=Paper=
{{Paper
|id=Vol-2608/paper30
|storemode=property
|title=Inter-domain routing method under normalized quality of service based on hierarchical coordination
|pdfUrl=https://ceur-ws.org/Vol-2608/paper30.pdf
|volume=Vol-2608
|authors=Oleksandr Lemeshko,Maryna Yevdokymenko,Zhengbing Hu,Oleksandra Yeremenko
|dblpUrl=https://dblp.org/rec/conf/cmis/LemeshkoYHY20
}}
==Inter-domain routing method under normalized quality of service based on hierarchical coordination==
https://ceur-ws.org/Vol-2608/paper30.pdf
Inter-domain routing method under normalized Quality
of Service based on hierarchical coordination
Oleksandr Lemeshko1[0000-0002-0609-6520], Maryna Yevdokymenko1[0000-0002-7391-3068],
Zhengbing Hu2[0000-0002-6140-3351] and Oleksandra Yeremenko1[0000-0003-3721-8188]
1
Kharkiv National University of Radio Electronics, Kharkiv, 14 Nauky Ave., Ukraine
2
Central China Normal University, Wuhan, Hubei, P.R.China
oleksandr.lemeshko.ua@ieee.org, maryna.yevdokymenko@ieee.org,
hzb@mail.ccnu.edu.cn, oleksandra.yeremenko.ua@ieee.org
Abstract. The inter-domain routing method under normalized Quality of
Service (QoS) based on hierarchical coordination in a Software-Defined
Network (SD-WAN, Hybrid SD-WAN) is proposed in the paper. The novelty
of the method is that the routing solutions are aimed at ensuring the normalized
QoS in terms of average transmission rate and average end-to-end packet delay.
The method is based on the use of a decomposition flow-based routing model,
which consists of the inter-domain routing interaction and ensuring the
normalized QoS conditions that obtained during tensor network modeling.
Therefore, the inter-domain QoS routing problem was presented as an
optimization problem with a quadratic optimality criterion. A number of
numerical examples confirmed the efficiency and effectiveness of the proposed
method in terms of providing the normalized QoS within the finite number of
iterations. Reducing the number of such iterations helps to decrease the amount
of service traffic transferred between routers and SDN controllers at different
levels, as well as minimize the time for solving the inter-domain QoS-routing
task.
Keywords: Method, Inter-domain routing, Hierarchical coordination, Quality
of Service, End-to-end delay, SDN.
1 Introduction
Providing a specified level of Quality of Service for user requests has been and
remains the primary purpose of the functioning of modern infocommunication
networks (ICNs), in which various technological means and protocols of distribution
and reservation of network resources, traffic management, etc. are involved. At the
same time, the problem of QoS provision is exacerbated in the conditions of
considerable territorial distribution and heterogeneity of ICNs, which significantly
influence the scalability of traffic management solutions.
An effective way to increase scalability is to use multi-domain Software-Defined
Networks (SDN) when a significant list of traffic management functions is translated
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
to many network operating system controllers, which in turn are built into a clear
functional hierarchy [1-6].
Assigning a separate controller for each network domain contributes to a
significant reduction in the amount of service traffic circulating on the network, the
size of the routing tables, and improving the timeliness of traffic management tasks
solutions, among which routing is of an important consideration. On the other hand,
full implementation of these advantages requires a radical modernization of models,
methods, and protocols of routing with their functional adaptation to the features of
the hierarchical architecture of SDN-controllers and the multidomain structure of
ICNs.
2 Overview of existing solutions regarding hierarchical routing
Currently the most well-known protocols that implement the principles of hierarchical
multi-domain routing are considered to be OSPF and Integrated IS-IS used in IP
networks, as well as the somewhat outdated PNNI in the ATM network [4-6].
However, these protocols still use Dikstra's combinatorial algorithm to calculate
routes, which does not take into account the hierarchical features of network
construction. It should also be added that QoS requirements in the same protocols are
organized indirectly only through routing metrics, which are usually related to the
bandwidth of ICN links and paths. Implementing such an approach does help improve
the overall QoS level on the network, but does not guarantee the numerical values of
the end-to-end QoS indicators, such as the average packet delay for a particular flow.
A number of solutions have been proposed in scientific papers on hierarchical
routing [7-14], which are mainly represented by flow-based models and optimization
methods of calculation. In articles [7, 8, 12-14], such solutions are adapted to the
features of SDN architectures. An important feature of the results obtained in [9-11] is
that they are based on the use of the provisions, principles, and postulates of the
theory of hierarchical multilevel systems [15, 16]. First, these solutions impose
several hierarchical levels of decision-making on routing in ICNs. Second, they imply
a decomposition representation of a network mathematical model, which can be
described, for example, by a system of differential equations [17]. Third, a mandatory
component of hierarchical routing is the coordination process, which is implemented
by the top level in relation to the routing decisions of the lower levels.
From the point of view of QoS routing implementation the approach [18-24] is
particularly noteworthy since is based on the use of tensor research methodology,
within which it was possible to obtain in an analytical form the conditions for
ensuring the Quality of Service on a number of indicators – bandwidth, average delay,
probability of packet loss. Therefore, in this paper, we will propose the solution to the
problem of hierarchical coordination of inter-domain routing in the Software-Defined
infocommunication network with the provision of normalized QoS, that is when the
requirements for the level of end-to-end QoS are set for each domain in the form of
corresponding norms. The presented solution is a further development and integration
of the results obtained in [9-11, 23, 24].
3 Decomposition model of inter-domain QoS routing in
Software-Defined infocommunication network
Suppose that the network structure is represented as an oriented graph G ( R, E ) ,
where R is the set of vertices that model the routers and E is the set of graph edges
that describes the communication links of the network. In the general case, a packet
flow is generated when providing a particular information service on the network. We
denote the number of flows circulating in the network by K , then K K is the
power of the set, which quantitatively characterizes the total number of flows in the
ICN. For each k th flow ( k K ), its average packet rate (intensity) kreq is known,
which is measured in packets per second (1/s) and defines the requirements for the
ICN bandwidth allocated to that flow.
When developing a decomposition model of inter-domain routing, suppose that the
network consists of N interconnected subnets – domains. Then let each p th
individual domain in the ICN be described by the graph G subgraph
G p ( R p , E p ) , where R p Rip ; i 1, m p is the set of routers of the p th
domain, E p Eip, j ; i , j 1, m p , i j is the set of links connecting the routers of
the p th domain, m p and n p are the total numbers of the routers and communication
links in the p th domain respectively.
During network decomposition, the boundary between domains passed through
network routers, as implemented, for example, in OSPF [10]:
R p R q 0 and E p E q 0 , p q , (1)
that is, some network routers may belong to several adjacent domains at a time. We
also define for each p th domain a set of border routers B p ( B p R p ). In turn, the
entire set of the p th domain border routers can be divided into two subsets: Binp , k is
the subset of the border routers through which the packets of the k th flow income
p,k
into the p th domain; Bout is the subset of the border routers through which the
packets of the k th flow outgo from the p th domain. For each communication link
Eip, j , we denote its bandwidth ip, j , which is measured in packets per second (1/s).
As a result of solving the hierarchical inter-domain routing task for each p th do-
p,k
main, it is necessary to calculate the routing variables xi, j that characterize the frac-
p
tion of the k th packet flow transmitted in the link Ei, j E p . Then, for each p th
domain router, the k th flow conservation conditions must be met to ensure the con-
nectivity of intradomain sections of the inter-domain routes.
If the p th domain is transit for the k th packet flow, then such conditions take the
form:
p,k p,k
xi , j x j ,i 1;
B p , k B p E p E p p
E j ,i E p
in i, j
p,k p,k
xi , j x j ,i 0; (2)
E p E p p
E j ,i E p
i, j
p,k p,k
xi , j x j ,i 1.
B p , k B p E p E p p
E j ,i E p
out i, j
The system of equations (2) must be met separately for each k th packet flow. The
first condition of the system (2) covers all the border routers through which the k th
flow arrives at the p th domain. The second condition in (2) is introduced for internal
p th domain routers that are transit for the k th packet flow. The third condition must
be satisfied for all border routers through which the k th flow outgoes from the p th
domain.
If the k th packet flow arrives at a network through the p th domain, and its source
is the router Rip , for example, then for this network the first condition of the system
(2) will be somewhat simplified and will look like: xip, ,jk 1 . The rest of the
p
Ei , j E p
equations in the system (2) will remain unchanged. When the router Rip from the
p th domain is the k th packet flow receiver, only the last equation of system (2) will
be simplified and will look as follows: x pj ,,ik 1 .
p
E j ,i E p
In addition, to prevent links congestion on the p th network domain, it is important
to fulfill the following conditions:
k p, k p
λreq xi, j i, j , p 1, N . (3)
kK
Let us denote as λip, j,k λreq
k
xip, ,jk as the average intensity of the k th packet
kK
p
flow transmitted in the link Ei, j E p . Then, when implementing multipath routing,
the routing variables are imposed by the constraints:
0 xip, ,jk 1 . (4)
Variables (4) are the coordinates of the routing vectors x kp that set the result of the
solution for the k th flow routing problem in the p th domain. During distributed
calculation of vectors x kp across each p th domain, it is important to ensure the struc-
tural and functional connectivity of inter-domain routes that are traverse multiple
routers of different domains. In order to ensure inter-domain connectivity, the model
(1)-(4) introduces the following inter-domain interaction conditions [10]:
С kp,q x kp Сqk, p xqk , p, q 1, N , p q , k K , (5)
where С kp,q is the interaction matrix of the p th and q th domains of the size
m p, q mxp ,k ; m p , q is the number of routers through which the border between the
p,k
p th and q th domains passes; mxp ,k is the number of coordinates xi, j of the x kp .
Thus for the network structure shown in Fig. 1 that consists of two domains, the
boundary passes through two routers. In the designations of the first domain (Fig. 1)
the border routers are R31 and R14 , while in the designations of the second the border
routers are R12 and R22 . In the gaps of communication links, their bandwidth is
shown (1/s).
Domain 2
Domain 1
R42
R31 R12 1
req
R12
150
R32
R11
1 R41 R22
req
Fig. 1. An example of the ICN structure to be investigated.
4 Terms of providing normalized Quality of Service over
domains in the infocommunication network
For each network flow, its transmission rate, average end-to-end delay, and packet
loss probability, certain limits are set with respect to their boundary (minimum and/or
maximum) values, which determine the level of customer QoS. In case of support of
multidomain ICN architecture, the provision of set values of the end-to-end QoS
indicators is often realized on the basis of their previous normalization. Let us
introduce the following notation:
kreq is the requirement for the boundary value of the average end-to-end delay of
the k th packet flow in the ICN, which is measured between the incoming router of
the source domain and the outgoing receiver router of the k th packet flow;
p, k
req is the normalized requirement for the average delay of packets of the k th
flow in the ICN p th domain ( p,k ).
Thus, for each flow k K , the requirements kreq for the average end-to-end delay
of packets are distributed (normalized) in some way between separate domains with
the following conditions:
N
p,k
req kreq and p,k req
p,k
. (6)
p1
Within the framework of this study, it is considered that kreq and req
p, k
are prede-
termined. This raises the problem of formulating the conditions of normalized QoS on
the network in terms of calculating expressions for p,k . To obtain such conditions it
is necessary to use the functionality of tensor analysis of networks. The results pre-
sented in [18-25] allowed obtaining analytical expressions for calculating the values
of end-to-end QoS indicators, which were evaluated and analyzed between a pair of
individual routers. For the case considered in this study, in the structure of an arbi-
trary network domain, multiple routers may simultaneously belong to each of the sets
p, k
Binp,k and/or Bout , which is a special characteristic of transit domains. The following
methodology is proposed to take into account the features of the multidomain ICN
architecture.
1. During the k th flow routing for each p th domain the pair of routers Rinp and Rout
p
is determined, between which p,k will be calculated. In the domain that served as
the source of the k th packet flow, the Rinp was the router through which the k th
flow arrived into the ICN. For the domain that served as the k th packet flow
p
receiver, the Rout was the router through which the k th flow outwent from the
ICN.
p
p
2. Additional imaginary routers Rin and Rout , which become adjacent for routers
p,k p, k
from Bin and Bout sets respectively through imaginary communication links,
are introduced to the ICN structure at the boundaries of the p th domain that
interacts with other domains through two or more routers. If the boundary between
the p th and q th domains passes through several routers, as shown, for example,
p
p
in Fig. 2, then the imaginary routers Rin and Rout coincide. The introduction of
imaginary routers is conditioned by the fact that value p,k can now be evaluated
p p
and analyzed already between a pair of routers Rin and Rout on the basis of the
approach proposed in [10, 18]. In order to prevent impact of packet delays p,k in
imaginary communication links that connect real border routers to imaginary ones,
their bandwidths must go to +∞ during the calculations.
3. With the aim of further geometrization of the ICN structure, the continuous
numbering of the communication links in the p th domain is adopted. For this
purpose, the set of network links belonging to the p th domain is denoted as
V p v zp , z 1, n ~p , where n ~p and m ~p are the number of communication links
and routers respectively in the p th domain taking into account the introduced
imaginary elements of the network. Thus, for an example of the structure of ICN
shown in Fig. 2, n1~ n2~ 6 and m1~ m2~ 5 . Such an increase in the number of
communication links and routers leads to an increase in the number of variables
xip, ,jk with the condition (2) being replaced by the following flow conservation
conditions on the p th domain routers:
p ,k p,k p p
xi , j x j ,i 1, if Ri Rin ;
Eip, j E p p
E j ,i E p
p ,k p,k p p p
xi , j x j ,i 0, if Ri Rin , Rout ; (7)
E p E p p
E j ,i E p
i, j
x p ,k x jp,,ik 1, if Rip Rout
p
p p i, j
.
p p
Ei , j E E j ,i E
Domain 2
Domain 1
R42
R31 R12 1
R12 req
150
R32
R11
1
req R14 1
R22
Rout Rin2
1 ,1 2 ,1
Fig. 2. The principle of introducing imaginary routers and links into the network structure.
According to the methodology of tensor modeling of ICN [18, 19, 23, 24], the do-
main structure determines the anisotropic space formed by coordinate paths. Network
edges (links), circuits, interpolar paths, and node pairs can act as coordinate paths
where the network poles are the routers Rinp and Rout
p
. The dimension of this space is
determined by the total number of edges in the network and is equal to n ~p [18, 24].
From all possible interpolar (namely, end-to-end from the source to the destination)
paths in the p th domain, we choose p linearly independent i , i 1, p . Whereas
the set of internal node pairs is represented by the set j , j 1, p . These sets form
the basis of the n ~p -dimensional space of the network structure:
~p n~p m~p 2 ; ~p m~p 2 ; n~p ~p ~p . (8)
When routing the k th flow in the selected space, the p th domain can be repre-
sented by a mixed bivalent tensor Q T , where is the tensor multiplication
operator and the components of the tensor are a univalent covariance tensor of aver-
age packet delays T and a univalent contravariant tensor of the average intensities of
flows in the coordinate paths of the selected domain. Further, the index p in all
tensor quantities and their projections will be omitted for greater clarity of informa-
tion perception, because it is always a question of only physical quantities that are
associated with the p th domain. The tensor can be written in the index form:
qij j i , ( i, j 1, n~p ), (9)
where j is the average packet delay along the jth coordinate path (s); i is the
average packet flow intensity along the ith coordinate path (1/s).
In the selected n ~p -dimensional space, the tensor (9) will be set in one of two
coordinate systems. The first is the coordinate system (CS) of the network edges
v , k 1, n , the second one is the CS of linearly independent interpolar paths
k
~
p
i , i 1, p and internal node pairs j , j 1, p , the projections of the tensor in
which will be denoted by the index .
In the case of modeling the operation of the network routers interface by the
queuing system M/M/1, the coordinates of the projection of the metric tensor G in
the basis of edges Gv represented by diagonal elements of the matrix will be
determined by the expression:
gvzz vz (z Βvz ) , (10)
where vz is the intensity of the k th th flow in the z th communication link when
using the continuous link numbering; Βvz is the intensity of the aggregated flow in the
z th communication link, which is defined as follows:
vz kreq xip, ,jk , Βvz kreq xip, ,jk under v zp Eip, j . (11)
kK
Projections of the twice contravariant metric tensor G when changing the CS of its
consideration are transformed by the law
G At Gv A , (12)
where G is the projection of the metric tensor in the CS of interpolar paths and
internal node pairs; A is the n~p n~p matrix of covariant coordinate transformation in
the transition from the CS of interpolar paths and internal node pairs to the basis of
edges; is the operation of the matrix transposition.
t
As shown in [23, 24], the matrix G can be represented as
1 2
G | G
G , (13)
3 4
G | G
1 4
where G (t ) is the square ~p ~p submatrix; G (t ) is the square ~p ~p sub-
2 3
matrix; G (t ) is the ~p ~p submatrix; G (t ) is the ~p ~p submatrix.
Then, as shown in [22, 23], the conditions for ensuring the normalized QoS in the
p th domain when routing the k th flow (8) take the form:
1 1
3
G G G G Treq ,
2 4
(14)
1
where is the matrix inversion operation; is the ~p -dimensional vector of
flow intensities in the interpolar paths of the selected domain with coordinates i
that are connected by the following condition
i req
k
; (15)
i 1
Treq is the ~p -dimensional vector of average packet delays in the interpolar paths
of the selected domain, each of which coordinates i corresponds to the condition
i req
p ,k
, i 1, ~p . (16)
5 Method of hierarchical coordination inter-domain routing in
Software-Defined infocommunication network with provision
of normalized QoS
The hierarchical coordination inter-domain routing method will be based on
solving an optimization problem for the calculation of vectors of routing variables x kp
( p 1, N , k K ) subject to constraints (3)-(7), (14)-(16) by using the following
optimality criterion:
min F , F ( x kp )t H kp x kp , (17)
pN kK
where H kp is the diagonal matrix of routing metrics of links of the p th domain.
The goal coordination principle [9-11, 15, 16] will be used to solve the
optimization problem (17). Then, moving to the problem at the unconditional
extremum, it is necessary to maximize by the Lagrangian of the form:
N N N
L ( x kp )t H kp x kp ( μ kp,q )t (С kp,q x kp Сqk, p xqk ) , (18)
p 1 kK p 1 q 1 kK
q p
where is the vector of Lagrange multipliers; p,q are subvectors of the vector
assigned to each of the vector-matrix domain interaction conditions (5).
Given that within the principle of goal coordination, the Lagrange multiplier vec-
tors are calculated at the upper level and for the lower level are values known, the
N
expression (18) can be represented in the following decomposition form: L L p ,
p 1
where
N N
L p ( x kp )t H kp x kp ( μ kp,q )t С kp,q x kp ( μqk, p )t С kp,q x kp , (19)
kK q 1 kK q 1 kK
pq p pq p
where K p is the subset of flows incoming to the p th domain from other domains;
K p is the subset of flows outgoing from the p th domain ( K p , K p K ).
Within the framework of the proposed method, the general problem of hierarchical
coordination of inter-domain routing is formulated as a two-level optimization prob-
lem:
1. At the lower level, SDN controllers of the domains calculate the routing variables
represented by vectors x kp during the minimization of Lagrangians (19) under
constraints (3), (4), (7), and (14)-(16). The results of the calculations are sent to the
top level, namely to the SDN controller of the network.
2. At the top level, the SDN controller of the network coordinates the lower-level
solutions to ensure that the conditions (5) are met by modifying the Lagrange
multiplier vectors:
μ kp,q (a 1) μ kp,q (a) μkp,q , μ kp ,q ( x) *
С p ,q x kp Сq , p xqk , (20)
xx
where a is the iteration number; μ kp,q is the gradient of the function (19).
3. The modified values of the Lagrange multiplier vectors μkp,q are transmitted to the
lower level for the calculation of new routing vectors x kp . The calculation process
becomes iterative. Inter-domain route connectivity will be ensured when the
gradient values (20) approach zero.
From the technological point of view, minimizing the number of iterations of the
procedure (20), when obtaining the desired optimal solution, aims to reduce the
amount of service traffic transmitted between hierarchical levels about the results of
calculations at each iteration, and to decrease the total time of solving the problem of
inter-domain routing in the ICN as a whole [9-11].
6 Investigation of the proposed method of hierarchical
coordination inter-domain QoS routing
Let us investigate the proposed method of hierarchical coordination inter-domain
routing in the ICN in order to confirm its functionality, adequacy, and efficiency of
the obtained calculation results. In the framework of the numerical example, let us
analyze the peculiarities of the solutions to the problem of hierarchical coordination
inter-domain QoS routing for the variant of the infocommunication network structure
shown in Fig. 1. As an example, consider a single-flow case when, in the course of a
study, the requirements for the QoS level in a multidomain network were given by the
following parameters:
1req 350 1/s and 1req 100 ms, 1,1 2,1
req 40 ms, req 60 ms. (21)
Then Fig. 3 presents a solution to the problem of inter-domain QoS routing prior to
the start of the coordination procedure (20). In Fig. 3, the link breaks show the follow-
ing data (top to bottom): packet flow intensity, bandwidth, and average packet delay
in this link.
The characteristic feature of the obtained solution (Fig. 3) is that the conditions for
providing the normalized QoS (6), (21) are fulfilled: the maximum end-to-end delay
in the first domain was 38.5 ms and in the second domain it was 48.6 ms. However,
the conditions for inter-domain interaction (5) were not met. Inter-domain route
connectivity was ensured after the third iteration of the coordination procedure (20).
Domain 1 Domain 2 R42
R21 R12
R31 129,43 350
150
48,6
130,5
350
R32
R11 4,6 R14 R22
350
Fig. 3. The initial solution to the problem of inter-domain QoS routing under requirements (21).
The coordinated solution to the problem of inter-domain QoS routing is presented
in Fig. 4, within which the specified normalized values of the average packet delays
in each of the domains (21) were provided: in the first domain the maximum end-to-
end delay was 38.5 ms, and in the second domain it was 58.3 ms.
Domain 1 Domain 2 R42
R12 R31 R12 87,66 350
150
16
44,47
350
R11 3,3 R14 R32
R22
350
Fig. 4. The final (coordinated) solution to the problem of inter-domain QoS routing under re-
quirements (21).
7 Conclusion
The paper proposes a method of hierarchical coordination inter-domain routing in
SDN, which is a further development of the solutions presented in [9-11, 23, 24]. The
novelty of the method is that the routing solutions obtained with it are aimed not only
at increasing the scalability of ICN, but also at ensuring the normalized QoS in terms
of average transmission rate and end-to-end average packet delay.
The proposed method is based on the use of the decomposition flow-based model
of inter-domain routing (3)-(7). The model was supplemented by the conditions for
the provision of normalized QoS (14)-(16), which were formulated in an analytical
form on the basis of tensor modeling of the ICN (8)-(13).
Within the proposed method, the problem of inter-domain QoS routing was
presented in the optimization form with a quadratic optimality criterion (17). The goal
coordination principle was used to solve the optimization problem. During the study
of the method, its functionality and efficiency were confirmed in terms of ensuring
the normalized QoS. It was found experimentally that the method converged to the
optimal solution for the finite number of iterations (20). For the structure of the
network that was selected as the test (Fig. 1), the number of iterations of the
coordination procedure (20) with the proper setting of the gradient search did not
exceed three iterations. Reducing the number of such iterations helps to decrease the
amount of service traffic that is transmitted across the network between routers and
SDN controllers at different levels, as well as minimizing the overall time for solving
the inter-domain QoS routing task.
The prospect of further research in this area is that the QoS metrics, which each
domain should provide, are not set statically, for example, on the SDN controller, but
can be redistributed dynamically between domains with the fulfillment of the
conditions (6) in accordance with their structure, capacity, and utilization.
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