Artem Volkov

Abdukodir Khakimov
email: abdukadir94@mail.ru

Ammar Muthanna

Ruslan Kirichek
email: kirichek@sut.ru

Andrei Vladyko
email: vladyko@sut.ru

Andrey Koucheryavy

Interaction of the IoT traffic generated by a Smart city segment with SDN core network

Keywords: IoT, SDN, data management, API, Smart city, round trip time, Mikrotik switches

The main purpose of this article is to test IoT management system based on SDN core network, as well as interaction IoT traffic with SDNswitsches. To conduct investigation of management system and network infrastructure behavior we carried out several IoT traffic tests, which were generated based on partnership project oneM2M specification. In this work, we considered "Smart city" model for Central district of Saint-Petersburg (Russia). During the testing of the network infrastructure were identified several parameters such as number of simultaneously supported sessions by the Mikrotik switch using different transport protocols, was proposed a recommendation for dynamically changing virtual buffers. During the testing of the IoT management system, we define reliability of IoT data management service for determined equipment in traffic conditions of the "Smart City". Also, we estimate relationship between RTT parameter using various IoT protocols and heterogeneous traffic in conjunction with "Smart city" segment in SDN network. In order to investigate the influence of the SDN network on the RTT traffic parameter of a large number of IoT and the condition of its transmission in conjunction with heterogeneous traffic in the network, a full-scale experiment was conducted on the developed model, which in turn reflected a possible distribution scheme of a certain monitoring and control system for the Central District Saint-Petersburg. The aim of the study is also to consider the possibility of implementing the IoT data management service as a central management system for monitoring urban ecological parameters in a dense buildings environment.

Introduction

Smart City -a futuristic idea or an inevitable future? Smart City, also known as "smart city" [START_REF] Naphade | Smarter Cities and Their Innovation Challenges[END_REF], "digital city" -a concept in which there is still no unambiguous defi-nition. It can be stated as, smart city -a city that uses information and communication technology for the efficient use of resources, resulting in cost savings and energy, improving the quality of life of inhabitants [START_REF] Bowerman | The Vision of a Smart City[END_REF], improving the ecological environment, etc. In recent years, many cities began to implement projects related to with the use of smart city technologies. For example, Singapore (use ERP «intelligent traffic system" to deal with traffic jams.), Vancouver (Power systems organized on the principle of renewable sources), Helsinki (program to increase the availability of information resources and to attract residents to their use) and so on. Course this is only the first step toward optimizing resources and saving their possible replacement by other, less harmful to the environment, information society. However, the first step has been taken. Services such as automatic collection of indications of house energy meters [START_REF] Zanella | Internet of Things for Smart Cities[END_REF], automation of urban transport service [START_REF] Fujdiak | Advanced optimization method for improving the urban traffic management[END_REF], which allows you to watch the buses moving, trolley buses and the like, and to know the approximate time of their arrival, the city multifunctional centers with electronic queue, e-health care [START_REF] Kirichek | Live substance in cyberspace -Biodriver system[END_REF], geographic information systems, and other systems that facilitate a person's life in the big city. But it's certainly not all aspects that includes the concept of "Smart City". For the full realization of these ideas, require new network infrastructure, new approaches to data organization, to meet the new requirements. As a result of these issues, there is such a thing as Big Data. It can be concluded that for effective work Smart City requires a deep integrated system consisting of many subsystems, which will take into account both the current needs of various city services, and taking into account the prospects of development in terms of new factors. This system should be resistant to different types of impact, for example, in terms of information security; this system must be protected, so in case of fails, the work of many city services will be difficult or limited. Resistant to various force majeure, that is to be provided back-up system ready from the first time to take over the functions of failed management system "Smart City". An important aspect that should be fulfilled is the organization of such systems on the basis of generally accepted standards throughout the telecommunications world. This enables many third-party companies to provide their services on general terms and protects them from monopoly in this area.

In this paper, as one of possible services examples for "Smart City", will be considered a system for monitoring environmental parameters of air in three types of sensors, for monitoring and to develop appropriate methods to optimize the ecological situation in the dense urban and highway traffic. Just ecological picture can be useful not only in terms of the environmental situation, but also for automation of control in the field of fire and gas safety.

The approach of software-defined networks (SDN) [START_REF] Alsmadi | A Systematic Literature Review on Software-Defined Networking[END_REF] allows to significantly automate and facilitate network management by allowing them to write management applications. This approach involves the separation levels and data transmission and control, wherein the operation to determine the packet transmission route identifies a controller (the "brain" in the concept), which has information about the topology of the network status for easy monitoring and network control [START_REF] Kirichek | Software-Defined Architecture for Flying Ubiquitous Sensor Networking[END_REF]. This functionality is determined by the controller API.

Specifications in the M2M and the proposed management system

The rapid pace of urbanization poses new challenges for city services, which certainly needs to be addressed to ensure the stable operation at such a high load. For centralized collection and management of Internet of Things, an appropriate service is required that will provide the necessary management functions. Also, for the further development of the "Smart City" architecture, required a system, which built, as already mentioned before, based on certain standards of interaction.

The need for standardization in field of machine-machine communications (M2M) has sharply increased recently in the development of infocommunications [START_REF] Himayat | Multi-radio heterogeneous networks: Architectures and performance[END_REF][START_REF] Gerasimenko | Energy and delay analysis of LTE-advanced RACH performance under MTC overload[END_REF]. To solve the set tasks, was created global partner project oneM2M [START_REF]oneM2M[END_REF]. The initiators of the creation were seven regional telecommunication standardization organizations ETSI, ARIB, ТТС, CCSA, TIA, ATIS and TTA. Currently partnership oneM2M actively developing specifications in the field of machine to machine and the Internet of Thing, which was last updated on September 29, 2016. In total, by September 29, 2016, 24 specifications have been developed, for example TS 0001 specificationdescribes the functional architecture of oneM2M interaction, in TS 0003 -it displays security issues, and in TS 0009, TS 0010, implements transmission based on HTTP and MQTT protocols, respectively. Community Opendaylight, which includes a considerable number of infocommunication companies, based on the specifications of oneM2M was developed the implementation of a broker (data warehouse) with Internet of Things management functions, organized using the REST API. Internet of Things Data Management is an open source software that acts as an intermediary between oneM2M resources and related applications, with the organization having a specific application access policy to appropriate resources. All resources (Internet Things) are displayed as a hierarchical tree. Typically, the interaction with the resource tree occurs using HTTP protocols (TS 0009), CoAP (TS 0008), MQTT (TS 0010). Where TS 0008, TS 0009, TS 0010 are the corresponding oneM2M specifications. By default, applications for extracting data can work with the resource tree. But it is also possible to use control systems for devices or large data, for analytical systems. Also, are possible applications for device configuration. In this paper, as the management of "Smart City" systems to test both the services and protocols of the Internet of Things, with data organization over SDN network service IoTDM, developed Opendaylight community was chosen because of its organization in accordance with the specifications oneM2M.

The study of interaction of Internet of Things traffic with SDN [START_REF] Akyildiz | A roadmap for traffic engineering in SDN-OpenFlow networks[END_REF][START_REF] Vladyko | Comprehensive SDN Testing Based on Model Network[END_REF][START_REF] Jararweh | SDIoT: A Software Defined Based Internet of Things Framework[END_REF][START_REF] Kirichek | Model networks for Internet of Things and SDN[END_REF] and on condition to transfer it together with heterogeneous traffic, was formed the task -to conduct SDN testing for speed the establishment of network infrastructure at the primary connecting of switches, organization of the switch buffers.

The study of the IoTDM system based on SDN was formulated the main task -to carry out testing the service in view of the real potential traffic load Internet of Things using protocols: HTTP, CoAP, MQTT, based on the model of the real area of St. Petersburg city. Testing essentially reduces to checking the interaction between IoT devices, the network infrastructure and the IoTDM service. Figure 1 and Table 1 shows the network infrastructure, organized in the SDN laboratory of the St. Petersburg State University of Telecommunications.

Fig. 1. The structure of the laboratory stand

As a load generator for testing the core of the SDN network, the iperf3 generator was used, which allows flexible configuration of traffic parameters. In this test, the generator was configured to simulate the load with IoT traffic [START_REF] Kirichek | Internet of Things Laboratory Test Bed[END_REF][START_REF] Koucheryavy | State of the art and research challenges for USN traffic flow models[END_REF][START_REF] Muthanna | The mixed telemetry/image USN in the overload conditions[END_REF]; this was reflected in the number of packets: less than 190 bytes.

In the process of work to increase the number of sessions that pass through each switch simultaneously. Testing was performed using the protocols: UDP and TCP.

The test results are shown in Figures 2 and3, with each of the graphs showing the dependency on each of the switches. As shown on the graphs in Figures 2 and3, by increasing the number of connections increases dramatically loss after a certain number of simultaneous connections in each of the SDN switches. Thus, it can be concluded that by using TCP, the number of possible simultaneous connections is smaller (the peak at ~ 360) than when using a UDP protocol (peak at ~ 400-410). A break in the graphs means the failure of the network infrastructure (shutdown of Mikrotik switches and their unplanned overload). According to the test results, we can conclude that this type of switch is possible only with the organization of internal corporate networks for small size.

Also after studying responses to switch the same type of traffic, we concluded on the use of buffers in the SDN switches. As we know, to fine-tune the buffer size in network nodes use the formula B = P * RTT where B is the buffer size, P is the throughput, and RTT is the (Round Trip Time). With this formula, you can easily configure the optimal buffer size (queue). However, this formula does not take into account the number of parallel flows that can be different types (independent of each other). In classical networks uses the addition to this formula N P RTT * , where N -the number of independent sessions. According to this law, determine the optimal size of the buffer. Moreover, the number N is taken as the averaged value from the exponential distribution, where P => 0.7. This method gives an error of up to 30%.

As a result of tests conducted on mikrotik equipment, we came to the conclusion that we can specify virtual buffers for each session. This will reduce the RTT parameter values for both normal network services and possibly for the tactile Internet. Since OpenFlow protocol allows to control the full resource of a network device, this task can be assigned to him, in the organization of the corresponding plug on the SDN controller.

IoTDM service testing as "Smart City" service management system

For IoTDM service testing, we created a model that highlights possible Internet of Things interaction to monitor ecological situation in the city in dense urban development. For an accurate research, we chose Saint-Petersburg central district, which has a more good shape for modelling and is divided into 6 municipal divisions: #78, Dvortsovy, Ligovka-Yamskaya, Liteyny, Smolninskoye and Vladimirsky. This allows to evenly distributing sensors when building the model. Fig. 4. shows a map of the central district of St Petersburg and its municipal divisions.

We used SDN as network infrastructure, whose structure is shown in the first section.

The Smart city hierarchical model designed as follows: * For a uniformly load distribution on network device, we connected two municipal divisions to each and every OpenFlow switch.

* In every division is involved around 40 crossroads. * Every crossroad has four traffic lights, which serve as Internet of Thing. * Every Internet of Thing contains three types of sensor for air ecological state control.

Fig. 4. Central district of St Petersburg

The model working mechanism was build based on the following algorithm: 1. Building resources tree, taking into account hierarchical division into Municipalities, crossroads, traffic lights.

2. Internet of Thing Initialization. When the IoTDM service is initialized to the resources tree, every Internet of Thing sends a request containing information about sensors readiness when connecting. Information from GPS sensor comes once.

3. Internet of Things traffic generation. Every Internet of Thing sends a request every second (Constant Instances, according to M2M specification) to the resources tree. The request contains sensors data, their registration time, value number and other metadata.

We also organized the transmission of every Internet of Thing successively from every crossroad while request to sources tree (IoTDM service) were sent simultaneously from every crossroad. Finally, we got a model with 960 Internet of Things while during one-time interval working with service of 240 Internet of Things. To build resource tree we wrote a corresponding script. To generate traffic, we developed an Internet of Thing traffic generator according to oneM2M specification and the designed "Smart city" model architecture based on HTTP, CoAP, MQTT protocols which sends requests containing, in the message body, JSON format. The IoT traffic generator was developed in Python programming language and API IoTDM.

The built resource tree is shown in Figure 5. Multiple endpoints of the tree in Figure 5, the simulated display all intersections with it at every crossroads there are 4 internet Things that are not shown in Figure 5, with a view to properly display the tree scale. During the experiment, the RTT (Round Trip Time) parameter was calculated for each of used protocols.

The value of RTT for the HTTP protocol is displayed in Figure 6, for CoAP in Figure 7, for MQTT in Figure 8. Where the number of established sessions is displayed on the abscissa, the value of Round Trip Time is displayed directly along the ordinate axis. Emissions on the graphs show the unstable operation of the service, after a certain time of testing, which consisted in closing the service ports, as a result, the delay in the successful registration of data on the IoTDM service increased. Based on the test results, we concluded which protocol is better to use for various purposes, when considering this architecture. The conclusions are shown in Table 2. According to the data displayed in Table 2, we concluded that for the registration of Internet things to the IoTDM service, the HTTP protocol is more appropriate than others due to its work in conjunction with the transport protocol TCP, which guarantees the transmission of the registration message over the network. If, when creating the main structure or registering the Internet of Things itself, a packet will be lost on the network, this will cause a failure in the structure of the resource tree, and eventually work with the resource tree (with the entities of this branch) will be difficult.

Because The IoTDM service will not be able to register the dependent entities or the data belonging to this branch and will issue an error about the unavailability of the resource. The CoAP protocol works in conjunction with the UDP transport protocol, which eventually failed and the error described above, therefore this protocol proved to be not stable for the organization of this function. To organize the work through the protocol, the registration of the MQTT broker is required first, that is, i.e., initially work through HTTP protocol is required to organize the MQTT workflow. However, when transmitting the data itself from the Internet of Things (sensors), the MQTT protocol proved to be on the best hand, if to perform a basic comparison based on the RTT parameter. With the same load (960 IW), it was possible to achieve an RTT of 4 ms. It should also be taken into account that after prolonged operation of the generators via the HTTP protocol, the IoTDM service began to behave unstably (closing ports), which led to delays in processing the package in the service As a result of the Round Trip Time values, we can safely conclude that the SDN network reduces the value of the RTT parameter several times over the organization of the classical network. In the issue the testing of the IoTDM service with this load profile, the instability of its operation was revealed, namely, the ports were closed, also in result was developed generators gave an appropriate network error about the unavailability of the receiver's ports. At the same time, the further the test passed, the response time from the service increased.

We conclude that IoTDM service has a big plus that is organized in accordance with the specifications project oneM2M, but the organization of it as a management system of a service "Smart City" is required to design a distributed server architecture and thus the resource tree for the stability of its work. It also requires an accurate calculation of the hardware used in the servers for the successful processing of this amount of traffic.

Conclusion

The paper examined the IoTDM service as a single service for organizing a smart city management system, also in the process of experiment, taking into account that the generated IoT traffic was transmitted over an SDN network organized on the basis of Mikrotik switches, switches were tested for stable operation under heterogeneous conditions Traffic and traffic IoT smart city. As a result of the work, it was found out that the concept of building SDN networks allows to reduce such a traffic parameter as RTT by organizing the control in the form of an SDN controller, namely: the processes of creating records in the flow table and the principle of message switching (record search). As a result, the delay in switching depends only on the physical capabilities of the switch itself (ports, memory, processor speed, etc.), with the already generated flow table, most of the delay was made by the service itself, while processing requests from Internet of Things.

Recently exponential growth of Internet connected devices and network management issues have become one of the most difficult tasks. Once IoT came to life, the volume of traffic in modern communication networks is drastically changed. The lately emerged SDN approach could bring us ineluctable benefits by automating daily network engineer's chores and facilitating overall network management through its programming. In this paper were considered the advantages of SDN for management simplification of IoT by introduction of Internet of things data management system as a service for "Smart city". The developed model, that reflected the possible distribution scheme of monitoring and management systems for the Central District of Saint-Petersburg, was used to conduct full-scale experiment.

Acknowledgment

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008), RFBR according to the research project No. 17-57-80102 "Small Medium-sized Enterprise Data Analytics in Real Time for Smart Cities Applications".

1

 1 Testing of the network infrastructure As a network infrastructure, an SDN network was built, based on Mikrotik switches supporting the openflow v.1.0 protocol and the OpenDayLight Berillium SR4 controller. As a service management acted IoTDM version Boron SR1. As data sourcesdeveloped traffic generators that implement the interaction in three protocols (HTTP, CoAP, MQTT), taking into account the specifications of the partnership project oneM2M and organization model district of St. Petersburg city.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Graph of udp packet loss by increasing the number of sessions

Fig. 5 .

 5 Fig. 5. IoTDM resource tree.

Fig. 6 .

 6 Fig. 6. RTT for HTTP.

Fig. 7 .

 7 Fig. 7. RTT for CoAP.

Fig. 8 .

 8 Fig. 8. RTT for MQTT.

Table 1 .

 1 The laboratory stand Structure

	Hardware	Features	Functions
	RAM: 16 Гб CPU: intel	Controller	The «Brainr» for Network
	Xeon(R) CPU E3-1220V2
	RAM: 12 Гб CPU: intel	Service IoTDM	Management service for
	Xeon(R) CPU E3-1220V2		Internet of Things
	Mikrotik RB201 1ui AS-RM	Network	SDN Core
	Cisco Catalyst 3750G Series	Network	Aggregation Layer

Table 2 .

 2 Recommendations on the used protocols for the interaction IoT with the IoTDM service over the SDN network

	Functions	HTTP	CoAP	MQTT
	Internet of things	+	-	-
	registration
	Data transmis-sion	-	-/+	+
	RTT/average	+(~40 ms)	+(~ 30-40 ms)	+ (~ 4ms)
	value for stable
	operation


Maria Makolkina
email: malokina@list.ru

Ruslan Kirichek
email: kirichek@sut.ru

Valeria Teltevskaya
email: valeria-telt@yandex.ru

Elisaveta Surodeeva
email: elisaveta.surodeeva@gmail.com

Research of Interaction Between Applications of Augmented Reality and Control Methods of UAVs

Keywords: Augmented reality, flying ubiquitous sensor networks, unmanned aerial vehicles, quality of service, quality of experience, Hurst exponent 1

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The management of unmanned aerial vehicles is one of the most important problem, which should be solved for the widespread implementation of UAV systems. The flying touch networks use the UAVs as devices to collect data from land sensors and transfer it to the server for processing. Such networks can be used, for example, in industrial production or agricultural industry for monitoring the processes or the UAVs can be used as flying routers [START_REF] Furukawa | Dynamic allocation and control of coordinated UAVs to engage multiple targets in a time-optimal manner[END_REF][START_REF] Park | Virtual, Augmented and Mixed Reality[END_REF][START_REF] Fu | Mixed and Augmented Reality (ISMAR)[END_REF][START_REF] Filonenko | Augmented Reality Surveillance System for Road Traffic Monitoring[END_REF].

There are three types of management of the UAV: manual control, automated management, automatic control. In case of remote manual control, the pilot is guided by the image transferred from the camera. Such control can be exercised by means of technologies of augmented reality and the tactile Internet. Augmented reality (AR) represents addition of the surrounding physical world with virtual data with the help of special devices of display, for example, of glasses [START_REF] Bilton | Google begins testing its augmented reality glasses[END_REF]. The main task of the tactile Internet is transfer information about impact on a remote subject and the return transfer of response of this subject to influence with the minimal delays [START_REF] Aijaz | Realizing the tactile internet: Haptic communications over next generation 5G cellular networks[END_REF].

The managing man has an opportunity to influence the UAV through the application of augmented reality turns of the head and a ducking, watching change of the image from the camera in the device of display of augmented reality.

Solving a problem of management of the UAV by means of applications of augmented reality, it is necessary to solve several subtasks:

• to provide transfer data about turn of the head from the device of augmented reality on the quadcopter; • to provide transmission of a video image from the camera UAV on the AR device;

• to estimate quality of service on the network;

• to estimate quality of experience of the user in augmented reality at management of the UAV.

FEATURES OF DATA TRANSFER

The pilot can control movements of the quadcopter or the camera mounted on it by means of turns and a ducking. As the suspension bracket of the camera provides rotation only on a vertical axis, for support of the maximum review it is necessary to turn the pilotless device. In the AR device, which is on the head of the pilot, display of a video stream from the camera is provided. Thanks to it, the pilot can understand location of the UAV and transfer information about desirable turn of the camera. For this purpose, high-quality information display from camera and a timely response of the UAV and camera to movements of the managing man should be provided. During transmission of a video image, we can face a problem of noises in data transfer channel. Transfer of video information is influenced by such parameters of quality of service of a network as losses and time delays [START_REF] Aijaz | Realizing the tactile internet: Haptic communications over next generation 5G cellular networks[END_REF]. It influences on quality of experience and can lead failures in control of the UAV, because in case of control the pilot can possess information about location of the device proceeding from the arriving video information. In this regard, for research was selected the model of a network (Fig. 1), in which the device of augmented reality exchanges data with the quadcopter with use technology of wireless data transfer of Wi-Fi of IEEE 802.11n. This technology allows to transfer the large volume of information with throughput to 150 Mbps [7], as it is required for high-quality transmission of video information. Within this paper, influence of quality of service of network on quality of perception of the user in the AR system at management of the UAV will be investigated.

SETTING OF EXPERIMENT

Purpose: A research of influence of quality of experience in systems of augmented reality on control of the UAV with use of the laboratory stand.

For this research the laboratory stand in laboratory of the Internet of Things of St. Petersburg State University of Telecommunications was developed [START_REF] Kirichek | Internet of things laboratory test bed[END_REF][START_REF] Kirichek | Model networks for internet of things and SDN[END_REF]. The hardware complex consists of the UAV (quadcopter 3D Robotics IRIS Plus) with the camera onboard. To capture video, an Intel Edison module connected to a Microsoft LifeCam HD-3000 camera is used, which allows to record HD video in 720p. Videostreaming is implemented by means of the FFServer library and using the RTP and RTSP protocols. Via the device of wireless access, the quadcopter is connected to AR glasses through Wi-Fi gateway. Epson Moverio BT-200 augmented reality glasses represent the transparent binocular video augmented reality glasses. They are equipped with such sensors as a gyroscope and the accelerometer, have an opportunity to interact through Wi-Fi access point. The AR glasses are equipped with the Android OS, which allowed us to use the LibVLC library and quickly develop an application for transmitting video from the quadcopter and managing its camera. The structural scheme of the stand is provided on Fig. 2.

Fig. 2. Structure of the experimental stand

For collection of the experimental data and entering of additional noises into a network, the additional server with installed NetDisturb software was implemented between augmented reality glasses and the quadcopter. NetDisturb allows to make different noises and distortions in a network between the quadcopter and points, such as time delays, losses, capacity reduction [START_REF] Koucheryavy | State of the art and research challenges for public flying ubiquitous sensor networks[END_REF]. NetDisturb was installed on a PC with two Gigabit Ethernet network cards. Two Wi-Fi access points were connected to this PC. The first AP was on channel 1 and the second AP was on channel 11, acting as router and repeater, correspondingly. Also software based on the pcap.net library for interception and the analysis of a traffic was developed to estimate influence of quality of service of a network on quality of experience of augmented reality in AR glasses in case of control of the quadcopter. The experiment was carried out in a room large enough to allow the UAV fly freely up to 7 meters away.

The software, created for determination of influence of quality of service on quality of experience in systems of augmented reality, intercepts a traffic of data between the quadcopter and AR glasses. On base of received data, exactly time, when the packet was received, and packet size calculation of Hurst exponent is made. Hurst exponent is the measure, used in time series analysis [START_REF] Makolkina | The quality of experience subjective estimations and the Hurst parameters values interdependence[END_REF][START_REF] Kirichek | Flying ubiquitous sensor networks as a queueing system[END_REF][START_REF] Paramonov | M2M traffic models and flow types in case of mass event detection[END_REF]]. Parameter will de-crease, if the time delay between couple of identical changes of values of a time series increases. In this case the coefficient reflects a level of self-similarity of a traffic:

• while 0 < H < 0,5 -a time series is not self-similar, antipersistent, more probable for changing of the direction of a deviation, high definitions of a deviation follow for low and conversely; • while H = 0,5 -random time series, the following value don't depend on the previous values; • while H > 0,5 -time series is self-similar, persistent.

• The self-similar traffic is a traffic which looks equally at any temporal scales. In other words, the probability that the traffic on the following step will deviate average value in the same direction, as on the previous step, is so high as Hurst exponent is closer to one.

For clear determination of Hurst exponent, interception of packages will be carried out during one minute. For 1 minute time series we have to calculate dispersion -a deviation of a random value from its average value among.

[ ]

H cn t S R M ) / ( , when n→∞ (1)
where (R/S)t -the normalized assessment of width of a range, c -a constant, nthe size of the researched unit of observations, H -Hurst exponent, i.e. a level of self-similarity of the researched process. For the given finite time series of X = X1, X2, …, Xn we will calculate average value of m:

 = ⋅ = n i i X n m 1 1 (2)
Then we will calculate a time series of deviations from average Y:

m t X t Y - = , t = 1,2,…,n (3)
Calculate a time series of deviations Z:

 = = t i i Y t Z 1 , t = 1,2,…,n (4)
Calculate a range series R:

R t = max(Z1, Z2, …, Zt) -min(Z1, Z2, …, Zt), t = 1,2,...,n (5)
Calculate a standard deviations series S:

 = - t i u i X t 1 2 ) ( 1 , t = 1, 2, …, n (6)
where u -average definition of values of a row from X1 to Xt. Calculate a normalized range series (R/S):

t S t R t S R = ) / ( , t = 1, 2, …, n (7)
To average a row (R/S)t on areas [X1, Xt] in case of different values t on an interval from 1 to n, one usually takes not all n points, but some enough set, which is evenly distributed on all interval from 1 to n.

The received averaged values and corresponding to them block lengths of averaging of t, need to be marked in logarithmic axes. The received points need to be approximated the linear function, constructed by means of the least-squares method. The slope (an inclination tangent of angle to the positive direction of an X-axis) the received line according to a formula (1) will be assessment of Hurst's coefficient of an initial time series.

In this research Hurst exponent is used for determination of correlation between quality of service and quality of experience in AR systems in case of control of the UAV.

DESCRIPTION OF EXPERIMENT

The examinee of augmented reality glasses, where information from the camera of the quadcopter is displayed, turns the head, thereby directing the camera, and subjectively estimates a response of the quadcopter on the done movements and change of the image in glasses. The experiment u be made several times, each time displays influence of different noises, such as a time delay, losses and reduction of throughput. For correct subjective evaluation, the experiment without introduction of noises was taken for a standard, i.e. as close as possible to ideal conditions of data transfer.

ANALYSIS OF RESULTS OF EXPERIMENT

After experiment without introduction of noises, Hurst exponent was calculated. It was equal to 0,61. It means that the traffic was self-similar and these results can be taken as a standard in case of further assessment of quality of experience, i.e. assess-ment of these results is 5. Further experiments with adding of a time delay were made. Results are provided in table 1.

Table 1. EXPERIMENT WITH DELAYS

Delay

Subjective score Hurst exponent Without delay 5 0,61 10-30 ms 4 0,60 50-150 ms 3 0,59 150-250 ms 2 0,56 From the table is seen, that in case of time delays less 100 ms, quality of experience of video remains at the satisfactory level, but there are a lot of difficulties in case of control with this delay. Because of delay the managing man doesn't know when it is necessary to stop movement, i.e. control is made at random, commands are transferred with delay, the response returns with a time delay. In this case Hurst exponent truly defines correlation between quality of service and quality of experience in the AR systems -the greatest value complies to the highest assessment of the testee. Thus, in case of time delays higher than 150 ms it is impossible to exercise control of the UAV by means of the application of augmented reality.

The next experiments were made with adding of random losses in link between the quadcopter and the AR device. Results of this experiment are provided in table 2.

Table 2. EXPERIMENT WITH LOSSES

Losses

Subjective score Hurst exponent Without losses 5 0,61 0%-1% 4 0,61 0%-3% 3 0,60 0%-5% 2 0,59 0%-7% 2 0,53 0%-9% 1 0,47 Proceeding from the received results, one may say, that losses significantly influence quality of experience. In addition to difficulties with control, there are also noises in recognition of the image on the device of augmented reality. Quality of experience of video promptly falls in case of increase in number of losses, it becomes difficult to sort the image, besides some timepoints "fall out" of video information, that exerts a negative impact on control of the quadcopter.

The last experiment was connected to throughput restriction, resulting in packet losses. 3 it is possible to draw a conclusion that throughput restriction critically influences quality of experience of the user in systems of augmented reality. Also in case of capacity reduction, control of the quadcopter significantly becomes more difficult, because the managing man ceases to hold information about any movement of the aircraft. All data are transferred with big time delays, part of them is lost, in case of observation in the device of augmented reality begins the dizziness.

CONCLUSION

For control of unmanned aerial vehicles, it is possible to use applications of augmented reality. Because control takes place in real time, it is necessary to impose certain requirements to quality of service of a network for support of high-quality and comfortable control of the UAV. In this paper, influence of quality of service of a network on quality of experience of the user in the device of augmented reality by transmission of a video image from the aircraft camera was considered. By the received results we will draw a conclusion that on a network with the minimal time delays to 100 ms it is possible to control the quadcopter by means of the application of augmented reality without loss of quality of experience and control. Further, it is possible to continue a research in the area of influence of quality of service of a network on a quadcopter response (the tactile Internet) in case of control by means of the DR applications, and also to consider the AR applications as a method of management of other different robotic systems.

Fig. 1 .

 1 Fig. 1. Model of network for interaction between the AR device and UAV.

Table 3 .

 3 EXPERIMENT WITH THROUGHPUT RESTRICTION

	Throughput	Subjective	Hurst exponent
		score
	not limited	5	0,61
	to 1700 kbps	5	0,61

ACKNOWLEDGMENT.

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008), RFBR according to the research project No. 16-37-00209 mol_a "Development of the principles of integration the Real Sense technology and Internet of Things".


Samuel Muhizi

Gregory Shamshin

Ammar Muthanna

Ruslan Kirichek
email: kirichek@sut.ru

Andrei Vladyko
email: vladyko@sut.ru

Andrey Koucheryavy

Analysis and performance evaluation of SDN queue model

Keywords: SDN controller, OpenFlow switch, flow table, AnyLogic, queue model, simulation model, analytical model

In this paper, we present an Openflow-SDN based network visualization and performance evaluation model that helps in network designing and planning to examine how networks' performance will be affected as the traffic loads and network utilization change. To achieve the aimed goal, as a research method, we used AnyLogic Multimethod simulation tool. This is a first of its kind where SDN performance evaluation is based on queuing model simulation to monitor change of average packet processing time for various network parameters. Using presented in this work SDN model, network administrators and planners can better predict likely performance changes arising from traffic variation. This allows them to make prompt decisions to prevent seemingly small issues from becoming major bottlenecks.

Introduction

The concept of software defined networks (SDN) is a growing trend in the domain of telecommunication network management, that offers to remove restrictions on existing infrastructure networks by dividing the network control plane and data plane by means of transferring control functions of network forwarding devices (routers, switches) in the applications running on a single entity (controller), which makes the network more centralized and improves its software management capabilities [START_REF] Kreutz | Software-Defined Networking: A Comprehensive Survey[END_REF][START_REF] Xia | A Survey on Software-Defined Networking[END_REF][START_REF] Alsmadi | A Systematic Literature Review on Software-Defined Networking[END_REF]. This simplifies the network usability and significantly reduces the network system cost and equipment. However, all these benefits come with a non-negligible problem in network functionality such as packet transmission rate and network performance, which are attributed to the use of the controller as a remote system to manage all transmission network devices (switches). The controller can manage one or several OpenFlow switches; it contains a network operating system that provides network services for low-level network management, network segments, and the state of net-work elements and applications, implementing a high-level network management and data flow. Each controller has at least one application that manipulates switches connected to it, and can provide a global view of physical network topology under the controller management. The idea of creating a unified, independent from the network equipment manufacturer [START_REF] Liu | Field Trial of an OpenFlow-Based Unified Control Plane for Multilayer Multigranularity Optical Switching Networks[END_REF][START_REF] Jararweh | SDIoT: A Software Defined Based Internet of Things Framework[END_REF][START_REF] Kirichek | Software-Defined Architecture for Flying Ubiquitous Sensor Networking[END_REF], program-controlled interface between the controller and the network transport infrastructure is defined in the OpenFlow standards and OpenFlow protocol [START_REF]OpenFlow[END_REF], which allows users to define and control with whom, under what conditions and with what quality can interact on the network. OpenFlow is an open standard, which describes the remote management requirements to a switch that supports OpenFlow protocol. According to OpenFlow standard specifications, the interaction between the controller and the switch is carried out through OpenFlow protocol. Each switch must contain one or more flow tables and group tables, which perform packet lookups and forwarding, and support OpenFlow secured channel to a remote controller. Each flow table in the switch contains a set of flow entries; each flow entry consists of match fields, counters, and a set of instructions to apply to matching packets. Data management in OpenFlow is carried out, not on the individual packet level, but at the level of their packet streams. Rules are dynamic. Packets which have no match are sent to the controller (packet in). Controller creates appropriate rule and sends packet back to switch (packet out) for processing. The rule in the switch is set only for the first packet, and then all the other packets of the flow use it.

In this paper is introduced an analytical and simulation analysis of an SDN model where the network is modelled as queueing system to capture the time costs associated with the controller and the switches activities.

SDN modelling concept

In case of SDN deployment, the controller usually manages multiple OpenFlow switches each connecting group of host. The typical SDN architecture is shown in Fig. 1. The OpenFlow switch packet forwarding procedure is shown in Fig. 2. The switch performs flow table lookups on packet arrivals. If the lookups succeed, the switch applies the actions in the matched table entry to the packet, typically forwarding it to the specified interface. Otherwise, the packet is supposed to belong to a new flow, and the switch sends it to the upper SDN controller in a packet-in message. The controller defines the corresponding flow rules and sends to the switch it in packet-out or flow_mod packet. As a result, the SDN controller receives a flow of packet-in messages from each OpenFlow switch. In the modern telecommunication networks, at the same time are processed different types of information (video and audio information, compressed video and audio information, and less sensitive to delay data) with different quality of service levels. Accordingly, traffic management methods play a key role in its optimization and to minimize network losses. To create a network model (topology and its elements characteristics), and dynamically simulate its operation mechanism, optimize its characteristics, analyze and manage the traffic, evaluate the performance bounds undoubtedly, it is more than necessary to use more advanced multimethod modeling and simulation tools for complex systems research [START_REF] Kirichek | Model Networks for Internet of Things and SDN[END_REF][START_REF] Vladyko | Comprehensive SDN Testing Based on Model Network[END_REF][START_REF] Vladyko | Fuzzy Model of Dynamic Traffic Management in Software-Defined Mobile Networks[END_REF].

Model description

Operations on SDN switches with different data transmission processes control capabilities lead to a significant delay change for flow entries configuration. In order to simulate different general arrival processes, describe and monitor flow exchange between the controller and the switches we presented the SDN as queuing system. The SDN queue model was built using AnyLogic Multimethod simulation modeling tool and is shown in Fig. 3. AnyLogic is a very flexible [START_REF] Borshchev | The Big Book of Simulation Modeling: Multimethod Modeling with Anylogic 6[END_REF], dynamic simulation tool with high flexibility and unlimited expansion possibilities due to operating systemindependant native Java environment. AnyLogic runs on Windows, Mac and Linux. AnyLogic initially designed to support multiple modeling methods and their arbitrary combinations it offers the modeler more flexibility than any other existing simulation tools by the means of reduction of development costs and -times: fast integration of pre-configured simulation elements with the comprehensive object libraries. It makes it possible to design various types of models with one single tool: agent-based, system dynamic, event-oriented, continuous or dynamic models. The SDN model consists of 6 OpenFlow switches and a controller. Switches are numbered from S0 to S5 and the controller C0. Source objects generate incoming traffic with a specified arrival rate at each and every switch connected to controller.

Packet processing on the switch

Fig. 4 shows a switch packet forwarding process. For a more accurate simulation of the information exchanges between the switch and the controller, incoming packets were divided in four categories; each of them is determined by specified occurrence probability. From the switch, packets to the controller are sent using specific communication channel. In this model the channel processing unit is built that it doesn't significantly affect on the overall evaluation of the model performance.

Packet processing on the controller

The controller manipulates multiple switches and therefore the arrival process of packets at the switch characterizes the packet processing rate at the controller. Accordingly, the model describes the packet transmission process management at different SDN model service units. We consider SDN controller model as shown in Fig. 5. Packet-in and Packet-out messages. On the arrival of a packet, the switch checks the flow table for presence of the destination address. The SDN model contains a central unit (controller) manage flow entries in the network. In this model switch numbers match the source and destination addresses. Forwarding rules and destination addresses for arrival packets are defined for each packets category arriving at the switch. First packet of the category is sent to the controller for rules and destination address confirmation. The controller determines the rule to assign to the respective packet category and sends it back as a response to the packet-in message to the switch. The switch then forwards the packet to the destination address. The next packets in this category then use the assigned forwarding rules and there won't be any requirement to confirm addresses. The designed controller model works with a given failure rate. If the failure occurs, the entire flow entry checking process starts again.

Modeling results

Using the above described SDN model, we measured the network load, therefore for given parameters a network administrator can simply establish required quality of service for different network nodes by managing the delay, delay variation (jitter), bandwidth, and packet loss parameters on a network. Experimental processes were performed using a modeling time of 3600 seconds, and the memory size for the simulation was set to 1024 MB.

To illustrate the impact of various network parameters on the quality of service exist multiple options: arrival traffic rate changes, trigger sequences of packet-in messages, controller performance impact on the overall packet processing mean time, etc. In Fig. 6, the plot highlights the switch average packet processing time for different packet arrival rates. The more packet arrival rate increases, the more average packet processing time increases, thus the increasing arrival traffic rate will result in network throughput decrease. The plot can be used to determine the maximum load that the network should reach before its performance is compromised. For a fixed packet arrival rate on each switch we measured changes in average packet processing time while increasing the controller service rate. The simulation results are shown in Fig. 7. The average packet processing time significantly decreases as controller service rate increases. Therefore, the network throughput increases. Analytical modeling framework

To assert the described above SDN model we proceeded to analytically evaluation of OpenFlow switch. For that we considered a queueing model [START_REF] Dombacher | Queueing Models for Call Centres[END_REF] for OpenFlowbased SDN [START_REF] Xiong | Performance evaluation of OpenFlow-based software-defined networks based on queueing model[END_REF][START_REF] Xiong | A Concise Queuing Model for Controller Performance in Software-Defined Networks[END_REF][START_REF] Ansell | Making Queueing Theory More Palatable to SDN/OpenFlow-based Network Practitioners[END_REF] as illustrated in Fig. 8. The switches and controller are modelled as queueing systems to capture the time cost of the network.

Fig. 8. OpenFlow-based SDN queueing model

We assume that the packet arrival process in the network follows a Poisson Process and the average arrival rate in the ith switch is λi, and that the arrivals in different switches are independent. Packets may not match any flow entries in which case they are forwarded to the controller via packet-in message. This happens with probability ρ. Packets are classified into two classes, both of them arrive in a Poisson process with an average arrival rate of λi*ρ and λi*(1-ρ). The packet service time of switches is assumed to follow an exponential distribution, and the expected service time is denoted 1/μ1 and 1/μ2, respectively. The mean service time of packet-in messages in the controller is denoted 1/μc. This service time includes the transmission time from the switches to the controller. In other, to simplify this model, both controller and switches are powerful enough for the traffic in the network, and there is no limit on the queue capacity. We queue all the packets arriving at a switch in a single queue instead of a separate queue on each ingress port and all the packets are processed in order of arrival time. Moreover, we assume that when the first packet of a connection arrives at a switch, the controller installs a flow entry. After that, the remaining packets arrive to the switch and are forwarded directly. We also assume that all the switches in our model have the same service rate, and the packet-in messages arrive the switch following a Poisson process.

OpenFlow Switch performance.

The flow entry matching for all packets are assumed to be independent and the packet processing time can be supposed to follow an exponential distribution. With the assumptions above the performance of OpenFlow switches can be modeled as a M/H2/1 queue, which means packets arrive at the ith switch at rate λi and the service time is represented by a two-phase hyperexponential distribution. The state transition diagram of this queue is shown in Fig. 9. With probability ρ, a packet receives service at rate μ1, while with probability 1-ρ it receives service at rate μ2. , where a is the total number of packets in the switch and b is the current service phase. In our case b can be only 1 or 2. The stationary distribution of this queue in the ith switch can be obtained by applying the Matrix-Geometric Method. We denote the stationary probability vector π(i) as π ( ) = (π 0 ( ) , π 1 ( ) , π

(

= < 1 (2)

0 = 1 - (3) = (1 -) ( 4 )
Where πk(i) is the probability of k packets in the ith switch. Then the mean number of packets in the queueing system can be computed as:

= ∑ ( ) ∞ =0 (5) = ∑ (1 -) ∞ =0 ( 6 )
For k = 0, the product is zero then we can start the sum from k = 1

= (1 -) ∑ ∞ =1 = (1 -) ∑ -1 ∞ =1 ( 7 )
Since can be written as

= Respectively = (1 -) ∑ ∞ =1 = (1 -) (∑ ) ( 8 ) Since ∑ ∞ =1 = ∑ ∞ =0 -1 = 1 1--1 = 1-
We can write

= (1 -) 1- ( 9 )
= 1-

,where (ρ<1) and ρ = = μ-

(

According to Little's law, the average packet processing time in the ith switch can be given by

= 1 = 1 μ- ( 1 2 )
The mean packet processing time of switches can be given by

= ∑ ∑ =1 =1 ( 1 3
)

Numerical evaluation and results

With the mentioned analytical framework and presented outcomes, we can evaluate the proposed queuing model with different parameters and report the upper bound of packet processing delay in the SDN switch. The switch average packet processing time is shown in Fig. 10. As packets arrival rate at the switch increases, the average packet processing time constantly increases. It sharply increases to the maximum when packet arrival rate is closer to the switch processing service rate. That matches the time when the switch runs out of resources and can't perform packet processing service.

Fig. 10. Average packet processing time of Switch

Conclusion

Understanding the performances and limitations of OpenFlow-based SDN is a prerequisite of its deployment. In this work we have proposed a model for an OpenFlow SDN based on queueing theory, and resolves its average packet processing time. We reviewed the optimal parameter combinations of Openflow switch and controller to allow future network architects and administrators to be able to compute an upper bound estimation of packet delay and buffer requirement of SDN switches and controller for a given packet arrival rate.

Furthermore, we will extend the analysis to the possibility of SDN network from a single controller to the case of controller clusters to evaluate how much switches a given controller can handle in a network without much performance loss.

Acknowledgment

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008), RFBR according to the research project No. 17-57-80102 "Small Medium-sized Enterprise Data Analytics in Real Time for Smart Cities Applications".

Fig. 1 .

 1 Fig. 1. A typical SDN architecture.

Fig. 2 .

 2 Fig. 2. The packet forwarding of an OpenFlow switch.

Fig. 3 .

 3 Fig. 3. SDN conceptual model in AnyLogic 7.3.6

Fig. 4 .

 4 Fig. 4. OpenFlow switch conceptual model in AnyLogic 7.3.6

Fig. 5 .

 5 Fig. 5. SDN controller conceptual model in AnyLogic 7.3.6

Fig. 6 .Fig. 7 .

 67 Fig. 6. Average packet processing time of switches

Fig. 9 .

 9 Fig. 9. State transition diagram of an M/H2/1 queueA state is represented by a pair (a, b), where a is the total number of packets in the switch and b is the current service phase. In our case b can be only 1 or 2. The stationary distribution of this queue in the ith switch can be obtained by applying the Matrix-Geometric Method. We denote the stationary probability vector π(i) as


Mariem Hmila

Manuel Fernández-Veiga

Energy-efficient Power Control and Clustering in Underlay Device to Multi-Device Communications

Keywords: Optimization, fractional programming, D2D multi-casting communication, 5G wireless networks

Underlay device to device multicast communication brings great benefits to cellular networks in term of energy and spectral efficiency, since a group of users can communicate directly by reusing cellular resources. In this paper, we propose a scheme to maximize network energy efficiency (EE) through transmission power control. In addition, to get a compromise between fairness and the overall EE, we analyse a second scheme with fairness factors to maximize minimum individual EE. The problem is formulated as a fractional programming optimization and solved with iterative algorithm. Two different EE metrics are analysed via extensive numerical simulations with a spatial Poisson process for the users' locations, and applying different clustering algorithms as K-nearest neighbour, distance limit and DBSCAN.

Introduction

The emergence of mobile multimedia rich services increases the number of connected devices and the requested data rate regularly. Consequently, the fifth generation (5G) supposes to have 1000x higher data volume, up to 100x more throughput and connected devices, 10x longer battery life, and low latency [START_REF] Ma | Key techniques for 5g wireless communications: network architecture, physical layer, and mac layer perspectives[END_REF]. Underlay device to device communication (D2D) is a new paradigm introduced to realize 5G. It allows users in proximity to communicate directly by using resource allocated to cellular user (CUE). This has advantages as [START_REF] Mach | In-band device-to-device communication in OFDMA cellular networks: A survey and challenges[END_REF]: high data rate, energy and spectral efficiency, increase network capacity, low delay. However, it can cause harmful co-channel interference to CUE. The main techniques to mitigate interference are power control and resource allocation. Currently, they are joint to propose a more EE solutions. Several works proposed EE power and resource allocation scheme subject to QoS. In [START_REF] Alamouti | Resource allocation for energy-efficient device-todevice communication in 4G networks[END_REF], a centralized solution had been conducted to minimize transmission power. The problem was formulated as mixed integer linear programming (MILP) and solved through Hungarian algorithm. While in [START_REF] Zhou | Distributed interference-aware energy-efficient resource allocation for device-to-device communications underlaying cellular networks[END_REF], the authors proposed a distributed solution to maximize users EE. The problem was formulated as a non cooperative game and solved by an iterative optimization algorithm. However, these works mainly consider unicast D2D communication where single transmitter and receiver communicate. Another interesting approach is to allow users with common content interest to form clusters where one device transmit to multiple receivers. This is called multicast D2D communication(D2MD). Compared to unicast, this mode reduces overhead signals and saves resources yet it is more challenging hence date rate is determined according to the weakest receiver so non fails to decode any of the transmitted data. Most of the available works target interference issue in D2MD communication focus on system throughput maximization subject to QoS constraints. The work in [START_REF] Gong | Particle swarm optimization based power allocation schemes of device-to-device multicast communication[END_REF], investigate power control for D2D multicast communication. The authors first proposed a distributed scheme for group formation. Then, they studied single and multiple CUE channels re-usage and developed power allocation scheme based on swarm algorithm (PSO). The authors in [START_REF] Meshgi | Joint channel and power allocation in underlay multicast device-to-device communications[END_REF] proposed a heuristic algorithm to solve mixed integer non-linear programming (MINLP) resource and power allocation problem. Moreover, they extended their work in [START_REF] Meshgi | Optimal resource allocation in multicast device-to-device communications underlaying LTE networks[END_REF] where D2D clusters can reuse the channel of multiple CUE instead of reusing single orthogonal channels and several D2D groups can share the same channel. They proposed greedy and heuristic algorithms and compared their performance. To this end, the paramount importance of green communication concept and the high potential of D2MD [START_REF] Rebecchi | Data offloading techniques in cellular networks: A survey[END_REF] motivated us to analysis spectral and energy efficiency in the scenario where underlay D2MD is applied in a cellular network. In this paper, we propose joint power and resource allocation model to maximize system and users EE. However, for analytical purpose we focus on a single channel sharing which lead us to EE power control schemes powered with stochastic geometry and clustering techniques. The rest of the paper is organized as follows. In section 2, we introduce system model. Power control algorithm and problem formulation is discussed in section 3. Finally, we discuss simulation results in 4 and conclude in section 5.

System Model

We consider a single cell environment with one base station (BS) located in the centre and multiple uniformly distributed users. On the uplink, M CUE transmit on M orthogonal communication channels. Reusing downlink resources requires sophisticated coordination between UEs and the BS, and has been shown to be less effective than uplink resource sharing. Therefore, we assume the coexistence of K D2MD clusters k = 1, ..., K, that reuse the same channels allocated to CUEs to communicate directly. Each group has head cluster (transmitter) and |D k | receivers where |D k | = 1 is a unicast case [START_REF] Meshgi | Optimal resource allocation in multicast device-to-device communications underlaying LTE networks[END_REF]. Here, the BS suffers from interference caused by the co-channel D2MD transmitters. Similarly, the |D k | receivers of group k suffer from interference caused by the CUE and other transmitters of D2MD groups sharing the same resource block. The SINR γ k,m,r ({p k } m , p m ) of a D2D receiver r in group k and channel m is given by

h k,m,r p k,m σ 2 + p m β k,m,r + j =k x j,m p j,m h j,m,r (1)
where h k,m,r are the deterministic link gain factors from the transmitter in group k to receiver r on channel m, and β k,m,r is similarly the link gain factor from CUE transmitter m to receiver r in group k. Symbol p k,m denotes the transmission power of the D2MD transmitter in group k on channel m, and p m is the transmission power of CUE user m. For a CUE user m, the SINR is similarly given by

γ m (p k , p m ) = h m p m σ 2 + k x k,m p k,m h k,m , m = 1, . . . , M (2)
where h m is the link gain from user m to the base station, p m is the transmitted power, h k,m is the link gain from the transmitter in D2D group k to the cellular base station on channel m and x k,m are binary variables defined for k = 1, . . . , K, m = 1, . . . , M as x k,m = 1 if D2D group k uses channel m, and 0 otherwise. The normalized transmission rate (in bits/s/Hz) of CUE m is the channel capacity r m = log 2 (1 + γ m ), for m = 1, . . . , M . For D2MD group k, the unique transmission rate is determined by the weakest receiver, i.e., by the receiver with the poorest channel quality. In addition, we account explicitly for the aggregated received rate in group k, which depends on the number of receivers per group

|D k |. Thus, R k = M m=1 x k,m |D k | min r∈D k log 2 (1 + γ k,m,r ), k = 1, . . . , K. (3)

Problem Formulation

The energy efficiency (EE) of a given user (in bits/Joule) can be defined as the ratio of the achievable transmission rate and the total consumed power:

η m r m s c,m + p m , m = 1, . . . , M (4)
for a CUE user; and

ζ k R k s c,k + p k 1 , k = 1, . . . , K. (5)
In ( 4)-( 5), s c,m (respectively, s c,k ) is the transmitter circuit power, p m is the power used by CUE transmitter m, p k = (p k,1 , . . . , p k,M ) ∈ R M + is the allocated power vector of the head cluster over the M channels, and || • || 1 denotes the 1norm. 1 We assume that p m and p k satisfy individual power constraints p k1 ≤ p k for k = 1, . . . , K, and p m ≤ P m for all m. Moreover, we explicitly include the assumption that minimum transmission rates have to be satisfied both for the CUE and the D2MD users,

r m ≥ r m , and R k ≥ R k (6)
for all indexes k, m, where r m (resp., R k ) are the target rates of CUE (D2MD) user m (resp., k). The above definition for energy-efficiency is user-centric. The notation can be extended to present the global network energy efficiency (GEE) η by considering the ratio of the aggregated rate and the total consumed powers. More formally, if r and R are the vectors of rates for CUE and D2MD groups, respectively, then

η ||r|| 1 + ||R|| 1 s c + k ||p k || 1 + ||p|| 1 (7)
Here, s c is the total circuit power network devices. The GEE targets the total performance of the cellular network EE. This does not depend on users devices which might not be fair for limited battery life devices. For this reason, we introduce a second performance metric for maximizing the minimum EE among all the users in the system. The following definition captures this idea and introduces the notion of fairness between users.

Definition 1. Let ω = (ω 1 , . . . , ω M ) ∈ R M + and θ = (θ 1 , . . . , θ K ) ∈ R K + be two arbitrary weight vectors. The (ω, θ)-weighted energy efficiency (WEE) is ψ min{min m ω m η m , min k θ k ζ k }. (8)
The uniform choice ω 2 = θ 2 = 1, gives equal weight to every user, yields maxmin fairness as the optimization criterion. With the above setting, the maximization of the global network energy efficiency can be mathematically formulated as (problem GEE ): solve max p,x k ∈P η, where η is equal to

m log 2 (1 + γ m ) + k m x k,m |D k | log 2 (1 + min r γ k,m,r ) s c + k ||p k || 1 + ||p|| 1 ( 9
)
where P is the feasible set of power vectors; namely, the set defined by the constraints

||p k || 1 ≤ p k , k = 1, . . . , K; p m ≤ P m , m = 1, . . . M (10)
R k ≤ R k , k = 1, . . . , K; r m ≤ r m , m = 1, . . . , m (11)
||x k || 1 ≤ s ||x •,m || ≤ r (12)
x k ∈ {0, 1} M (p, p 1 , . . . , p K ) ∈ R (K+1)×M + (13)
Here, constraints [START_REF] Meshgi | Joint channel and power allocation in underlay multicast device-to-device communications[END_REF] bound the maximum transmission power per user; constraints [START_REF] Meshgi | Optimal resource allocation in multicast device-to-device communications underlaying LTE networks[END_REF] are the minimum rate conditions, where the rates have been defined previously; constraints [START_REF] Rebecchi | Data offloading techniques in cellular networks: A survey[END_REF] enforce the maximum split factor s for every D2MD group and the maximum reuse factor r per subcarrier; and finally ( 13) is simply the nonnegativity of all the power vectors. Clearly, [START_REF] Rebecchi | Data offloading techniques in cellular networks: A survey[END_REF] are the integer constraints, [START_REF] Meshgi | Optimal resource allocation in multicast device-to-device communications underlaying LTE networks[END_REF] are the coupling constraints on the transmission powers, and the set {p k } are the coupling variables of the problem. Finally, note that the QoS constraints [START_REF] Meshgi | Optimal resource allocation in multicast device-to-device communications underlaying LTE networks[END_REF] are user-specific. In the same fashion and subject to the same constraints (10)-( 13), the minimum-EE optimization problem can be formulated, for fixed weight vectors, as: solve max p∈P ψ.

To better understand the influence of D2MD communication on the network performance, we analyze in depth a special case when M = 1 or x k,1 = 1 for all k. This means a single CUE channel is shared among all uses D2D groups. This will give us an idea about maximum capacity of the channel and allows us to clearly see the impact of other system parameters. In such a case the problem turns to a power control problem lies under the fractional optimization class [START_REF] Zhou | Distributed interference-aware energy-efficient resource allocation for device-to-device communications underlaying cellular networks[END_REF] where the decision part is absent, and has canonical form

max x∈C f (x) g(x) . (14)
Here, closed-form sufficient and necessary conditions for feasibility can be given, a result adapted from [START_REF] Zappone | Achieving global optimality for energy efficiency maximization in wireless networks[END_REF]. For single channel case, users are re-indexed such as 0 is the CUE, |D 0 | = 1 is the BS and j = 1, . . . , K are the D2D transmitters.

Theorem 1. Define γ k = 2 r j -1 for k = 0, . . . , K, and the matrix

W = [W ] k,j 0, j = k h k,j γ k h k , j = k. (15)
A solution exists iff the spectral radius of W is less than one and (I -W ) -1 s ≤ p where p = [p 0 , . . . , p K ] T and s has elements

s j = σ 2 γ j /h j .
If the problem is feasible then it can be solved by finding the unique zero of F (λ) where a point x ∈ C solves ( 14) if and only if x * = arg max x∈C {f (x * )λ * g(x * )},with λ * being the unique zero of F (λ) = max x∈C {f (x) -λg(x)}. To do this, we use Dinkelbach's algorithm [START_REF] Dinkelbach | On nonlinear fractional programming[END_REF] (presented in Algorithm 2 jointly for GEE and MEE) to solve one convex problem in each iteration, where f (x) and g(x) are concave and convex respectively. However, in our case the feasible set is convex yet the numerator of ( 9) is non-concave thus we use a sequential convex programming approach given by log 2 (1 + γ) ≥ a log 2 γ + b, where

a = γ 1 + γ , b = log 2 (1 + γ) - γ 1 + γ log 2 γ (16)
Putting all pieces together, we resume the solving procedure in Algorithm 1.

Simulations and Results

Stochastic geometry models have been commonly used to map the network into a collection of points over a spatial area so that its actual performance (spectral efficiency, coverage, etc.) can be analyzed and characterized [START_REF] Ak | Gaussian approximation for the downlink interference in heterogeneous cellular networks[END_REF][START_REF] Ak | Tractable framework for the analysis of general multi-tier heterogeneous cellular networks[END_REF]. Here, we use a standard homogeneous Poisson point process (PPP) distribution to determine the number and locations of the cellular users and of the D2MD transmitters and receivers, with density λ. The received signal or interference power is assumed to vary due to the path loss resulting from the random spatial distribution. Specifically, the channel quality between a transmitter at y ∈ R 2 is P r = P t •(1+|y/d 0 | α ) Algorithm 1 EE maximization for M = 1

1: if Problem feasible (Theorem 1) then 2: i = 0. Pick any p (0) ∈ P. If p (0) is feasible then 3: repeat 4:

i = i + 1 5:
Maximize ( 9) or (8) with a

(i)
k and b

(i) k 6: Set p (i) k = 2 q (i) k
, where q

(i) k = arg max ψi 7: Set γ(i) k = γ k (p (i) ) 8:
Update

a (i)
k and b

(i)
k with (16) 9:

until convergence 10: end if Algorithm 2 Generalized Dinkelbach's algorithm. The case I = 1 is the simple Dinkelbach's algorithm.

1: > 0, λ = 0 2: repeat 3:

x * = arg maxx∈C min 1≤i≤I {fi(x) -λgi(x)} 4:

F = mini fi(x * ) -λgi(x * ) 5: λ = mini fi(x * )/gi(x * ) 6: until F ≤
where P r is the received power, P t is the transmitted power, d 0 is a reference distance (100 m in our case), α is the path loss exponent. Also, we chose the CUE with the best channel quality to share his RB with D2D groups [START_REF] Lin | Modeling, analysis, and optimization of multicast device-to-device transmissions[END_REF]. This will allow us to focus on the effect of D2MD communications without considering the case of shared channel quality. Concerning the D2MD groups, the head cluster and group formation were done following three different algorithms presented and discussed in bellow. The parameters used for the numerical results reported here are listed in Table 1 and were taken or inspired by similar works [START_REF] Zappone | Achieving global optimality for energy efficiency maximization in wireless networks[END_REF][START_REF] Zhou | Distributed interference-aware energy-efficient resource allocation for device-to-device communications underlaying cellular networks[END_REF][START_REF] Gong | Particle swarm optimization based power allocation schemes of device-to-device multicast communication[END_REF].

K-Nearest Neighbour clustering (KNN)

This is the first algorithm used to classify users into K disjoint groups. The K head clusters are randomly selected among S, the set of points randomly drawn from a homogeneous Poisson point process with density λ. The remaining users/points in S are then are assigned to the closest group head. Finally, only the groups that reach the target size |D k | are retained.

Feasibility was tested for variates of λ = 50, 300 with 50 as step. The constraints were set to 0.2 b/s/Hz as minimum rate and 0 dBm transmission power for 5 groups of size 2 sharing CUE channel averaged over 200 feasible cases. Clearly, a solution exist for low λ values as 50 users and a relatively large average distance from the head cluster (approx., 120 m) and the weakest receiver, which is naturally decreasing down to 40 m as the density increases up to 300. The percentage of feasibility was high hence 0 infeasible Feasibility is analysed with different λ and d max values. The minimum rate is set to 0.2 bit/s/Hz and maximum allowed transmission power is 0 dBm with 5 groups. Taking an example λ = 250 and d max ratios is [1/3, 1/10] average group size goes from 20 down to 2 with distance between 160 m and 40 m. Clearly, having bigger group did not affect problem feasibility as we still have 0 infeasible cases in total. The problem also continuous to be feasible as we increase number of groups per channel yet that has opposite affect on EE. Increasing number of users from 1 up to 11 EE decrease from 591.4391 down to 424.2723 while rate increase from 12.6849 up to 53.5086. The main reason behind low EE is that the average consumed power increase to satisfy minimum rate constraint under high level of interference. Sum-rate Capacity and EE was tested in DL using similar constraints values as KNN. We set λ = 150, 200 and 250 to ensure multicast cast communication in minimum. Vales of d max ratio were 1/5, 1/6 and 1/7 respectively with average group size 3. Figure 3 show global and minimum rate respectively for different λ. Obviously,we have similar behaviour as in KNN as aggregate rate or minimum rate increase logarithmically with maximum transmission up to saturates point hence the aggregate interference level prevents further improvement in data rate. This behaviour is confirmed by global and maximum minimum EE as illustrated in Figure 4. Compared to KNN, higher values were attained here hence we have larger groups. We notice also small difference between values among various λ due to d max control at this level Rate constraints were testes with λ = 250 and d max ratio is 1/8. The maximum transmission power was fixed to 0 dBm and minimum rate is in the range of [0.1, 0.4] b/s/Hz with a step 0.1. The results are shown in Table 2. Again, we notice similar but higher values of GEE, global rate, MEE and minimum rate as in KNN. This confirm that setting a higher value for the minimum transmission rates forces the devices to use higher power to satisfy the constraint.

Density-Based Spatial Clustering of Applications with Noise

The DBSCAN algorithm [START_REF] Khan | Dbscan: Past, present and future[END_REF] is used to identify dense zones by taking a reference point and searching over its neighbourhood within a limited distance d max . If the density of points in this area is above a threshold, the area is identified as a potential group. The same process is applied to neighbours until all points are checked. If some point is not a neighbour of a group, it is regarded as a noise.

In the original version of DBSCAN, a minimum number of neighbours |D k | is identified to specify the core, border and noise points. Here, we follow a similar process (but varying d max ) and declare the core point of the discovered groups as the cluster heads. Feasibility As in the previous cases, we start the performance analysis by assessing problem feasibility for some typical densities (here, λ = 50, 100, 150) and several d max ratios {1/3, 1/19}. The minimum rate is set to 0.2 bit/s/Hz and maximum allowed transmission power is 0 dBm. In contrast to the previous clustering algorithm, DBSCAN allows us either to have many groups with moderated sizes, or few groups with large sizes. The unbalance (in the size of its groups) appears due to the indirect control of points number per given dense area. This fact explains why the number of infeasible cases is significantly larger than with the other clustering techniques (e.g., a maximum of 831 not solvable cases were found). For instance, for λ = 100 and ratio of 1/4, we had 2 D2MD groups of size 52 and a maximum distance inside a cluster of 350 m. Reducing d max to 1/7 yielded more reasonable (and feasible) configurations, with 18 D2MD groups of size 3, a diameter equal to 71 m and without infeasible instances. As the transmission power budget decrease, some infeasible cases appear with -5 dBm and -10 dBm whereas -15 dBm generates extremely low feasibility percentage. Sum-rate Capacity and EE Both measures have been tested in DBSCAN using the usual parameters for the power and rate constraints. We tried λ = 50, 100, 150 to study the effect of density on this algorithm. For the d max ratio, we chose 1/5 and 1/7, with 9 and 18 as the average number of groups and 2, 3 and 6 receivers per group, respectively. Figure 5 shows the global EE and aggregated rate, respectively, for different λ. We notice a similar performance to the results by the previous algorithms for the aggregate and individual rates. Similarly, Figure 6 illustrates the minimum rate and EE. As proven previously, each channel has limited users capacity such as EE and minimum rate decrease while average rate increase. This can be seen clearly as low λ values as higher MEE and minimum rate are. Rate constraints We repeated the numerical computations for assessing how a stricter rate constraint could change the fundamental trade-off between rate and energy efficiency. To this end, we pick λ = 100 and a configuration by design with 18 groups and 3 receivers per group. Now, the GEE decreases with the minimum acceptable rate. The same pattern happens for MEE, as detailed by Table 3. Discussion The EE and rate curves have similar shape in all the clustering algorithms. This means that the clustering technique is not determinant to the fundamental performance of this type of systems, if one ignores the practical issues of use a particular clustering technique in a real network, and with a distributed implementation. Nevertheless, the performance can be enhanced under certain conditions. The KNN algorithm is highly sensitive to the users density, λ. Its performance improves as λ increases, and this means a shorter distance between head cluster and the receivers. Clearly, since this distance is explicitly controlled in DL, the performance with DL is only slightly depending on the density. In addition, the flexibility of DL concept makes possible to have heterogeneous groups in area and number of UEs, and particularly the coexistence of unicast and multicast groups. Also, DL clustering offers higher EE and transmission rates, again as a immediate consequence of the closeness between the cluster head and a typical receiver in its group, shorter that the average distance observed with other clustering algorithms. The feasibility test shows that the problem can be solved for a wider distance, yet the fraction of feasible cases is largely influenced by the power budget.

Conclusion

In this paper, we proposed a general model to study global and users individual EE in D2MD. The problem is formulated as a joint power and resource allocation, yet for analytical tractability we limited the number of shared channel to one. Then, optimal power control was investigated. We proposed a combined frame work of optimization and stochastic geometry which allow us to assess a number of performance measures as D2D coverage, global and users EE and rate, or the capacity of a RB. The clustering algorithms do not have significant impact on EE or rate, yet can be used to slightly improve the fundmental performance. Also, under certain conditions a single resource block has a limited capacity where as more users sharing the channel as the EE decrease.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Global and Maximum Minimum rate vs. transmission power in KNN.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Global and Maximum Minimum Rate vs. Transmission Power in DL.

Fig. 5 :

 5 Fig. 5: Global Rate and EE vs. Transmission Power in DBSCAN.

Fig. 6 :

 6 Fig. 6: Minimum Rate and EE vs. Transmission Power in DBSCAN.

Table 1 :

 1 System Parameters.

	parameter	values	parameter	values
	bandwidth	100 MHz	Max. tx. power	[-15, 15] dBm
	cell size	500m	Noise power density N0 -100 dBm/Hz
	Number of D2D groups	[1, 11]	Number of Iterations	200
	Network density (λ)	[50, 250]	Circuit Power	10 dBm
	Minimum tx. rate	[0.1, 0.4] bit/Hz/s Path loss exponent	2.5

Table 2 :

 2 Global and minimum EE, rate in KNN (left) and DL (right). Rate Constraints were tested with range of [0.1, 0.4] b/s/Hz. The number of groups per channel was set to 5 of size 2 and maximum transmission power 0 dBm averaged over 200 feasible cases. The results are shown in Table2. Clearly, GEE and global rate as well as MEE and minimum rate decrease as minimum rate level increase. This is a clear indication that setting a higher value for the minimum transmission rates forces the devices to use proportionally higher power in order to satisfy the constraint. But, since the rate increases only logarithmically with the SINR in the low-or moderate SINR region, these increased rates do not compensate the extra energy expenditure.

	Min Rate GEE Avg Rate MEE Min Rate GEE Avg Rate MEE Min Rate
	0.1	226.280 14.538 133.876	1.472	593.807 37.790 207.066	2.277
	0.2	222.999 14.352 139.819	1.538	587.773 37.457 209.762	2.307
	0.3	218.606 14.093 133.746	1.471	576.695 36.764 211.694	2.328
	0.4	216.362 13.980 132.662	1.458	559.525 35.735 204.938	2.254

case appeared during test cases. The problem also continuous to be feasible as we increase number of groups per channel yet that has opposite affect on EE. Increasing number of users from 1 up to 11 EE decrease from 303.3774 down to 144.2761 while rate increase from 6.6283 up to 53.5086. The main reason behind low EE is that the average consumed power increase to satisfy minimum rate constraint under high level of interference. Sum-rate Capacity and EE were analysed while considering a wide range of available transmission power budget [-15,15] dBm. The minimum rate were fixed to 0.2 b/s/Hz with 5 D2MD per channel of size 2. Figure

1

show global and maximum minimum rate respectively for different λ. Obviously, aggregate and minimum rate increases logarithmically as maximum transmission power increase to saturates to a maximum value hence the aggregate interference level prevents further improvement in data rate. This behaviour is confirmed by global and maximum minimum EE as illustrated in Figure

2

.

Table 3 :

 3 Global and minimum EE, rate in DBSCAN.

	Min Rate GEE Avg Rate MEE Min Rate
	0.1	261.4748 53.2012 89.8905 0.9886
	0.2	252.3485 51.0620 83.3020 0.9152
	0.3	233.2863 47.0388 79.7355 0.8715
	0.4	214.7058 44.1950 67.0430 0.7149

For vectors x ∈ R n , the p-norm, for any 1 ≤ p ≤ ∞, is ( n i=1 |xi| p ) 1/p . Hence, the 1-norm is x1 = n i=1 |xi|,

is the usual Euclidean norm, and x∞ = maxi |xi|.