the vector of management of ex-
pression (18) with the subsequent equating of the got re-
sult to a zero will define the vector of management of ù as
1T T
TTT
,
.
uRCCQCN
uNCQCCR







 (19)
The got management (193) is certain through the un-
known quadratic form matrix of Q, entering in the com-
plement of expression (16), which determines the Bell-
man-function. For determination of Q-matrix will put
expression (19) in equalization of Bellman (18). After
some transformations will get equalization of Rikatti in
the following form:
T1T 0
22
PQ EEQQCCRCCQ



 . (20)
Deciding equalization (20), will find the sought-after
Q-matrix. Putting the found matrix in expression (20)
will get final expression for a regulator, which will have
the following kind:
1T T
NCRCCQCN



. (21)
Analyzing expression (21), easy to notice that at any
initial values of vector of the guided variables the ad-
justing system aspires to the stable state, when compo-
nents of this vector is equal between itself, and the sum
of values of components during all process of adjusting
remains permanent. So set the problem it can consider
decided.
It is important to mark that before the beginning of the
use of SD it is necessary to co-ordinate speed of work of
mechanism of redistribution of carrying capacities of SD
ports with the current dynamics of pulsations of package
traffic by the selection of value of index of fading of
Bellman-function. In practice the index  is used for the
concordance of speed of work of mechanism of redistri-
bution of carrying capacities of switch equipment ports
with the current dynamics of pulsations of package traf-
fic, acting on these ports.

. (16)
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S. ALOMAR ET AL.
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1011
4. Basic Results and Conclusions
1) Absence of mechanisms of the dynamic retuning of
parameters of switch equipment ports in real time (in
particular, retuning of bandwidths of its ports) in the
conditions of considerable traffic pulsations results in
appearance of good few of time intervals, when intensi-
ties of streams of protocol block units (PDU) are exceed-
ed by the set values of carrying capacities of these ports.
As a result, there are substantial losses of PDU even in
the conditions of comparative to the small load of equip-
ment by useful traffic. A method, which is based on the
dynamic redistribution of the throughput of switch
equipment between carrying capacities (bandwidths) of
its ports in real time, can substantially increase the load
of equipment and, at the same time, save the values of
package loss coefficient on possible levels.
2) The structural scheme of adaptive control of the
bandwidths of switch equipment ports is considered. In
basis of scheme, the process of tracking after changing
intensity of package traffic on ports of switch equipment
in real time is fixed. The proper changes of the band-
widths of switch equipment ports are fixed so that more
high intensity streams are taken considerable parts of the
general throughput of switch equipment.
3) The formal task raising of dynamic redistribution of
the general throughput of switch equipment of package
networks between the carrying capacities (the band-
widths) of its ports in real time is executed. The general
decision method of this task is offered. It is marked that
its decision is taken to the decision of task of the dy-
namic smoothing of loading factors of switch equipment
ports on condition of maintenance of their sum. It is also
marked that in the process of decision it is necessary to
execute the analytical constructing of adaptive regulators
of bandwidths of ports in the dynamic mode taking into
account quality of transient process of adjusting. It is for
this purpose expedient to use one of varieties of method
of the dynamic programming of Bellman.
4) In accordance with the chosen method of the dy-
namic programming, the type of Bellman’s function is
set and the proper equalization of tuning of the automatic
control system is synthesized, which are allowed to get
mathematical expression for an optimizing functional
taking into account that it is necessary to provide the set
speed of process of smoothing of variables, and also a
periodical (not shake) character of changes of the guided
variables. Further Bellman’s equation is built. The con-
trol vector is found. The substitution of the found control
vector in Bellman’s equation is gotten equalization of
Rikatti. Deciding Rikatti’s equalization, after some ma-
thematical transformations, final expression is gotten for
a regulator in an analytical form. Useful property of the
built regulator is exposed: For any initial values of the
controlled variables, vector control system tends to be a
steady state, the components of this vector are equal, and
the sum of the components throughout the regulatory
process remains constant, so that the task can be consid-
ered solved.
5) Decision results of dynamic redistribution task of
basic resource of switch—to his throughput—can be
used for the increase of load of package networks in the
conditions of considerable pulsations of useful traffic.
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