=Paper=
{{Paper
|id=Vol-2332/paper-02-002
|storemode=property
|title=
Optimal Multicast Subgrouping in Mobility-Aware 5G Systems: Challenges, Modeling, and Opportunities
|pdfUrl=https://ceur-ws.org/Vol-2332/paper-02-002.pdf
|volume=Vol-2332
|authors=Vitalii A. Beschastnyi,Darya Yu. Ostrikova,Alexander I. Zeifman,Irina A. Gudkova
}}
==
Optimal Multicast Subgrouping in Mobility-Aware 5G Systems: Challenges, Modeling, and Opportunities
==
https://ceur-ws.org/Vol-2332/paper-02-002.pdf
13
UDC 004.4
Optimal Multicast Subgrouping in Mobility-Aware 5G Systems:
Challenges, Modeling, and Opportunities
Vitalii A. Beschastnyi* , Darya Yu. Ostrikova* ,
Alexander I. Zeifman†‡ , Irina. A. Gudkova*S
*
Department of Applied Probability and Informatics
Peoples’ Friendship University of Russia (RUDN University)
6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
†
Department of Applied Mathematics
Vologda State University
6 Orlova St, Vologda, 160000, Russian Federation
‡
Institute of Informatics Problems
Federal Research Center "Computer Science and Control"
of the Russian Academy of Sciences
44-2 Vavilov St, Moscow, 119333, Russian Federation
S
Faculty of Electrical Engineering and Communication
Brno University of Technology
3058/10 Technická, 61600 Brno, Czech Republic
Email: beschastnyy_va@rudn.university, ostrikova_dyu@rudn.university, a_zeifman@mail.ru,
gudkova_ia@rudn.university
The expected growth in the mobile video (including streaming video, video downloading,
conferencing, etc.) now is the key driver for rapid development of 5G wireless network
technologies. This paradigm forces wireless networks to manage their resources as effectively
as possible. One of the most appropriate solutions for video traffic that may provide the
sufficient spectral efficiency is multicasting. Multicast sessions allows a group of users to
simultaneously access the same multimedia content with the same QoE parameters. In this
paper we consider different methods of multicast subgrouping. An analytical framework in the
from of a queuing network is proposed to study the network performance, and a comparative
study of network performance metrics under different user movement scenarios is presented.
Key words and phrases: multicast, subgrouping, 5G, analytical model, optimization.
Copyright © 2018 for the individual papers by the papers’ authors. Use permitted under the CC-BY license —
https://creativecommons.org/licenses/by/4.0/. This volume is published and copyrighted by its editors.
In: K. E. Samouylov, L. A. Sevastianov, D. S. Kulyabov (eds.): Selected Papers of the 12th International Workshop on
Applied Problems in Theory of Probabilities and Mathematical Statistics (Summer Session) in the framework of the
Conference “Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems”,
Lisbon, Portugal, October 22–27, 2018, published at http://ceur-ws.org
14 APTP+MS’2018
1. Introduction
According to [1], video will exceed the 82 percent of global Internet traffic by 2022.
For network operators this leaves no other option but to strive for higher spectral
efficiency as video data demands both high data rates and strict Quality of Experience
(QoE) requirements. One of possible solutions is to employ the existing "enhanced"
multimedia broadcast multicast services (e-MBMS) architecture [2], standardized by
the Third Generation Partnership Project, by adopting it to the 5G systems. This will
enable 5G networks with all the opportunities of the point-to-multipoint services which
are crucial to support large-scale consumption of mass multimedia services on mobile
devices [3].
In this paper we consider multicast approaches of network offloading. In [4] an
approach based on splitting users into multicast subgroups (subgrouping) was proposed.
This approach allows to achieve better results in terms of considered metrics rather
then allocating the whole pool of resources to a single multicast group. The author also
propose an algorithm that allows to find a sub-optimal network configuration consisting
of two sets (groups) of users and resources allocation scheme for them. The algorithm
considers maximization of Aggregate Data Rate (ADR) metric, thus improving the
overall throughput of the network. Due to its low complexity the algorithm satisfies
computation timing constraints since it should be run every Time Transmission Interval
(TTI) during which channel quality between a multicast user and the base station is
considered to be constant and may be just 1 ms long. Besides, for distant users it is
extremely important to take into account their spatial positions as the amount of utilized
resource significantly varies [15], mainly due to the effect of interference [16, 17].
An analytical model for characterizing the impact of the users’ mobility in the
multicast subgroup formation problem was proposed in [5] since queuing theory [7, 18]
is typically employed in description of telecommunication networks . It is shown that,
under the condition of constant number of multicast users within the service area, user
mobility can be modeled as a queuing network. The model allows for close analytical
calculation of average experienced bit rate and maximum aggregate data rate as an
optimal solution of the subgroup formation problem stated in [4].
In this paper we study the range of applicability of the algorithm proposed in [4]. We
also extend the model proposed in [5] to take into account the ’ON-OFF’ (active-passive)
operation mode of user devices. As ADR metric is usually unfair towards end users we
also consider other metrics that may be more appropriate in different scenarios.
2. System Model
Each device in a multicast group transmits periodic or aperiodic feedback signals
that allow base station (BS) to define Channel Quality Indicator (CQI). On collecting
the state information from all the devices inside the coverage area, the BS makes a
decision on subgrouping of these devices. As the time for taking a decision is limited by
one Transmission Time Interval (TTI) an effective mechanism is required for resource
allocation, which can operate within very short run time.
The simplest way to distribute multicast resources is to maintain equal data rate
across all the devices. Among the many alternative solutions, the subgrouping method
are given most of attention, as they can provide the highest throughput. Group-based
methods consist of dividing a set of multicast objects into several subgroups consisting
of receivers. Each subgroup is served with MCS that can be applied to the subgroup
member with the worst channel conditions [12, 14]. Time-free and multi-layer coding
techniques [6, 11] can be applied to subgroups to guarantee continuity and integrity of
data transmission, and to efficiently handle subgrouping process.
The main problem in subgrouping is the computational complexity (and time) needed
to find an optimal subgroup configuration (see Fig. 1). It is usually calculated using
exhaustive search schemes. Run-time is critical in any wireless system where multicast
Beschastnyi V. A. et al. 15
objects can experience channel fluctuations during the time interval required by BS to
form subgroups according to the collected CQIs.
2.1. Subgroup Formation Problem
We refer to a single-cell coverage area with one multicast group, composed of set
A = {1, · · · , 𝐴} of members. The BS allocates 𝐾 RBs according to the Channel Quality
Indicator (CQI) feedbacks [13]. Let M = {1, · · · , 𝑀 } be the set of available CQIs, 𝑛𝑚
be the number of members reported 𝑚-CQI, 𝑛 = (𝑛1 , · · · , 𝑛𝑚 ). Since each CQI is
associated with supported MCS, we indicate with 𝑏𝑚 , 𝑚 ∈ M the data transmitted
over one Resource Block (RB) by using the Modulation and Coding Scheme (MCS)
corresponding to the 𝑚-th CQI. The BS enables the subgroup configuration, i.e., the
number of subgroups with their relevant MCS and amount of allocated resources that
maximizes the ADR. Let us denote L = {1, · · · , 𝐿}, L ∈ M the set of subgroups in the
current moment, M𝑙 = {𝑚 ∈ M : 𝑛𝑚 > 0} the set of CQIs which are reported by at least
one user, and 𝑙𝑚 ∈ L, 𝑚 ∈ M the affiliation of 𝑚-th CQI to 𝑙-th subgroup. Reported
CQIs are divided into existing subgroups. Let 𝑘𝑙 represent the number of resource blocks
allocated to 𝑙-th subgroup, k = (𝑘1 , · · · , 𝑘𝐿 )
2.2. Mobility Model
The number of members and the values of CQIs reported by each member. Never-
theless, if we would like to know the situation not only at the current moment but also
predict it in the future we could add stochastic nature in the problem formulation. In
this paper we analyze the scenario of users that are moving within the circular cell of 𝑅
radius . The directions the users are moving are learned from statistics of event-based
simulation to find the probability that a user will change the area of the some MCS
within a timeslot [5, 10]. A circular cell is divided in disjoint areas of the same CQI. We
assume free space, so the areas have forms of annulus. Users are distributed according
to a Poisson Point Process (PPP) on the plane and thus are uniformly deployed within
a cell. Let us denote 𝜃𝑚,𝑚−1 the probability of events when a user moves farther from
the BS and changes the reported CQI from 𝑚 to 𝑚 − 1; 𝜃𝑚,𝑚+1 = 1 − 𝜃𝑚,𝑚−1 the
probability of events when a user moves closer to the BS and changes the reported CQI
from 𝑚 to 𝑚 + 1; and 𝛼𝑚 the average time when a user does not move from the area of
𝑚-MCS, i.e. he does not change its CQI from 𝑚.
16 APTP+MS’2018
Figure 1. Subgroup configuration example
3. Mathematical Model
In this section we first present a queuing network, where each node describes the
channel quality level 𝑚 ∈ M, where M is the set of all channel quality indicators (CQIs).
The considered network is closed, i.e. it is a network with a set of nodes without source
and drain, in which a constant number 𝑁 of similar arrivals are circulating [9].
3.1. Case of Active Users
Earlier in [5] the queuing network was considered only with "active" users, that is,
the subscribers which use the mobile network continuously. The transition digram for
the considered queuing network is schematically presented in Fig. 2.
Figure 2. Transition diagram for queuing network with ’active’ users only
The state space of the system 𝑋(M, 𝑁 ) satisfies the relation (1):
𝑀
∑︁
𝑋(M, 𝑁 ) = {𝑛 : 𝑛𝑖 = 0, · · · , 𝑁 ; 𝑛𝑖 = 𝑁 }. (1)
𝑖=1
Beschastnyi V. A. et al. 17
In this case, the stationary probabilities 𝑝(𝑛) of the states of the system are calculated
as (2).
𝑀
∏︁ (ℎ𝑚 𝑎𝑚 )𝑛𝑚
𝑝(𝑛) = 𝐺−1 (M, 𝑁 ) . (2)
𝑚=1
𝑛𝑚 !
∑︀ ∏︀𝑀 (ℎ𝑚 𝑎𝑚 )𝑛𝑚
where 𝐺(M, 𝑁 ) = 𝑛∈𝑋(M,𝑁 ) 𝑚=1 𝑛𝑚 !
and ℎ𝑚 , 𝑚 ∈ M is calculated
as (3). ⎧
⎨ ℎ1 = ℎ2 (1 − 𝜃12 );
⎪
ℎ𝑚 = ℎ𝑚−1 𝜃𝑚𝑚−1 + ℎ𝑚+1 (1 − 𝜃𝑚𝑚+1 ), 2 ≤ 𝑚 ≤ 𝑀 − 1; (3)
⎪
ℎ𝑀 = ℎ𝑀 −1 𝜃𝑀 𝑀 −1 .
⎩
3.2. Case of Active and Passive Users
Similarly, we may describe the model for devices operating in two modes (the ’ON-
OFF’ model), where the 0-node describes the ’passive’ (or ’OFF’) mode, when devices
do not exchange the data with the BS (Fig. 3).
Here passive node is denoted as 0-node, and 𝑁 is the total number of customers in
the system in both active and passive nodes. 𝜃𝑛𝑚 , 𝑚 = 1, 𝑀 indicate the probabilities of
transitions of active users between adjacent nodes, while 𝜃0𝑚 , where 𝑚 = 1, 𝑀 , indicate
the probabilities of transitions from the passive node to the active ones. The average
time until the user moves from the area 𝑚 is similarly indicated with 𝛼𝑚 . In order to
prove that a given physical system exists, we show that passive node is in one of the
available states, that is, satisfies the normalization condition (4):
𝑀
∑︁
𝜃0𝑚 = 1. (4)
𝑚=1
The state space of the system 𝑋(M, 𝑁 ) satisfies the relations (1) and (5):
(︁𝑀 + 𝑁 − 1)︁
|𝑋(M, 𝑁 )| := , 𝑀 ≥ 0, 𝑁 ≥ 0. (5)
𝑀 −1
In this case, the stationary probabilities 𝑝(𝑛) of the states of the system are calculated
as (2), where ℎ𝑚 , 𝑚 ∈ M is calculated as (6).
⎧
⎨ ℎ1 = ℎ2 𝜃21 + ℎ0 𝜃01 ;
⎪
ℎ𝑚 = ℎ𝑚−1 𝜃𝑚𝑚−1 + ℎ𝑚+1 𝜃𝑚𝑚+1 + ℎ0 𝜃0𝑚−1 , 2 ≤ 𝑚 ≤ 𝑀 − 1; (6)
⎪
ℎ𝑀 = ℎ𝑀 −1 𝜃𝑀 𝑀 −1 + ℎ0 𝜃0𝑀 .
⎩
18 APTP+MS’2018
Figure 3. Transition diagram for queuing network with ’active’ and ’passive’
users
4. Optimization Problems
The problem of calculating the subgroup configuration for a wireless multicast network
can be considered in the context of two possible scenarios: in the first scenario, the
total data rate is found in order to achieve maximum throughput of the whole network.
In the second scenario, the rates are somehow evenly distributed among all devices.
In this section, the main goal for scenario 1 is to analyze the range of applicability of
the algorithm proposed in [4], while for the second scenario is to study the fairness of
resource distribution between devices by the Jain’s fairness index [8] for the considered
utility functions.
4.1. Aggregate Data Rate Maximization
Aggregate Data Rate shows the overall size of data that can be downloaded within
one TTI by the devices what is extremely important for applications that involve on-line
video streaming and thus require higher throughput.
To calculate the Aggregate Data Rate we use an objective function (7) and the
algorithm proposed in [4].
(︀ )︀
𝑈 𝜎 = {M1 , · · · , M𝐿 }, 𝑘 = (𝑘1 , · · · , 𝑘𝐿 ) =
𝐿 (︁
∑︁ ∑︁ )︁ (7)
= 𝑏min𝑚∈M (𝑚) · 𝑘𝑙 · 𝑛𝑚 := 𝐴𝐷𝑅 → 𝑚𝑎𝑥.
𝑙
𝑙=1 𝑚∈M𝑙
Beschastnyi V. A. et al. 19
In Fig. 4 relative difference of results obtained with use of the considered algorithm
and brute force analysis is shown. The results include 3 possible scenarios: uniform,
centered and boundary trend of users’ disposition.
Figure 4. Relative difference between the ADR maximization algorithm
and brute force analysis
The presented plot shows that the algorithm offers good results only for large number
of RBs, which are applicable to wide bandwidth (15, 20 MHz), but might be ineffective
in case of narrow bands (1.4 – 10 MHz).
4.2. Fairness Spectrum Allocation
In order to equalize distribution of data rates among devices, we consider three ob-
jective functions: Fair Data Rate (FDR), Balanced Data Rate (BDR), and Proportional
Fairness (PF) [6].
FDR tries to minimize difference in average rates (8):
(︀ )︀ (︁ )︁
𝑈 𝜎 = {M1 , · · · , M𝐿 }, 𝑘 = (𝑘1 , · · · , 𝑘𝐿 ) = max 𝑏min𝑚∈M (𝑚) · 𝑘𝑙 −
1≤𝑙≤𝐿 𝑙
(︁ )︁ (8)
min 𝑏min𝑚∈M (𝑚) · 𝑘𝑙 := 𝐹 𝐷𝑅 → 𝑚𝑖𝑛.
1≤𝑙≤𝐿 𝑙
BDR maximizes the minimal rate without taking into account higher rates (9):
(︀ )︀
𝑈 𝜎 = {M1 , · · · , M𝐿 }, 𝑘 = (𝑘1 , · · · , 𝑘𝐿 ) =
(︁ )︁ (9)
= min 𝑏min𝑚∈M (𝑚) · 𝑘𝑙 := 𝐵𝐷𝑅 → 𝑚𝑎𝑥.
1≤𝑙≤𝐿 𝑙
PF maximizes the total network bandwidth and evenly distribute the rates (10):
(︀ )︀
𝑈 𝜎 = {M1 , · · · , M𝐿 }, 𝑘 = (𝑘1 , · · · , 𝑘𝐿 ) =
𝐿 (︂
(10)
∑︁ )︂
(︀ )︀ ∑︁
= log 𝑏min𝑚∈M (𝑚) · 𝑘𝑙 · 𝑛𝑚 := 𝑃 𝐹 → 𝑚𝑎𝑥.
𝑙
𝑙=1 𝑚∈M𝑙
20 APTP+MS’2018
Table 1
Input data for numerical experiment
Parameter Value
𝑀 15
𝑁 50
𝐾 16
𝑛Uniform (4, 3, 3, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3)
𝑛Centered (1, 1, 1, 1, 1, 1, 13, 15, 10, 1, 1, 1, 1, 1, 1)
𝑛Boundary (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 13, 15)
Table 2
Numerical results for data rate equalization functions
User Distribution Type FDR BDR PF
Uniform 0.95 0.89 0.77
Centered 0.98 0.96 0.89
Boundary 0.75 0.96 1
We analyze the proposed functions using the Jane’s fairness index, which is calculated
as (11):
)︀ 2
(︂ )︂
∑︀𝐿 (︀ ∑︀
𝑙=1 𝑏 min 𝑚∈M𝑙 (𝑚) · 𝑘 𝑙 · 𝑚∈M𝑙 𝑛 𝑚
𝐽= (︂ )︂ , 0 ≤ 𝐽 ≤ 1. (11)
∑︀𝐿 (︀ )︀2 ∑︀
𝑁 · 𝑙=1 𝑏min𝑚∈M (𝑚) · 𝑘𝑙 · 𝑚∈M𝑙 𝑛𝑚
𝑙
where ’0’ indicates that the rates are distributed poorly, and 1 in the best possible way
in term of fairness.
For input data presented in Table 1 we present numerical results (Table 2). The
obtained results show that in case of uniform and centered distribution of users over the
service area, the FDR function allows to find the finest network configuration. But in
case the users are distributed mainly by the cell’s boundaries, it is much more effective
to use PF function. If users behave in the way that they are always either closer to the
center or to boundaries, the preferred decision should be to select BDR function.
5. Conclusions
In this paper we considered different methods of multicast subgrouping. We intro-
duced an analytical model for multicast-enabled network cell that includes user mobility
and in-off operation modes. We also provided the numerical analysis of the range of
applicability for the ADR maximization algorithm. Finally, we presented three objective
functions that allow for data rate equalization among users with different channel quality
conditions, and provided the numerical analysis based on Jane’s fairness index to reveal
the scenarios that are applicable for the functions.
Beschastnyi V. A. et al. 21
Acknowledgments
The publication has been prepared with the support of the “RUDN University
Program 5-100” and funded by RFBR according to the research projects No. 18-00-
01555(18-00-01685) and No. 18-37-00231.
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