=Paper=
{{Paper
|id=Vol-2654/paper18
|storemode=property
|title=Investigation of Tensor Approach for Providing Multimedia Quality in Infocommunication Networks
|pdfUrl=https://ceur-ws.org/Vol-2654/paper18.pdf
|volume=Vol-2654
|authors=Maryna Yevdokymenko
|dblpUrl=https://dblp.org/rec/conf/cybhyg/Yevdokymenko19
}}
==Investigation of Tensor Approach for Providing Multimedia Quality in Infocommunication Networks==
https://ceur-ws.org/Vol-2654/paper18.pdf
Investigation of Tensor Approach for Providing
Multimedia Quality in Infocommunication Networks
Maryna Yevdokymenko[0000-0002-7391-3068]
Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
maryna.yevdokymenko@ieee.org
Abstract. An approach based on a tensor mathematical routing model, due to
which a given level of quality of experience is provided according to the
Multimedia Quality indicator, is proposed in the paper. The QoE routing
problem has been presented in the optimization form. The tensor formalization
of the QoE routing model allowed obtaining the conditions for ensuring the
specified values of Multimedia Quality in the analytical form, which were used
as the main restrictions in solving the formulated optimization problem.
Keywords: multimedia quality, quality of experience, end-to-end delay, packet
loss, tensor, routing.
1 Introduction
For the past few years, there has been a sharp increase of multimedia traffic in
infocommunication networks. This is dictated by emergence of many multimedia services
and applications provided to end users. In this regard, due to a shortage of the network
resource in the existing infocommunication networks, a significant decrease in the Quality
of Service (QoS) indicators occurs. Therefore, today the problem of providing the required
values of several network indicators simultaneously – bandwidth, delay, jitter and packet
loss [1-3] – is quite acute, especially when transmitting multimedia traffic.
In addition to assessing quality of service at the network level, today it is also necessary
to evaluate the quality at the user level using the Mean Opinion Score, the so-called
Quality of Experience (QoE) indicator. The use of QoE indicators allows to more
adequately take into account the features of providing and assessing the quality of a
multimedia service, taking into account not only the parameters of the transport network,
but also the characteristics of the traffic generated by the application [4, 5, 8-14].
Providing specified values of QoE indicators is possible using routing tools. However,
when solving QoE-based routing tasks, it is worth considering that MOS indicators, as
shown in [6-8, 15-18], are a rather complicated and generally non-linear function of
network performance indicators [9, 17]. Therefore, an approach based on the
implementation of tensor models of QoS routing [5, 9], capable of providing specified
values of the end-to-end bandwidth, delay, jitter and packet loss, is worth noting.
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0). CybHyg-2019: International Workshop on
Cyber Hygiene, Kyiv, Ukraine, November 30, 2019.
Therefore, an approach is proposed based on the Routing Tensor Model with Providing
MultiMedia Quality (MMq).
2 Routing Model for Assessment of Multi Media Quality
The main requirements for the developed Routing Model for assessment of Multi Media
Quality should include ensuring maximum consideration of the features related to the
processes of both multimedia traffic transmission and QoE assessment. Therefore, when
transmitting multimedia traffic, the most stringent requirements are put forward not only
to the average delay of packets and the probability of their loss along the calculated routes,
but also to the issues of synchronizing the delivery of packets of audio and video flows
transmitted in the same multimedia session [7].
In the framework of the proposed routing model, the structure of an infocommunication
network is described using a one-dimensional simplicial complex (one-dimensional
is a set of zero-dimensional simplexes
network) S (U ,V ) , where U ui , i 1, m
– network nodes (routers), and V vz (i, j ); z 1, n; i, j 1, m; i j is a set of
one-dimensional simplexes – network edges, where edge vz (i, j ) connects routers
ui and u j .
Further, we agree that K is a set of multimedia sessions on the network. Then by
speech
k we denote an audio flow, and by k video we denote the video flow of the
k th multimedia session. Then, in the course of solving the routing problem of the
audio and video flows of the k th multimedia session, it is necessary to calculate a set
speech video
of route variables xik, j and xik, j , each of which characterizes the fraction of
the intensity of audio and video flows generated during the k th multimedia session
and flowing in the link (i, j ) , respectively.
In order to implement the multipath routing strategy, the following restrictions are
imposed on these route variables:
speech video
0 xik, j 1 and 0 xik, j 1. (1)
In addition to conditions (1), the routing variables are subject to restrictions
represented by the conditions for conservation of audio and video flows on ICN
routers. Therefore, for example, for the flow k speech , these conditions, considering
possible packet losses caused by the overload of the queue buffer, take the following
form [4, 5, 21-24]:
k speech
xi , j 1 if k speech K , ui bk ;
j:(i , j )V
(2)
k speech speech
xi , j x kj ,i (1 p j ,i ) 0 if k speech K , ui bk , ui d k ; a
j:(i , j )V j:( j ,i )V
speech speech
x kj ,i (1 pi , j ) k if k speech K , ui d k ,
j:( j ,i )V
where bk and d k are the source router and the destination router for packets of
speech
audio and video flows of the k -th multimedia session, respectively; k is the
speech
fraction of rate of the audio flow k serviced by the network, i.e. packets of
which have been successfully delivered to the destination router; pi , j is the
probability of packet loss on the j -th interface of the i -th router.
The conditions for video flow k video conservation have a similar form (2)
k video
xi , j 1 if k video K , ui bk ;
j:(i , j )V
(3)
k video video
xi , j xik, j (1 p j ,i ) 0 if k video K , ui bk , ui d k ;
j:(i , j )V j:(i , j )V
video video
xik, j (1 p j ,i ) k if k video K , ui d k ,
j:(i , j )V
video
where k is the fraction of rate of the video flow k video successfully serviced
by the network.
The probability of packet loss, if the j -th interface of the i -th router is modeled
by a queuing system with failures of the type M / M /1/ N , can be calculated as
follows:
1 ρi , j ρi , j
N
i, j
pi , j , (4)
1 ρi , j
Ni , j 1
λi, j
where ρi, j is the utilization coefficient of the j -th interface on the i -th
φi , j
router; Ni, j denotes the maximum number of packets in the queue of the j -th
interface on the i -th router; φi , j denotes the bandwidth of the j -th interface of
the i -th router measured in 1/s. λi, j is the total rate of all flows of various
multimedia sessions in the link (i, j ) V (1/s), which is calculated as:
speech k speech video k video
λi , j λ k xi, j λk xi , j , (5)
kK
speech video
where λ k and λ k are the average packet rates of the audio and video
flows of the k -th multimedia session, respectively.
Then the rates of the lost packets of audio and video flows belonging to the k -th
multimedia session on the j -th interface of the i -th router will be respectively
determined as:
speech speech req speech video video req video
rik, j =k xik, j pi , j and rik, j =k xik, j pi , j (6)
speech video
The rate of successfully transmitted packets of audio λik, j and video λ ik, j
flows of the k -th multimedia session through the j -th interface of the i -th router
is calculated as:
speech speech req speech video video req video
ik, j =k xik, j (1 pi , j ) and ik, j =k xik, j (1 pi , j ) (7)
To ensure control over the process of overloading links and queues taking into
account (7), the following restrictions are introduced into the model structure [5]:
λi, j φi, j , (i, j ) V . (8)
4 Conditions for Providing MultiMedia Quality in
Infocommunication Network
The main requirement when implementing QoE routing is to meet the conditions for
ensuring a given level of MultiMedia Quality. In accordance with the ITU-T
Recommendation G.1070 [7], the requirements for MultiMedia Quality ( MM q ) are
generally defined as
MM qreq MM q , (9)
where
MM q m1MM SV m2 MMT m3MM SV MMT m4 , at 1 MM q 5 . (10)
where MM qreq are the requirements for the MultiMedia Quality level; MM SV
denotes the quality of transmission of audiovisual information; MM T denotes
degradation in quality due to delays and desynchronization of processes for
transmitting audio and video flow packets; mi denotes coefficients depending on the
size of the display and the purpose of communication [7]. The task is to support the
possibility of analytical calculation of the MM q indicator in order to fulfill the
conditions (9) for each multimedia session during the routing of each pair of audio
and video flows. For clarity, the index k , i.e. the number of such a session, will be
omitted during further transformations.
Moreover, the terms included in (10), as well as the transmission quality of audio
( S q ) and video flows ( Vq ), are the functions of the average end-to-end delays of
packets of audio ( TS ) and video ( TV ) flows, the probabilities of losing packets of
audio ( P S ) and video ( PV ) flows in the network, and are determined in accordance
with the recommendation [7]. For example, the transmission quality of audiovisual
information MM SV is determined using the following expressions:
MM SV m5 Sq m6Vq m7 SqVq m8 , at 1 MM SV 5 . (11)
MMT max AD MS ,1 , at 1 MMT 5 . (12)
AD m9 (TS TV ) m10 , (13)
min m11 (TS TV ) m12 , 0 , if TS TV ,
MS (14)
min m13 (TV TS ) m14 , 0 , if TS TV ,
where MS is the coefficient which takes into account the desynchronization
between the sound and the image; AD is the parameter reflecting the effect of
average delays of packets of audio ( TS ) and video ( TV ) flows.
Based on (14), we can conclude that during QoE routing it is important to ensure
maximum closeness of TS and TV values for audio and video flows of each
multimedia session. Then, in accordance with the recommendation [7], the presented
expressions, in this case similar to (11)-(14), can be used to form restrictions of the
type (7) based on the known required level of Quality of Experience MM qreq . The
main problem in the MM q calculation is the definition of expressions for finding
the values of the end-to-end delays TS and TV , as well as the probabilities of
packet loss P S and PV for audio and video flows, respectively. These indicators
directly depend on the route variables (1), traffic characteristics and network
parameters. Therefore, based on the model (1)-(6), the expressions for calculation of
P S and PV will take the form:
speech
PS 1 k , (15)
video
PV 1 k . (16)
To derive analytical expressions for determining TS and TV taking into
account the results obtained in [5, 9, 21], it is advisable to use the functional of tensor
modeling of routing processes in infocommunication networks.
5 Tensor Formalization of Routing Model with Providing
Multimedia Quality
In accordance with the methodology for tensor modeling of an ICN proposed in
[5, 9, 21], the network structure determines the anisotropic space formed by many
loops and node pairs. The dimension of this space is determined by the total number
of branches (communication links) in the network and is equal to n . Moreover, each
independent path (branch, loop, or node pair) determines the coordinate axis in the
space structure. As a rule, an ICN is modeled by a connected one-dimensional
network, i.e. it contains one connected component, then the cyclomatic number
and the rank of the network determine, respectively, the number of basis loops
and node pairs, for which the following expressions are true:
n m 1, m 1 , n . (17)
In the selected space when transmitting packets of each pair of audio and video
flows generated during the k th multimedia session, the infocmmunication network
can be represented by a mixed bivalent tensor
T Λ, (18)
where is the tensor multiplication operator, and the components of the tensor
are the monovalent covariant tensor of average packet delays T and the monovalent
contravariant tensor of flow rates in the coordinate paths of the network.
In the framework of the proposed model (1)-(8), when the interface is modeled by
a queuing system with failures of the type M / M /1/ N , the average packet delay in
an arbitrary ICN communication link for both audio and video flows is approximated
by the expression
ρ ρ N 2 ( N 1) ρ N 1 (1 ρ)
τ . (19)
λ(1 ρ N 1 )(1 ρ)
Moreover, in accordance with the postulate of G. Kron second generalization [25]
and the results of [5, 9, 21], expressions (18) written for each of the network links
determine the following vector-matrix equation:
v GvTv , (20)
where v and Tv are the projections of the tensors and T , respectively, in the
coordinate systems of the branches represented by the n -dimensional vectors of the
flow rate and average packet delay in the communication links; Gv g v is a
ij
diagonal n n matrix, the elements of which correspond to the branches (links) of
the network and are calculated as an example of servicing the audio flow according to
the expression [25]
v
λi (1 ( ρiv ) Ni 1 )(1 ρiv ) λiv
gvii v v
, (21)
ρiv ( ρiv ) Ni 2 ( Niv 1)( ρiv ) Ni 1 (1 ρiv )
where the index i indicates the belonging of a particular interface parameter to the
link vi V ; λi is the total rate of all flows of various multimedia sessions in the
link vi V (4); λiv denotes packet rate of the considered audio flow in the link
vi V . The projections of the tensors of the average packet delays and flow rates in
the coordinate system of the loops and node pairs are connected by the expression
similar to (20):
G T . (22)
According to the inverse tensor attribute, the tensor G is a twice contravariant
metric tensor, the projections of which are transformed as follows when the
coordinate system of its consideration is changed:
G At Gv A , (23)
where G is the projection of the tensor G in the coordinate system of loops and
n n covariant transformation matrix;
t
node pairs; A is the is the
transposition operation. As shown in [5, 25], the matrix G can be represented as a
block structure, i.e.
1 2 4,1 4,2
G | G G | G
G , G
4
,
3 4 4,3 4,4
G | G G | G
where G and G are the square submatrices of the sizes and ,
1 4
respectively; G is the submatrix of the size ; G is the submatrix of the
2 3
size ; G
4,1 4 4,2
is the first element of the matrix G ; G is the second
element of the matrix G of the size 1 ( 1) ; G
4 4,3
is the third element of the
matrix G of the size ( 1) 1 ; and G
4 4,4
is the fourth element of the matrix
G of the size ( 1) ( 1) .
4
In the framework of the tensor description of the infocommunication network in
the context of the multipath routing strategy [5, 17, 21], the average end-to-end delay
of the audio flow packets can be calculated as:
1
speech k speech 4,2 4,4 speech
λk Gπη Gπη kη1
TS , (24)
1
Gπη Gπη Gπη
4,1 4,2 4,4 4,3
Gπη
k speech
where η1 is the rate vector of lost packets on the interfaces of routers, the
coordinates of which are determined by the expression:
m speech k speech
ληi λ k xi , j pi , j . (25)
j 1
The average end-to-end delay of video flow TV packets is determined in a similar
way and calculated as:
1
video k video 4,2 4,4 video
λk Gπη Gπη kη1
TV , (26)
1
4,1 4,2 4,4 4,3
Gπη Gπη Gπη Gπη
video
where η1
k
is the intensity vector of the lost packets of the video flow on the
interfaces of the routers, the coordinates of which are determined similarly to
expression (25). In the course of solving the multipath QoE routing problem, a
condition related to maximizing the overall performance of the infocommunication
network was selected as a criterion for the optimality of the obtained solutions [21]:
speech k speech video k video
max λ k λk , (27)
x, kK
if there are restrictions (1)-(3), (5), (8) taking into account their detalization in (9)-
(27).
6 Investigation of Tensor Approach for Providing Multimedia
Quality
To assess the adequacy of the proposed model (1)-(27) and the demonstrativeness of
the obtained calculation results, we will solve this problem for a fragment of the
infocommunication network as shown on Fig.1. Assume that the network under
investigation consists of sixteen routers and twenty-four communication links,
indicating their capacity (1/s) in the gaps of the links.
Let the packet speech k speech and video k video flow be transmitted between the
first and sixteenth routers with the following QoE requirements:
speech req video req req
λk 100 1/s, λk 300 1/s, MMq 3.5 , when some users
dissatisfied [6].
0.0007
0.002150.3059 27.6514 14.0419
100 1/s
150.9177 82.6542 42.1258
300 1/s R1 R2 R3 R4
280 200 195
0.0013
0.0040
49.6921 22.6545 16.6094 14.0419
149.0762 67.9635 40.8283 42.1258
270 190 215 190
16.6412 13.4970 10.4032
49.0235 40.4911 31.2097
R5 R6 R7 160 R8
180 190
33.3509 25.4986 16.7033 24.4452
100.0527 76.4959 50.1098 73.3355
220 200 175 185
18.6203 23.3890 24.0675
55.8608 70.1669 72.2026
R10 250 R11 190 R12
R9 210 0.3771
16.0247 1.1314
14.7306 20.7299 48.1356
44.1919 62.1898 48.0741 144.4067
210 260 170 210
14.7306 35.4606 50.9642
44.1919 106.3817 152.8927
R14 240 R15 220 R16
R13 215
0.5210
1.5630
Fig. 1. The routing order of a flow of audio and video packets that is transmitted
As a result of the calculations (see Table 1), which quantitatively meet the
requirements for ensuring the level of Multimedia quality in the network (9) at
req
MMq 3.5 , the following values have been obtained:
MMq 3.5455 ,
at MM SV 3.3634 ; MMT 3.9149 ; TS TV 0.0976 s; P S PV 0.009 .
Thus, the analysis of the effectiveness of the proposed approach for QoE-routing
of multimedia packet flows for different network topologies and flow characteristics
has been also conducted in the work. The efficiency has been estimated by the amount
of link resource used by the network while meeting the established requirements for
multimedia quality.
The results were compared with the solutions that were obtained using two classes
of flow-based routing models:
the flow-based model based on the bandwidth metrics, by analogy with the
EIGRP and OSPF protocols [9];
the flow-based routing model based on the load balancing and principles of
Traffic Engineering [13, 14].
Table 1. Results of solving the problem of providing MMq.
Example QoE requirements:
speech req video req
λk 100 1/s, λk 300 1/s, MMq req 3.5
Link Calculation results for the
Calculation results for the video flow
speech flow
φi , j , 1/s speech k speech video video
λik, j , 1/s ri , j ,1/s λ ik, j , 1/s rik, j , 1/s
(1,2) 280 50.3059 150.9177 0.0021
0.0007
(1,5) 270 49.6921 149.0762 0.0040
0.0013
(2,3) 200 27.6514 0 82.6542
0
(2,6) 190 22.6545 0 67.9645 0
(3,4) 195 14.0419 0 42.1258 0
(3,7) 215 16.6094 0 40.8283 0
(4,8) 190 14.0419 0 42.1258 0
(5,6) 180 16.6412 0 49.0235 0
(5,9) 220 33.3509 100.0527
0 0
(6,7) 190 13.4970 40.4911
0 0
(6,10) 200 25.4986
0 76.4959 0
(7,8) 160 10.4032 31.2097
0 0
(7,11) 175 16.7033 50.1098
0 0
(8,12) 185 24.4452 73.3355
0 0
(9,10) 210 18.6203
0 55.8608 0
(9,13) 210 14.7306
0 44.1919 0
(10,11) 250 23.3890
0 70.1669 0
(10,14) 260 20.7299
0 62.1898 0
(11,12) 190 24.0675 72.2026 0
0
(11,15) 170 16.0247 48.0741 0
0
(12,16) 210 48.1356 144.4067 1.1314
0.3771
(13,14) 215 14.7306 44.1919
0 0
(14,15) 240 35.4606 106.3817
0 0
(15,16) 220 50.9642 152.8927
0.5210 1.5630
The proposed approach of QoE-routing of multimedia packet flows ensured the
fulfillment of multimedia quality requirements when using an average of 20-27% less
link resource than the flow-based model based on the bandwidth metrics. When
comparing with the routing model organized on the principles of Traffic Engineering,
the gain ranged from 14-17% to 22-25% depending on the features of the network
topology and the bandwidth of the communication links. The biggest gain
corresponded, firstly, to the use of networks with a heterogeneous topology when the
connectivity of different routers was significantly different. Secondly, the network
was heterogeneous, that is, different communication links had significantly different
bandwidth. The obtained results of the efficiency analysis determine the
corresponding field of practical application of the obtained solutions, which are
presented by the method of QoE-routing of multimedia flows.
7 Conclusions
The paper proposes an approach based on the tensor mathematical routing model, due
to which a given level of Quality of Exprience is provided according to the
Multimedia Quality indicator. The model underlying this solution belongs to the class
of flow-based routing models based on the conditions for implementing the multipath
routing strategy (1), flow conservation taking into account possible losses at the
network nodes (2), (3) and preventing overloading of communication links (8). The
novelty of the proposed solution is to ensure that in the course of solving the routing
problem, the Multimedia Quality conditions are fulfilled (9). Due to the tensor
formalization of the QoE routing model, it was possible to obtain the conditions for
ensuring the specified values of Multimedia Quality (15), (16), (24), (26) in the
analytical form, which were used as the main restrictions in solving the formulated
optimization problem. This was achieved due to the possibility of analytical
calculation of the quality of service indicators: packet loss probabilities for audio (15)
and video (16) flows, as well as the average end-to-end packet delay (24), (26) for the
same flows transmitted within the multimedia session. At the same time, obtaining
expressions (24) and (26) linking the end-to-end QoS-indicators, network parameters
and flow characteristics was possible using the tensor research methodology. In the
framework of this approach, the ICN was modeled for each multimedia session by the
divalent mixed tensor (18) presented in a discrete space determined by the network
structure.
To investigate the proposed approach, the functionality of the MatLab package
was used. The calculation performed on a fragment of the infocommunication
network allowed to evaluate the adequacy and effectiveness of the proposed
approach, in which the end-to-end QoS indicators were calculated. Based on these
indicators, it was possible to control the influence of the time desynchronization in the
delivery processes of packets of audio and video flows on Multimedia Quality. The
proposed approach, in comparison with existing solutions, allows using an average of
20-27% less link resource than the flow-based model based on using bandwidth
metric, and 14-17% up to 22-25% less when comparing with the routing model
organized on the basis of the Traffic Engineering principles.
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