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BOUNDED ALGORITHM FOR COLLECTIVE DYNAMIC ROUTING METHOD OPTIMAL ROUTES EVALUATION IN BROADBAND
RADIO ACCESS NETWORKS
Yuliya S. Vintenkova,
Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia, vintenkova.yulia@gmail.com
Sergei V. Kozlov,
Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia, ks16v@yandex.ru
Elena A. Spirina,
Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia, selenaa_kazan@mail.ru
DOI 10.24411/2072-8735-2018-10068
Keywords: routing, integer linear programming, recurrent algorithm, computational complexity, quality criterion.
Collective dynamic routing method was proposed to increase the throughput of broadband radio access networks. Proposed method operates in two stages: analysis stage and routing stage. In routing stage proposed method defines the set of routes that will allow to transfer all collected data with the least possible delivery time. This problem is the integer linear programming problem (ILP) which means that routing stage has high computational complexity and it is difficult to apply proposed method in actual networks. There are two ways to solve ILP: the usage of exact algorithms and the usage of approximate algorithms. The quality of obtained solutions depends on applied approximate algorithms. The most efficient among them are metaheuristic algorithms. To solve the routing stage problem of collective dynamic routing method, recurrent metaheuristics-based approximate algorithm (ARO) was proposed. It was defined that ARO transmits more data than it is necessary. Additional data occur from the situation when the amount of data that can be transmitted by the selected route has greater value than amount of data to be transmitted. Thus, it is necessary to modify ARO to decrease the amount of additional data. The purpose of the work is to develop the modification of designed recurrent algorithm that considers the amount of data to be transmitted. Modified algorithm should provide solutions quality improvement and further decrease of computational complexity due to lack of additional amount of transmitted data. Collective dynamic routing operation was simulated in MATLAB to compare both algorithms. Obtained solutions were compared to exact brunch-and-bound method. It was shown that modified algorithm solutions were closer to optimal than ARO. Thus, modified recurrent algorithm with bounds will be more efficient than ARO for сollective dynamic routing optimal routes evaluation problem.
Information about authors:
Yuliya S. Vintenkova, postgraduate student, Department of Radioelectronic and Telecommunication Systems, Kazan National Research Technical
University named after A.N. Tupolevt, City of Kazan, Russia
Sergei V. Kozlov, Dr. Sc. in Technical Sciences, professor, Department of Radioelectronic and Telecommunication Systems, Kazan National Research
Technical University named after A.N. Tupolev, City of Kazan, Russia
Elena A. Spirina, Ph. D. in Technical Sciences, associate professor, Department of Radioelectronic and Telecommunication Systems, Kazan National
Research Technical University named after A.N. Tupolev, City of Kazan, Russia
Для цитирования:
Винтенкова Ю.С., Козлов С.В., Спирина Е.А. Разработка алгоритма определения набора маршрутов метода совместной динамической маршрутизации для сетей широкополосного радиодоступа // T-Comm: Телекоммуникации и транспорт. 2018. Том 12. №4. С. 68-71.
For citation:
Vintenkova Yu.S., Kozlov S.V., Spirina E.A. (2018). Bounded algorithm for collective dynamic routing method optimal routes evaluation in broadband radio access networks. T-Comm, vol. 12, no.4, pр. 68-71.
7ТЛ
1. Introduction
Collective dynamic routing method (CDR) was proposed in [1-2] to increase the throughput of broadband radio access networks (BRAN) and its efficiency was concluded. Proposed method operates in two stages: analysis stage and routing stage. The main purpose of analysis stage is to define the routes that allow to transfer collected data and to estimate potential data transfer rates of defined routes [3-4].
This article focuses on the routing stage of CDR method which defines the optimal routes set according to:
Nopt = art; mini
8 i
N ^=1
I Nh-I,b>I,. b=l
Nb >0, Nh eZ,
/ = 1,1, b = LB
(1)
where Tb - amount of data, received by node / in a T1 frame
duration on the route b, defined on analysis stage [1], /1 - amount of data to be transferred to node /.
The solution of system (1) is an integer linear problem (ILP). Optimal solutions of ILP problems are possible to obtain using the exact methods such as branch and bound, Gomory cuts, etc. They are characterized by high computational complexity if the input data is huge [5].
One of the possible ways to solve this problem is to use simplex method with rounding to gel integer solutions. However, its usage will lead to delivery time increase for greater OFDM frame durations (Fig. 1).
16
14 12 10
8 6 4 2 0
.—- / —/ / / -
96 128 160 172 180 192 256 548 -ILP --Simplex with rounding
1076
Fig. 1. The effects of rounding on delivery time
To lower the computational complexity of method used in routing stage, the recurrent algorithm was designed based on ant colony optimization probabilistic rule (Ant Recurrent Optimization - ARO) [6]. The route selection rule is described below (2):
L
b* = arg max Y(7/ f ■(/,)P
L I fi ' '
/> = l./i
/=1
As a quality criterion for optimal routes set Ai the sum of
all used routes ff was proposed in [6]. This value is directly
proportional to delivery time.
The results which were obtained in [6] proved that ARO is efficient in CDR method routing stage for reducing its
computational complexity from 80 to 5000 limes depending on input data size but with growth of the Nopt value by 11%. The
efficiency of ARO depends on the number of acceptable routes B and OFDM frame duration T . If 0 is relatively small ( i?=!32) then ARO is efficient when OFDM frame duration is greater than 166 ps. With the growth of the number of acceptable routes the border value of OFDM frame duration is also increases. This leads from fact that amount of data is directly
proportional to , therefore, \>r)jJI is in reverse proportion with
(Fig.2).
** -
r.
7"",|15
20 15 10 5 0
96 128 160 172 180 192 256 548 1076 - ILP --Simplex with rounding „., . ARO
Fig, 2. Delivery time comparison for different methods
During the execution of an algorithm the value of constantly decreases and the situation may occur when value of Jb is greater than the value of ¡¡. In that case ARO forms
optimal routes set that transfers more data than it is needed. That leads to the growth of Nopl value and therefore to the growth of
delivery time.
The main purpose of this work is to design the new recurrent algorithm which will reduce the amount of additionally transferred data and, thus, the value of # .
Problem solution
The ARO implementation described in [6] has the values of tuning parameters: a = 1, fi = I. In that case the probabilistic
route selection rule will be written as: L
b* = arg max Y 7*-// <3>
According to (3), algorithm chooses the route that will transfer the largest amount of data Jj*. As a result if jl <
the amount of transferred data will be larger llian it is needed and the value of N will increase.
To exclude that situation the introduction of value
constraint is necessary. The route selection rule for the new recurrent algorithm (Bounded Recurrent Algorithm - BRA) will be written as:
h* = arg max ^ //
h-\ji
/=1
I, > 7j h äff
(4)
7TT
It can be seen lhat BRA route selection rule (4) considers the amount of data which is left to transmit To estimate the effect of proposed constraint the series of experiments were carried out.
Analysis of ARO and BRA
To compare the efficiency of ARO and BRA for the CDR method routing stage, three different BRAN options and the analysis stage parameters were calculated hy OFDM Analyzer software |7| (Table t).
For the calculated BRAN options on the analysis stage the values of data transfer rates and possible routes were defined. The values of Jb were defined based on that parameters.
To define the value of delivery time by means of ARO and BRA, according to (1), the operation of routing stage was simulated in MATLAB software environment. The simulation was carried out for three BRAN options described in Table 1.
Table 1
BRAN options
Parameter GRAN option
! 2 3
Number of transmitters M 2 3 6
Number of receivers L 11 10 15
Number of possible routes B 132 1020 13344
The obtained results were compared to the exact I LP method - branch and bound method. It was implemented with a built-in MATLAB scripts.
Delivery time dependencies lor all algorithms and for all BRAN options are presented on the Figures 3-5.
18
.s . У
V
_____ — — — '—
___. —-—"
H-
96 192 256 548 724 1076 2128
-!LP ----ARO--BRA
Fig, 3, Delivery time dependencies for the first BRAN option
25 20 15 10 5 0
Ax,ms
■ I LP ----ARO--BRA
Fig. 4. Delivery time dependencies for the second BRAN option
22 21 20
17
*x,ms
/
/ /
__- 7
_____— --- _---- ---*
rr.)15
96 192 256 548 724 1076 2128
-1LP ----ARO--BRA
Fig. 5. Delivery lime dependencies for the third I3RAN option
Presented dependencies point that the application of BRA allow to reduce the delivery time in comparison with ARO, however, if the number of possible routes is large, BRA is equivalent to ARO. Average processor time for considered algorithms is presented in Table 2.
Table 2
Computational complexity comparison
BRAN option
I 2 3
Average processor time (branch and bound), s 7,956 35,734 502,877
Average processor time (ARO), s 0,1! 1 0,133 0,152
Average processor time (BRA), s 0,025 0,09 0,137
With a relatively small number of possible routes the computational complexity of BRA is significantly lower than ARO. With the decrease of the possible routes BRA loses its computational complexity advantage.
Conclusion
As a result of the analysis, we can conclude that for small amounts of data to be delivered and with small total number of routes used, the proposed limitation for the ARO algorithm reduces the total number of routes and thereby the delivery time, and also reduces the CDR method routing stage computational complexity.
References
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7. Kozlov S.V., Spirina E.A., Vintenkova Ju.S, (2016). Svidetel'stvo о gosudarstvennoj regisiracii program my dlja JeVM №2016663493. Programme OFDM Analyzer - Zajavka №2016661064; Registered: 8.12.2016. (in Russian)
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РАЗРАБОТКА АЛГОРИТМА ОПРЕДЕЛЕНИЯ НАБОРА МАРШРУТОВ МЕТОДА СОВМЕСТНОЙ ДИНАМИЧЕСКОЙ МАРШРУТИЗАЦИИ ДЛЯ СЕТЕЙ ШИРОКОПОЛОСНОГО РАДИОДОСТУПА
Винтенкова Юлия Сергеевна, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ,
г. Казань, Россия, vintenkova.yulia@gmail.com
Козлов Сергей Владимирович, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ,
г. Казань, Россия, ks16v@yandex.ru
Спирина Елена Александровна, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ,
г. Казань, Россия, selenaa_kazan@mail.ru
Дннотация
Целью работы является разработка алгоритма, позволяющего снизить суммарное количество маршрутов, входящих в оптимальный набор маршрутов метода совместной динамической маршрутизации. Проведён анализ ранее предложенного рекуррентного алгоритма, основанного на метаэвристическом алгоритме оптимизации муравьиной колонии, и показано, что формируемые им наборы маршрутов передают больше данных, чем это необходимо, при большем суммарном количестве используемых маршрутов. Разработан модифицированный рекуррентный алгоритм, предусматривающий введение ограничения на объём данных, передаваемый через приёмный узел, который позволяет снизить суммарное количество используемых для доставки данных маршрутов и время доставки данных, а также вычислительную сложность определения оптимального набора маршрутов. В программной среде MATLAB проведен сравнительный анализ суммарного количества используемых для доставки данных маршрутов и вычислительной сложности точного метода ветвей и границ, а также предложенного ранее и разработанного модифицированного рекуррентных алгоритмов, показавший, что введение ограничения позволило приблизить суммарное количество используемых маршрутов к оптимальному значению. Разработанный алгоритм позволяет снизить время доставки данных и дополнительно снизить вычислительную сложность этапа маршрутизации метода совместной динамической маршрутизации.
Ключевые слова: маршрутизация, целочисленное линейное программирование, рекуррентный алгоритм, вычислительная сложность, критерий качества.
Литература
1. Спирина Е.А. Оптимизация распределения информации в фиксированных сетях широкополосного радиодоступа с учетом внутрисистемных помех // Журнал радиоэлектроники [электронный журнал]. 2015. No 9. URL: http://jre.cplire.ru/jre/sepl5/5/text.pdf. (Дата обращения: 20.03.2018)
2. Винтенкова Ю.С., Козлов С.В., Спирина Е.А. Анализ эффективности метода совместной динамической маршрутизации в сетях широкополосного радиодоступа с трафиком протоколов TCP, HTTP, FTP // Журнал радиоэлектроники [электронный журнал]. 2016. No 1. URL: http://jre.cplire.ru/jre/janl6/5/text.pdf. (Дата обращения: 20.03.2018)
3. Петрова Е.А. Оценка гарантированной информационной скорости в сетях широкополосного радиодоступа с учетом внутрисистемных помех // Журнал радиоэлектроники [электронный журнал]. 2014. No 10. URL: http://jre.cplire.ru/jre/octl4/7/text.pdf. (Дата обращения: 20.03.2018)
4. Спирина Е.А., Козлов С.В. Анализ эффективности использования алгоритмов оптимального приема OFDM сигналов в IP сетях с совместной динамической маршрутизацией // Журнал радиоэлектроники [электронный журнал]. 2017. No 2. URL: http://jre.cplire.ru/jre/febl7/3/text.pdf. (Дата обращения: 20.03.2018)
5. Шевченко В.Н., Золотых Н.Ю. Линейное и целочисленное линейное программирование. Нижний Новгород: Издательство Нижегородского госуниверситета им.Н.И.Лобачевского, 2004. 154 с.
6. Винтенкова Ю.С. Анализ эффективности методов определения оптимального набора маршрутов для сетей широкополосного радиодоступа // Нелинейный мир. №6. Т. 15, 2017. С. 11-16.
7. Козлов С.В., Спирина Е.А., Винтенкова Ю.С. Свидетельство о государственной регистрации программы для ЭВМ №2016663493. Программа OFDM Analyzer - Заявка №2016661064; Зарегистрирована в Реестре программ для ЭВМ 8.12.2016.
Информация об авторах:
Винтенкова Юлия Сергеевна, аспирант кафедры Радиоэлектронных и телекоммуникационных систем, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, г. Казань, Россия
Козлов Сергей Владимирович, профессор кафедры Радиоэлектронных и телекоммуникационных систем, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, г. Казань, Россия
Спирина Елена Александровна, доцент кафедры Радиоэлектронных и телекоммуникационных систем, Казанский национальный исследовательский технический университет им. А.Н. Туполева - КАИ, г. Казань, Россия
f I л
