To the analysis of the dynamic assignment of radio resources in wireless networks with a network slicing mechanism

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 suficient condition for fulfilling terms of Service Level Agreement (SLA), but this assignment can lead to the significant ineficiencies 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 trafic requirements. These mechanisms allow to diferentiate slices and prioritize services that correspond to slices.

Keywords

• 5G
• elastic trafic
• Network Slicing
• virtualization
• resource allocation
• scheduling
• infrastructure sharing

1. Introduction

It is expected that in the coming years, mobile Internet trafic 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 applications. This will lead to a significant increase in the costs of network operators: costs that are not comparable with the growth of operators’ profits. nEvelop-O Workshop on information technology and scientific computing in the framework of the X International Conference

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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).

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).

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 efectively 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 trafic. 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 eficiency 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 eficient 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 efective 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 eficient 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 efective 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

of service and the eficient using of the resources. The reason is in the stochastic behavior of wireless channel and the stochastic fluctuations of network trafic. To overcome these dificulties, 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 diferent network slices. Let be the set of created network slices or tenants, since in this paper it is assumed, that the tenant controls a single slice. Let be the set of users in the system, be the subset of active users of slice ∈ . Each tenant ∈ 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) , ∈ . The arrival of packets is distributed according to Poisson’s law, where is the average arrival rate of the incoming packet stream of slice . Let be the length of the packet of slice , [] be the total number of packets, arriving in the system for user at the time slot . Let [] be the total number of served packets of user at time slot . 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 bufer of infinite length for each network slice. The parameter [] ∈ {0, 1} shows the state of the -th bufer: whether it is empty or busy at the time slot . It is assumed, that packets are served according to the discipline First-In-First-Out (FIFO) in each bufer. 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 diferent bufers, are served on the base of a scheduling policy, that ensures customization and diferentiation of slices. To implement this statement, let be the set of network performance indicators, such as, average user throughput, minimum latency. For each element ∈ let’s define a utility function in a general form: ( ( ), ), ∀ ∈ , ∀ ∈ , where is the network slice’s requirement for the specific performance indicator ∈ , and ( ) is a function, that determines the resources allocated to the network slice for all its users . Here and [] is the share of resources, allocated by the scheduler to user at time slot . At last, it is assumed that the scheduler has complete information about the channel, and let [] be the maximum achievable rate of user at time slot .

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

= ∑ ∑ [] ∈ ∈ 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 bufer before this packet is transmitted. Now we define the maximum latency: max = max{( − ), ∀ ⩽ ∶ [] = []}, ∀ ∈ , which describes the maximum packet latency for a slice . Next we define the average latency: ∈

= 1 | | ∑

determines the average latency for all users of the slice .

we define a utility function: where is the latency of one packet and is the total number of packets arrived in the ̂ ( , ) = ⎨

− ⎪ ⎧ , if ⩽ ⎩⎪ min, if ⩾ max,

max − − min)( − ) , if ⩽ ⩽ max (1) where is the latency variable, that is either max or ; is the latency requirement for the network slice .

It is assumed, that each network slice defines its interval of the required latency, that is, the

target latency

and the maximum allowable latency max, therefore = { , max}. min is the minimum value of the utility function, 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 ̂ are

calculated according to the Algorithm 1.

Data: y Result: ̂

( , ) 1 if ⩽ then

̂ ( , ) = 2 4 6 5 else 7 end

̂ ( , ) = min 3 else if

< ⩽ max then ̂ ( , ) = − ( − min)(− ) max−

Algorithm 1: The values of ̂ .

Based on the definitions given above, the overall latency utility function is defined as follows: = ⋅ ̂ ( max, ) + (1 − ) ⋅ ̂ (

, ), ∀ ∈ , where is the weight coeficient specified by the tenant. The coeficient priority of the network slice using the latency utility function in terms of max or . determines the Throuhgput utility function. We define the total user throughput for one slice: = 1 ∑ [ ] ⋅ , ∀ ∈ , where [ ] is the total number of packets, transferred to the user , and time, during which bufer is active for packets transmission. The throughput utility function is is the total defined as follows: ( , ) = ⎪ ⎪

− ⎧ , if ⩾ , ⎪

− ⎨ min min − ⎪ ⎩0, if ⩽

, − min)( − ) min −

, if ⩾ ⩾ min, , if min ⩾ ⩾ , (2) where = is the aggregate throughput of the user of slice and = { , min, } are the throughput requirements;

— the basic bit-rate for each slice; min — the minimum guaranteed bit-rate, which is necessary to provide the standard quality of service; min — the value of the utility function corresponding to min; — the bit-rate, which is necessary to function ̂ are calculated according to the Algorithm 2. provide a high quality of service; is the maximum value of the utility function corresponding to . The general view of the throughput utility function is in Figure 4. The values of the 2 4 6 8 7 else 9 end

Result: ( , ) 1 if ⩽ 3 else if

then ( , ) = 0

− ( , ) = min min−

< ⩽ min then 5 else if min < ⩽

then ( , ) = − ( − min)(− )

min− ( , ) =

Algorithm 2: The values of .

The resource allocation problem. The scheduler assigns physical resources to users based on utility function , defined above. In addition, we introduce a specific parameter the requirements of the network slice, using the latency utility function and the throughput for a network slice in order to start the mechanism that allows tenants themselves to determine the weights of the corresponding utility function. problem [ 13, 14 ] in the following statement where =1 ∑ [] ⩽ 1, ∀ ∈ ,

[] ⩽ [ − 1], ∀ ∈ , ∀ ∈ , ∈ ∑ [] ⋅ [] ⩽ [] ⋅ , ∀ ∈ , ∀ ∈ ,

∑ [] ⋅ [] ⩾ [] ⋅ , ∀ ∈ , ∀ ∈ , [] = { 0, if [] = []

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, = { , }, = { , }. The first constraint ensures, that the scheduler does not assign more resources than those are available in network at every time slot . 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 , taking into account the total number of received bits. Finally, the fith constraint determines the state of the bufer.

The proposed formulation of the resource allocation problem always guarantees the maximization of the utility function for each network slice. Therefore, in the case of a suficient 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 max ∑ ⋅ , ∈ =1 allows tenants: 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 for the slice, we enable a tenant to configure and diferentiate 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 — 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. slices, that require higher priority.

— to prioritize slices (slice diferentiation ). In this case, when the MNO is not able to provide maximum value of the utility function for all slices, parameter indicates the most critical

Note, that the utility function is defined for both latency and throughput. Therefore, it is

possible to consider services with diferent 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: ̂

( , ), ̂ ( ,

), ̂ ( , ), ( ,

), based on (1).

̂

), based on (2).

TI and cMTC services relate to URLLC (Ultra-Reliable Low Latency Communication) applications. 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 afected by delays in scheduling decisions. It is shown in Figure 6 the throughput utility functions for four types of the slices, namely: ( , ),

It is assumed, that for applications with weak throughput requirements, achieving a minimum guaranteed bit-rate is suficient 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 diferent 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 tarifs 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 diferent types of slices and how tenants determine weights by choosing the parameter . 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 bufer, 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 efective 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. Diferentiation 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 efect 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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