=Paper=
{{Paper
|id=Vol-2639/paper-07
|storemode=property
|title=
To the analysis of the dynamic assignment of radio resources in wireless networks with a network slicing mechanism
|pdfUrl=https://ceur-ws.org/Vol-2639/paper-07.pdf
|volume=Vol-2639
|authors=Ekaterina V. Bobrikova,Anna A. Platonova,Sergey Ya. Shorgin,Yuliya V. Gaidamaka
|dblpUrl=https://dblp.org/rec/conf/ittmm/BobrikovaPSG20
}}
==
To the analysis of the dynamic assignment of radio resources in wireless networks with a network slicing mechanism
==
https://ceur-ws.org/Vol-2639/paper-07.pdf
To the analysis of the dynamic assignment of radio
resources in wireless networks with a network
slicing mechanism
Ekaterina V. Bobrikovaa , Anna A. Platonovaa , Sergey Ya. Shorginb and
Yuliya V. Gaidamakaa,b
a
Peoples’ Friendship University of Russia (RUDN University), 6, Miklukho-Maklaya St., Moscow, 117198, Russia
b
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (FRC CSC RAS), 44-2,
Vavilov St., Moscow, 119333, Russia
Abstract
Network Slicing is one of the latest technologies of modern telecommunication systems. Network Slicing
involves dividing the 5G physical architecture into multiple virtual networks or slices. Each slice has
its own characteristics and is aimed at solving a particular business problem. In the nearest future it
is expected that Network Slicing principle will radically change the approach, in particular, of mobile
operators to support vertical applications with specific and rigorous performance requirements. Network
resource tenants can manage these requirements. The static assignment of resources to tenants, that is,
the assignment of resources on a permanent basis, is a sufficient condition for fulfilling terms of Service
Level Agreement (SLA), but this assignment can lead to the significant inefficiencies of the frequency
resource and to the high cost of renting it for virtual mobile operators. As an alternative solution, the
method of a dynamic resource sharing can be proposed. In this paper we consider the principle of setting
network slices using an utility function. This principle implements resource planning mechanisms for
tenants taking into account traffic requirements. These mechanisms allow to differentiate slices and
prioritize services that correspond to slices.
Keywords
5G, elastic traffic, Network Slicing, virtualization, resource allocation, scheduling, infrastructure sharing
1. Introduction
It is expected that in the coming years, mobile Internet traffic will not only continue to grow
rapidly, but will also change and reorient in connection with an unprecedented number and
variety of network-connected devices and the necessity to support a wide range of new applica-
tions. This will lead to a significant increase in the costs of network operators: costs that are
not comparable with the growth of operators’ profits.
Workshop on information technology and scientific computing in the framework of the X International Conference
Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems (ITTMM-2020),
Moscow, Russian, April 13-17, 2020
Envelope-Open bobrikova-ev@rudn.ru (E. V. Bobrikova); aaplatonova@list.ru (A. A. Platonova); sshorgin@ipiran.ru
(S. Ya. Shorgin); gaydamaka-yuv@rudn.ru (Y. V. Gaidamaka)
Orcid 0000-0002-7704-5827 (E. V. Bobrikova); 0000-0003-0571-1496 (A. A. Platonova); 0000-0001-5261-0159
(S. Ya. Shorgin); 0000-0003-2655-4805 (Y. V. Gaidamaka)
© 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
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Ekaterina V. Bobrikova et al. CEUR Workshop Proceedings 83–92
Therefore, it is extremely important for network operators to use the capabilities of the new
5G networks and review business behavior. The Next Generation Mobile Networks (NGMN)
Alliance assigned to Network Slicing a decisive role in the further development of 5G networks
and in the impact on updating the interaction of operators with business [1, 2]. Network
Slicing allows service providers to create virtual end-to-end networks, adapted to application
requirements (Figure 1).
Figure 1: 5G network slicing
Using of Network Slicing allows operators to provide parts of their networks for the specific
use cases of customers, for example, a smart home, Internet of things (IoT) factory, connected
car, smart energy grid. Network Slicing allows to place on one physical medium with its own
infrastructure various end-to-end logical networks called network slices.
Slices manage the sets of virtualized communication resources, network elements. The
Network Slicing architecture can be considered as consisting of two blocks, one is for the
actual implementation of the slice, and the other is for the control and configuration of a slice
(Figure 2).
Figure 2: Network Slicing architecture
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Ekaterina V. Bobrikova et al. CEUR Workshop Proceedings 83–92
The first block is designed as a layered architecture. It consists of three levels: service
layer, network function layer, infrastructure layer. Each layer contributes to the definition and
deployment of the slice. The second block is implemented as a centralized network element.
This is usually a controller of a network slice. The controller monitors and manages functionality
between the three layers to effectively coordinate the existence and interaction of several slices.
In recent years wireless network slicing has become a central research topic to address
the challenges of ever-increasing network traffic. Sharing of wireless infrastructure is widely
discussed in various literature.
The paper [3] gives a rigorous mathematical formulation of the scheduling problem with
multiple operators so called Generalized Resource Sharing (GRS). Authors give deep insight in
the most important parameters of this scheduling and analytical and numerical characteristics
of the impact of these parameters on rate-dependent utilities. Most of these results are valid for
an arbitrary number of users and operators.
The paper [4] proposes the concept of Multi-Operator Scheduling (MOS). This approach
allows to exchange sharing guarantees for spectral efficiency at the Base Station (BS). In addition,
authors move on to a more general problem so called Anticipatory Multi-Operator Scheduling
(AMOS).
It should be noted, that Network Slicing creates new problems that need to be addressed.
They must be considered in order to be accepted in practice. One of the solutions is the concept
of a network slice broker that acts as arbitration entity. The broker must be responsible for the
meeting of the heterogeneous requirements of slices from tenants while guaranteeing the most
efficient use of infrastructure resources. The paper [5] is based on the concept of brokers and
develops an online network slice (ONETS) brokering solution, corresponding to the development
of the new 3GPP Network Slicing architecture. The goal of ONETS solution is to develop an
effective online network slice broker. It analyzes the past information about network slices and
maximizes the gains of network slice resources multiplexing.
In [6] authors propose a general scheme, that describes the management of radio resource
for Network Slicing; a market mechanism, that governs the allocation of radio resources for
slices and an economic game, that allows to evaluate the strategies of tenant behavior at Nash
equilibrium. The work [6] focuses on development a mechanism, that allows tenants to engage
in a dynamic resource market. The mechanism allows tenants to optimize their solutions
according to the current state of the network.
In [7] the statement of the problem considers the economic issue of the network that arises
in wireless Network Slicing. The issue includes cash profit for infrastructure providers (InP)
in terms of strategies for the efficient allocation of resources for several associated operators
and the economic interaction of mobile virtual network operators (MVNOs) and their users.
The work [7] focuses on the two-level resource allocation problem to maximize individual
and total valuation of MVNOs. Here, the most important issue is the allocation of resources
between MVNOs with fairness guarantee. To solve the aforementioned problems, associated
with the resource allocation in wireless Network Slicing, an effective resource allocation system,
using generalized Kelly mechanism (GKM), is built in [7]. The concept of GKM is based on
works [8, 9]. A number of articles are known, for example [10, 11], where the problems of
network slicing are solved by the methods of queuing theory [12].
Static resources distribution at each network slice does not always provide the proper quality
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Ekaterina V. Bobrikova et al. CEUR Workshop Proceedings 83–92
of service and the efficient using of the resources. The reason is in the stochastic behavior of
wireless channel and the stochastic fluctuations of network traffic. To overcome these difficulties,
it is proposed to use the mechanism of dynamic resource distribution [13]. With this mechanism
network slices dynamically share network resources, and it becomes possible to ensure the
specific requirements of slices. In this paper it is proposed a general approach, based on the
introduction of an utility function, which depends on throughput and latency.
2. Main problem description
The statement of the problem and the approach to solving the problem are based on [13]. We
consider a situation where a single mobile network operator (MNO) controls the downlink
of a base station scheduler, whose wireless physical resources are used mutually by different
network slices. Let 𝑆 be the set of created network slices or tenants, since in this paper it is
assumed, that the tenant controls a single slice. Let 𝐾 be the set of users in the system, 𝐾𝑠 be
the subset of active users of slice 𝑠 ∈ 𝑆. Each tenant 𝑠 ∈ 𝑆 sets its slice requirements, which
are transmitted to the base station scheduler in the form of Key Performance Indicators (KPIs),
including latency and throughput.
The sharing of radio resources is modeled as a queuing system (QS), considered in discrete
time. Packets arrive randomly to the base station scheduler at the beginning of each time
interval (slotted time) 𝑛, 𝑛 ∈ 𝑁. The arrival of packets is distributed according to Poisson’s law,
where 𝜆𝑠 is the average arrival rate of the incoming packet stream of slice 𝑠. Let 𝑏𝑠 be the length
of the packet of slice 𝑠, 𝐷𝑘 [𝑛] be the total number of packets, arriving in the system for user 𝑘
at the time slot 𝑛. Let 𝑧𝑘 [𝑛] be the total number of served packets of user 𝑘 at time slot 𝑛. It is
considered that the packet is received successfully, when the total number of transmitted bits is
equal to the size of the packet.
The base station scheduler allocates one buffer of infinite length for each network slice. The
parameter 𝑄𝑠 [𝑛] ∈ {0, 1} shows the state of the 𝑠-th buffer: whether it is empty or busy at the
time slot 𝑛. It is assumed, that packets are served according to the discipline First-In-First-Out
(FIFO) in each buffer. The reason is that each slice defines a unique type of service, and therefore
all packets are handled the same within one slice. Packages, belonged to different buffers, are
served on the base of a scheduling policy, that ensures customization and differentiation of
slices. To implement this statement, let 𝕆 be the set of network performance indicators, such as,
average user throughput, minimum latency. For each element 𝑜 ∈ 𝕆 let’s define a utility function
in a general form: 𝑈𝑠𝑜 (𝑓 𝑜 (𝑥𝑠 ), 𝛽𝑠𝑜 ), ∀𝑜 ∈ 𝕆, ∀𝑠 ∈ 𝑆, where 𝛽𝑠𝑜 is the network slice’s 𝑠 requirement
for the specific performance indicator 𝑜 ∈ 𝕆, and 𝑓 𝑜 (𝑥𝑠 ) is a function, that determines the
resources allocated to the network slice 𝑠 for all its users 𝑥𝑠 . Here
𝑥𝑠 = ∑ ∑ 𝑥𝑘 [𝑛]
𝑛∈𝑁 𝑘∈𝐾𝑠
and 𝑥𝑘 [𝑛] is the share of resources, allocated by the scheduler to user 𝑘 at time slot 𝑛. At last, it
is assumed that the scheduler has complete information about the channel, and let 𝑟𝑘 [𝑛] be the
maximum achievable rate of user 𝑘 at time slot 𝑛.
It is assumed that each network slice determines its own specific service, for which the
tenant requires specially designed and customized network configuration. Network slice
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customization is modeled using piece-wise linear utility functions, which display the achieved
network performance indicators, based on requirements, established by tenants.
In this paper it is considered two indicators of network performance: latency and throughput,
and a utility function is constructed for each of them.
Latency utility function. We define the latency for each packet as the waiting time of a packet
in the buffer before this packet is transmitted. Now we define the maximum latency:
𝐿max
𝑠 = max{(𝑛 − 𝑖), ∀𝑖 ⩽ 𝑛 ∶ 𝑧𝑘 [𝑛] = 𝐷𝑘 [𝑖]}, ∀𝑠 ∈ 𝑆,
𝑘∈𝐾𝑠
which describes the maximum packet latency for a slice 𝑠. Next we define the average latency:
1 1
𝐿𝑎𝑣𝑒
𝑠 = ∑ ∑ 𝑙 , ∀𝑠 ∈ 𝑆,
|𝐾𝑠 | 𝑘∈𝐾 𝐷𝑘 𝑑∈𝐷 𝑑
𝑠 𝑘
where 𝑙𝑑 is the latency of one packet 𝑑 and 𝐷𝑘 is the total number of packets arrived in the
system to user 𝑘. 𝐿𝑎𝑣𝑒
𝑠 determines the average latency for all users of the slice 𝑠.
max 𝑎𝑣𝑒
For 𝐿𝑠 and 𝐿𝑠 we define a utility function:
𝑈 𝐿 , if 𝑦 ⩽ 𝜏𝑡𝑎𝑟
⎧ 𝑡𝑎𝑟
⎪ 𝐿 𝐿
𝐿 − (𝑈𝑡𝑎𝑟 − 𝑈min )(𝑦 − 𝜏𝑡𝑎𝑟 ) ,
𝑈̂ 𝑠𝐿 (𝑦, 𝜏𝑠 ) = 𝑈𝑡𝑎𝑟 if 𝜏𝑡𝑎𝑟 ⩽ 𝑦 ⩽ 𝜏max (1)
⎨ 𝜏max − 𝜏𝑡𝑎𝑟
⎪ 𝐿
⎩𝑈min , if 𝑦 ⩾ 𝜏max ,
where 𝑦 is the latency variable, that is either 𝐿max
𝑠 or 𝐿𝑎𝑣𝑒
𝑠 ; 𝜏𝑠 is the latency requirement for the
network slice 𝑠.
It is assumed, that each network slice defines its interval of the required latency, that is, the
𝐿 is
target latency 𝜏𝑡𝑎𝑟 and the maximum allowable latency 𝜏max , therefore 𝜏𝑠 = {𝜏𝑡𝑎𝑟 , 𝜏max }. 𝑈min
the minimum value of the utility function, 𝑈𝑡𝑎𝑟 𝐿 is the maximum value of the utility function.
The general view of the latency utility function is in Figure 3. The values of the function 𝑈̂ 𝑠𝐿 are
calculated according to the Algorithm 1.
Data: y
Result: 𝑈̂ 𝑠𝐿 (𝑦, 𝜏𝑠 )
1 if 𝑦 ⩽ 𝜏𝑡𝑎𝑟 then
2 𝑈̂ 𝑠𝐿 (𝑦, 𝜏𝑠 ) = 𝑈𝑡𝑎𝑟
𝐿
3 else if 𝜏𝑡𝑎𝑟 < 𝑦 ⩽ 𝜏max then
𝐿 𝐿
4
𝐿 − (𝑈𝑡𝑎𝑟 −𝑈min )(𝑦−𝜏𝑡𝑎𝑟 )
𝑈̂ 𝑠𝐿 (𝑦, 𝜏𝑠 ) = 𝑈𝑡𝑎𝑟 𝜏max −𝜏𝑡𝑎𝑟
5 else
6 𝑈̂ 𝑠𝐿 (𝑦, 𝜏𝑠 ) = 𝑈min
𝐿
7 end
Algorithm 1: The values of 𝑈̂ 𝑠𝐿 .
Based on the definitions given above, the overall latency utility function is defined as follows:
𝑈𝑠𝐿 = 𝛿𝑠 ⋅ 𝑈̂ 𝑠𝐿 (𝐿max ̂ 𝐿 𝑎𝑣𝑒
𝑠 , 𝜏𝑠 ) + (1 − 𝛿𝑠 ) ⋅ 𝑈𝑠 (𝐿𝑠 , 𝜏𝑠 ), ∀𝑠 ∈ 𝑆,
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where 𝛿𝑠 is the weight coefficient specified by the tenant. The coefficient 𝛿𝑠 determines the
priority of the network slice using the latency utility function in terms of 𝐿max
𝑠 or 𝐿𝑎𝑣𝑒
𝑠 .
Throuhgput utility function. We define the total user throughput for one slice:
1
𝑅𝑠 = ∑ 𝑧𝑘 [𝑁 ] ⋅ 𝑏𝑘 , ∀𝑠 ∈ 𝑆,
𝑇𝑠𝐴𝐶𝑇 𝑘∈𝐾𝑠
where 𝑧𝑘 [𝑁 ] is the total number of packets, transferred to the user 𝑘, and 𝑇𝑠𝐴𝐶𝑇 is the total
time, during which buffer is active for packets transmission. The throughput utility function is
defined as follows:
𝑈 𝑇 , if 𝑦 ⩾ 𝜌𝑡𝑎𝑟 ,
⎧ 𝑡𝑎𝑟
⎪ 𝑇 𝑇
𝑇 − (𝑈𝑡𝑎𝑟 − 𝑈min )(𝑦 − 𝜌𝑡𝑎𝑟 ) , if 𝜌 ⩾ 𝑦 ⩾ 𝜌
⎪𝑈𝑡𝑎𝑟 𝑡𝑎𝑟 min ,
𝑈𝑠𝑇 (𝑦, 𝜌𝑠 ) = 𝜌min − 𝜌𝑡𝑎𝑟 (2)
⎨ 𝑇 𝑦 − 𝜌𝑧𝑒𝑟𝑜
⎪𝑈min 𝜌 , if 𝜌min ⩾ 𝑦 ⩾ 𝜌𝑧𝑒𝑟𝑜 ,
⎪ min − 𝜌𝑧𝑒𝑟𝑜
⎩0, if 𝑦 ⩽ 𝜌𝑧𝑒𝑟𝑜 ,
where 𝑦 = 𝑅𝑠 is the aggregate throughput of the user of slice 𝑠 and 𝜌𝑠 = {𝜌𝑡𝑎𝑟 , 𝜌min , 𝜌𝑧𝑒𝑟𝑜 } are
the throughput requirements; 𝜌𝑧𝑒𝑟𝑜 — the basic bit-rate for each slice; 𝜌min — the minimum
guaranteed bit-rate, which is necessary to provide the standard quality of service; 𝑈min 𝑇 — the
value of the utility function corresponding to 𝜌min ; 𝜌𝑡𝑎𝑟 — the bit-rate, which is necessary to
𝑇 is the maximum value of the utility function corresponding
provide a high quality of service; 𝑈𝑡𝑎𝑟
to 𝜌𝑡𝑎𝑟 . The general view of the throughput utility function is in Figure 4. The values of the
function 𝑈̂ 𝑠𝐿 are calculated according to the Algorithm 2.
Data: y
Result: 𝑈𝑠𝑇 (𝑦, 𝜌𝑠 )
1 if 𝑦 ⩽ 𝜌𝑧𝑒𝑟𝑜 then
2 𝑈𝑠𝑇 (𝑦, 𝜌𝑠 ) = 0
3 else if 𝜌𝑧𝑒𝑟𝑜 < 𝑦 ⩽ 𝜌min then
𝑇 𝑦−𝜌𝑧𝑒𝑟𝑜
4 𝑈𝑠𝑇 (𝑦, 𝜌𝑠 ) = 𝑈min 𝜌 −𝜌
min 𝑧𝑒𝑟𝑜
5 else if 𝜌min < 𝑦 ⩽ 𝜌𝑡𝑎𝑟 then
𝑇 −𝑈 𝑇 )(𝑦−𝜌 )
(𝑈𝑡𝑎𝑟
6
𝑇 −
𝑈𝑠𝑇 (𝑦, 𝜌𝑠 ) = 𝑈𝑡𝑎𝑟 min 𝑡𝑎𝑟
𝜌min −𝜌𝑡𝑎𝑟
7 else
8
𝑇
𝑈𝑠𝑇 (𝑦, 𝜌𝑠 ) = 𝑈𝑡𝑎𝑟
9 end
Algorithm 2: The values of 𝑈𝑠𝑇 .
The resource allocation problem. The scheduler assigns physical resources to users based on
the requirements of the network slice, using the latency utility function 𝑈𝑠𝐿 and the throughput
utility function 𝑈𝑠𝑇 , defined above. In addition, we introduce a specific parameter 𝛼𝑠 for a network
slice in order to start the mechanism that allows tenants themselves to determine the weights
of the corresponding utility function.
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Ekaterina V. Bobrikova et al. CEUR Workshop Proceedings 83–92
Figure 3: The general view of Figure 4: The general view of
the latency utility function the throughput utility function
Let us formulate the resource allocation problem, oriented to network slices, as an optimization
problem [13, 14] in the following statement
max ∑ 𝑈𝑠 ⋅ 𝛼𝑠 ,
𝑠∈𝑆
where
∑ 𝑥𝑘 [𝑛] ⩽ 1, ∀𝑛 ∈ 𝑁 , 𝑧𝑘 [𝑛] ⩽ 𝐷𝑘 [𝑛 − 1], ∀𝑘 ∈ 𝐾 , ∀𝑛 ∈ 𝑁 ,
𝑘∈𝐾
𝑛 𝑛
∑ 𝑥𝑘 [𝑖] ⋅ 𝑟𝑘 [𝑖] ⩽ 𝐷𝑘 [𝑛] ⋅ 𝑏𝑘 , ∀𝑘 ∈ 𝐾 , ∀𝑛 ∈ 𝑁 , ∑ 𝑥𝑘 [𝑖] ⋅ 𝑟𝑘 [𝑖] ⩾ 𝑧𝑘 [𝑛] ⋅ 𝑏𝑘 , ∀𝑘 ∈ 𝐾 , ∀𝑛 ∈ 𝑁 ,
𝑖=1 𝑖=1
0, if 𝐷𝑘 [𝑛] = 𝑧𝑘 [𝑛]
𝑄𝑠 [𝑛] = { , ∀𝑛 ∈ 𝑁 , ∀𝑘 ∈ 𝐾𝑠 , ∀𝑠 ∈ 𝑆.
1, otherwise
Here the optimal solution provides maximum weighted sum of the utility functions of the slices
for all slices of the network. The problem is formulated for both performance indicators, that
is, 𝑈𝑠 = {𝑈𝑠𝐿 , 𝑈𝑠𝑇 }, 𝛼𝑠 = {𝛼𝑠𝐿 , 𝛼𝑠𝑇 }. The first constraint ensures, that the scheduler does not assign
more resources than those are available in network at every time slot 𝑛. The second constraint
shows, that the packet can be considered successfully transmitted only at the end of the time
slot or at the beginning of the next time slot. The third constraint ensures, that the number
of bits transmitted cannot be more than the total number of bits received in the system at one
time slot. The fourth constraint updates the total number of received packets at each time slot
𝑛, taking into account the total number of received bits. Finally, the fifth constraint determines
the state of the buffer.
The proposed formulation of the resource allocation problem always guarantees the max-
imization of the utility function for each network slice. Therefore, in the case of a sufficient
amount of resources in the system, we can assume that each network slice reaches maximum of
its utility function. However, the mobile network operator (MNO) must be ready for situations
when resources are not enough, for example, due to network congestion. Therefore it is assumed
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Ekaterina V. Bobrikova et al. CEUR Workshop Proceedings 83–92
that the tenant can monitor the performance of the slice in real time and can change its priority
indicators in order to scale the utility function and get various network performance indicators.
By introducing the specific parameter 𝛼𝑠 for the slice, we enable a tenant to configure and
differentiate the network slice. This becomes especially impotant in case of congestion of the
network, since MNO has to make decisions how to deal with slices, when it is known beforehand
that the execution of all the requirements may not be possible. In this sense, the adjusting of 𝛼𝑠
allows tenants:
— to prioritize a set of network performance indicators within a single slice (slice customization).
That is, whenever MNO is not be able to fulfill all the requirements for the slice, resources is
allocated to maximize utility of the indicator with higher priority.
— to prioritize slices (slice differentiation). In this case, when the MNO is not able to provide
maximum value of the utility function for all slices, parameter 𝛼𝑠 indicates the most critical
slices, that require higher priority.
Note, that the utility function is defined for both latency and throughput. Therefore, it is
possible to consider services with different parameters of latency and throughput, using the
capabilities of Network Slicing. Let’s consider the following services: TI (Tactile Internet), eMBB
(enhanced Mobile BroadBand), mMTC (massive Machine Type Communication), cMTC (critical
Machine Type Communication) [13]. These services are supported by 5G, the principles of
Network Slicing are applicable to which, and for which it is possible to construct utility functions,
that take into account both latency and throughput. It is shown in Figure 5 the latency utility
functions for four types of the slices, namely: 𝑈̂ 𝑇𝐿𝐼 (𝑦, 𝜏𝑇 𝐼 ), 𝑈̂ 𝑒𝑀𝐵𝐵
𝐿 (𝑦, 𝜏𝑒𝑀𝐵𝐵 ), 𝑈̂ 𝑚𝑀𝑇
𝐿
𝐶 (𝑦, 𝜏𝑚𝑀𝑇 𝐶 ),
𝑈̂ 𝑐𝑀𝑇 𝐶 (𝑦, 𝜏𝑐𝑀𝑇 𝐶 ), based on (1).
𝐿
TI and cMTC services relate to URLLC (Ultra-Reliable Low Latency Communication) ap-
plications. These two slices are the most critical applications in terms of latency. Latency
requirements can even have values below 1 ms [13]. These applications also require high
throughput. It is assumed that eMBB and mMTC slices are more flexible with respect to latency
requirements and their utility is less affected by delays in scheduling decisions. It is shown
in Figure 6 the throughput utility functions for four types of the slices, namely: 𝑈𝑇𝑇𝐼 (𝑦, 𝜏𝑇 𝐼 ),
𝑇
𝑈𝑒𝑀𝐵𝐵 𝑇
(𝑦, 𝜏𝑒𝑀𝐵𝐵 ), 𝑈𝑚𝑀𝑇 𝑇
𝐶 (𝑦, 𝜏𝑚𝑀𝑇 𝐶 ), 𝑈𝑐𝑀𝑇 𝐶 (𝑦, 𝜏𝑐𝑀𝑇 𝐶 ), based on (2).
Figure 5: Latency utility functions for Figure 6: Throughput utility functions for
different services: TI, eMBB, mMTC, cMTC different services: TI, eMBB, mMTC, cMTC
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It is assumed, that for applications with weak throughput requirements, achieving a minimum
guaranteed bit-rate is sufficient to provide satisfactory service, which means a high value for
utility. It takes place for TI, cMTC, mMTC. On the contrary, for the eMBB slice, the utility
value is set much lower, which means low provide quality. As we can see, as a result of strict
latency requirements, for applications TI and cMTC, an increase in throughput leads to a
decrease in latency. On the contrary, applications, which are not latency-critical, are more
demanding in terms of aggregate throughput. Namely, for the mMTC slice it is assumed that
the minimum guaranteed bit-rate should be provided, but the aggregate throughput can be
high, given the huge number of connected devices. It is assumed for the eMBB slice, a high
throughput requirement for each user, but with relatively few users at the same time active per
cell.
The parameters for the utility functions in Figures 5, 6 are derived according to [13]. But we
consider slightly different combinations of parameters for the presented slices.
The approach considered in this paper, using the construction of the utility function of the
slice, can be recommended to MNO. For their set of services, operators will be able to evaluate
the profitability of these services and determine the tariffs for users. So, in [13] a numerical
analysis was performed for TI, cMTC, eMBB, mMTC slices. The scheduling tactics depend
mainly on two factors: how utility functions are defined for the different types of slices and how
tenants determine weights by choosing the parameter 𝛼𝑠 . Some recommendations are given.
In order to maximize the utility of the latency-critical slices, it is necessary to schedule user
service, as soon as the packet arrives at the buffer, regardless of the state of their channel. This
method gives the highest priority to such users and does not allow the scheduler to make more
effective scheduling decisions. On the contrary, for slices that are oriented to high throughput,
the state of the user channel may also influence the increase in utility.
3. Conclusions
In this paper we propose an algorithm for the dynamic sharing of network resources by network
slices. The utility function of the network slice is described, which allows to customize the
behavior of various types of slices. Differentiation between tenants is achieved through change
in specific parameters of the slices. These parameters, in turn, dynamically change the view
of the utility function of the slice. In the future it is planned to study in detail the effect of
parameter changes in some slices of the network on service latency in other slices. It is planned to
investigate the minimum value of the utility function, corresponding to the minimum guaranteed
bit-rate for each slice. It is planned to consider the impact of changing of the parameters of the
task in connection with the interaction between tenants and mobile network operators.
Acknowledgments
The work is supported by RUDN Program «5-100» and by RFFR in the framework of the scientific
projects № 18-07-00576, 19-07-00933. The authors thank Natalia Yarkina for the materials that
were used in the Introduction.
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Ekaterina V. Bobrikova et al. CEUR Workshop Proceedings 83–92
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