Impact of trimet graph optimization topology on scalable networks

Abstract

In the year 2015 per person is having 3.47 devices that will be around 25 billion devices, In future years 2020 expected devices per person are 6.58 which is around 50 billion devices. From this statistic, major problems for IoT devices are scalability and survivability was identified. To address these problems a novel architecture design was proposed named as TGO (Trimet graph optimization) topology for Wireless sensor networks and IoT. As the number of devices increases, scalability increases leads to decrease of Quality of service (QoS). In this paper graph based solution was given for scalability and survivability using TGO topology. In Scalability model an algorithm and flowchart was proposed. Experiments are conducted on Star of star, TGO of TGO, Wheel of wheel networks. In analysis part we observed TGO consumes less power than star and wheel networks. For parameters like received packets, lost packets, hops etc. TGO lies between star and wheel. In Survivable model Hexagon and TGO are 2 edge survivable networks are compared, whereTGO shows better performance in all parameter.

Keywords

Wireless sensor network peer to peer network topology graph optimization quality of service

1 Introduction

In the IOT, Cyber systems a situation like, initially a large group of devices is connected and do rescue or search operation, latter these large groups will be divided into small groups and they become independent. In these independent groups an edge survival and scalable network are required for better QoS. There are mainly models like centralized, decentralized and distributed architecture in designing IOT applications [1]. These existing models may not fulfill above issues effectively so hybrid architectures with novel topologies is needed. The basic partitions of network topology are physical and logical. In Physical topologies devices are connected with cables called as wired networks, similarly in logical topology devices are connected through signals called as wireless networks. Logical topology was mainly operated in two modes they are ad-hoc and infrastructure [2]. In the ad-hoc mode, the central coordinator is not required, whereas in infrastructure mode central coordinator is required. The usage of the topologies is increasing now a day and applied in many engineering applications [3]. The bases for these topologies are derived from graph theory a branch of mathematics. In graph theory many specialized graphs are present, one among them is complete graph or fully connected graph. This paper was mainly divided into four parts, in the first part introduction, preliminaries, taxonomy about different topologies are presented. In the second part of the paper, theoretical models are explained. In third part implementation of scalability and survivability was explained with a flow chart and algorithm. Finally, in last part results and applications of TGO was generated [3].

1.1 Wireless sensor networks

WSN is a special type of wireless networks having a large number of independent units or devices. Each device is equipped with micro-controller, transceiver, power source, memory, antenna and different type of sensors. The functionality of WSN is to collect data from the surroundings and send it to the base station. Sensors are largely deployed and they are connected by star, tree, mesh topologies [4]. WSN are categorized into different types like terrestrial, mobile, underwater, multimedia wireless sensor networks and architecture consists of five layers namely physical, data link, network, transport, application layers and three cross layers namely task, mobility, power management.

1.2 Survivable network

The process of generating a better Quality of Services (QoS) network, so that it can handle different failure scenarios. There are many features which can improve survivable networks. The survivable network has to analyze thoroughly in case of network failures, may be obtained by failure of the node or edge. Generating a better network design, architecture, optimal rules will protect from network failures and network attacks in the system. Survivable networks should have important properties like maintain and cost-effectiveness [5]. Prevention of network failure, security threats is the best remedy. Design a survivable network with multiple resources which can recover from failure. In Survivable networks, if failure occurred then it has to detect failure and heal the network.

1.3 Contiki OS and COOJA simulator

It is an open source operating system for IOT. These devices are connected with optimal power, optimal process with low cost to the external word. The main design goal of this operating system is to communication devices with optimal power to the internet [6]. It can handle IPv6 IPv4, 6lowpan, RPL, CoAP etc.Contiki OS is having a file structure consists of different files examples, app, CPU, regression-test, doc, tools, core, platform. COOJA is a network emulator for Contiki OS and specifically designed for Wireless Sensor Networks. This emulator can support small, medium and large networks with Contiki motes. These motes can be emulated at hardware level. It is a java based extendable simulator and capable of convert’s laptop as a Z1 mote, sky mote etc.It provides a platform for developers to check their code before deploying on hardware. The applications of Contiki OS are like health, industry, home monitoring systems [7].

2 Taxonomy

In IOT architecture has different layers like sensor layer, network layer, service layer, application layer are presented. In this paper our main concentration is on sensor layer, it has different sensors like analog, digital, photo electronic, RFID etc are used in this basic layer. To co-ordinate all these sensors different communication technologies are need, which will co-ordinate sensor data to the next layers [8]. In the proposed taxonomy for IOT was explained in Fig. 1 and 2 this model is based on detail elements of communication technologies like. 1. Technology, 2. Topology 3. devices is categorized and also different sensors are listed for designing various applications.

Fig.1

Various topologies in IOT Communication Technology.

Fig.2

Taxonomy of research in IoT Communication technologies.

2.1 Sensors

In the following Taxonomy list of different sensors like light, heat, moisture, temperature, environmental, chemical, audio, video sensors for sensing different parameters are listed [9].

2.2 Communication technology

Taxonomy was mainly focused on different communication technologies and the topologies used by the devices in IOT.

2.2.1 Technology

Various popular technologies in IOT are ZigBee, 6LowPan, Bluetooth, Ethernet, Z-wave, thread, sigfox, Lara WAN.

2.2.2 Topology

Different topologies like star, tree, mesh, point-point, piconet, cluster tree, star of star etc are used by above technologies [10].

2.2.3 Devices

Each technology has its own devices like ZigBee coordinator, router, end devices, host, master, slaves, border router, objects, sigfox gateway, sigfox cloud, and gateway etc.

2.3 Applications

In the following taxonomy important applications are listed, they are smart home, smart city, smart health, smart agriculture, smart waste management, smart environment and smart parking.

3 Preliminaries

3.1 Trimet graph

G is simply connected and planar graph. Based on number of vertices two cases will be formed first is If number of vertices are odd then one vertex called dominant vertex with a degree (V-1) and other nodes having (V-1) number of vertices with degree 2 [11]. In case two even number of vertices are selected as V then one vertex called dominant vertex with a degree (V-1),special vertex with degree 3 and (V-2) number of Hanging vertices with degree 2. Trimet is less complex (Simple), low cost, no need for edge controls algorithm because it is having an optimal number of edges.

3.2 Semi complete graph

A Graph G’ is said to be semi-complete if and only if (iff) it is simple and for any two vertices u, v of G there is a vertex w of G’ such that w is adjacent to both u and v (in G’) (i.e., Fu;w; VG is a path in G’). K2is complete, but not semi-complete. K1 is trivially semi-complete. To avoid trivialities, throughout this paper a non-trivial graph, with at least three vertices. Properties are as below [12].

3.3 Diagrammatic transformation of different hub topologies

Diagrammatic representations of all possible hub networks are shown in Fig. 3. The process was initiated at star topology which is the optimal topology, next optimal was TGO (Trimet Graph Optimization) topology followed by wheel, semi-complete and complete or full mesh topologies [13]. TGO is an incremental model for star topology, by connecting a minimum number of edges to star TGO was formed and the benefit achieved was for every node is having two edges, even any edge was lost we can recover data from another node. But in the star topology, if any edge was the lot then node will become orphan.

4 Mathematical graph model

To design an engineering concept a strong mathematical model is need. In this proposed model a novel TGO topology was compared with existing topologies. The base for designing a new topology initialized from graph theory, in our previous work a novel graph called Trimet graph was proposed and it was converted into TGO topology. In this mathematical graph model, basic definitions of different graphs and theoretical analysis of TGO topology with existing models are explained [14]. Comparison of the star, TGO, wheel, complete graphs were done with standard graph theory parameters like vertices, edges, diameter, girth, chromatic number-connected and K-edge connected are explained in Table 1. To know the potentiality of the proposed graph, comparison was taken with theoretical parameters like radius, diameter, girth, the chromatic number with standard graphs are explained in Table 2 [15].

Table 1
Theoretical Analysis of star, TGO, wheel, complete graphs

Parameter Star TGO wheel complete

Vertices N N(n ≥3) N N

Edges N-1 (3n-2)/2,
(3n - 3)/2 2(N-1) (N-1)/2

Diameter 2 2 2 1

Girth ∞ 3 3 3

Chromatic Number 2 3 3,4 N

K-Connected 1 1 3 N - 1

K-Edge Connected 1 2 3 N - 1

Notation Sk Tk Wk Kn

Parameter	Star	TGO	wheel	complete
Vertices	N	N(n ≥3)	N	N
Edges	N-1	(3n-2)/2, (3n - 3)/2	2(N-1)	(N-1)/2
Diameter	2	2	2	1
Girth	∞	3	3	3
Chromatic Number	2	3	3,4	N
K-Connected	1	1	3	N - 1
K-Edge Connected	1	2	3	N - 1
Notation	Sk	Tk	Wk	Kn

Table 2

Analysis of TGO with other popular graphs

Name of Graph	R	D	G	CN
K4 (Full Mesh)	1	1	3	4
Trimet graph (TGO Topology)	2	2	3	3
Star graph (Star Topology)	1	2	∞	2
Wheel graph (Partial Mesh)	1	2	3	4
K33	2	2	4	2
Petersen graph	2	2	5	3
Heawood graph	3	3	6	2
Mobius-kantor graph	4	4	6	2
Pappus graph	4	4	6	2
Desargues graph	5	5	6	2
Nauru graph	4	4	6	2
F26A graph	5	5	6	2
Coxeter graph	4	4	7	3
Tutte coxeter graph	4	4	8	2

4.1 Theoretical analysis of TGO topology

In this phase TGO topology with star, wheel, and complete graphs are compared in terms of N.In this comparison standard parameters like R, D, G, and CN from graph theory are considered. From this comparison, clearly observed that TGO will bridge the gap between star and wheel., an analogy was taken for better understanding, Fan speed can be controlled by a regulator having different speed options like 1,2,3,4 etc. Here compare low to high speed as 1,2,3,4. Similarly topology are regulated as a star, TGO, wheel and complete graph respectively. Finally, analysis of TGO was done with popular graphs like tutte Coxeter graph, F26A graph, Nauru graph, Desargues graph etc.

Table 3
Notations used in the proposed algorithms

Symbol Description

N_k Network

S_t Star topology

T_g TGO topology

W_e Wheel topology

R_c Receiver

R_u Router

T_r Transmitter

H_x Hexagon topology

Symbol	Description
N_k	Network
S_t	Star topology
T_g	TGO topology
W_e	Wheel topology
R_c	Receiver
R_u	Router
T_r	Transmitter
H_x	Hexagon topology

Table 4

Comparison Star of star, TGO of TGO, Wheel of wheel networks respectively.

Parameter	Star of Star Network	TGO of TGO Network	Mesh of Mesh Network
Received	2400	6503	6952
Power consumption at receiver (S1)	0.175	0.25	4.5
Power consumption at router (S2)	0.75	0.07	3.5
Power consumption at transmitter (S7)	0.06	0.06	1.15
Batter Consumption at receiver (S1)	23	45	60
Batter Consumption at at router (S2)	17	30	45
Batter Consumption at transmitter (S7)	5	10	10

Input: R_c,R_u,T_r, X = {S_tT_gW_e}.

Output: S_tofS_t, T_g of T_g, W_e of W_e.

1. Start

2. Deployment of R _c at the center of a network which act as a sink.

3. Deploy and connect allR_utoR_c.

4. Number ofT_rto connected to eachR_uwill be obtained from count =(T_r/R_u) and Select network to be generatedN_k = X.

5. Select network to be generatedN_k = X.

6.If (X = = S_t) ConnectT_rtoR_u

7. Else if(X = = T_g) ConnectT_rtoR_uand join alternate edges ofT_randR_u.

8. Else if(X = = W_e) ConnectT_rtoR_uand join all outer edges ofT_randR_u.

9. Stop

Table 5

Comparison of Hexagon and TGO topologies

Parameter	Hexagon	TGO
Received	82	111
Dups	0	0
Lost	1.6	0
Hops	3	1.6
Rtmetric	28.03	13.696
ETX	1.079	1.082
Churn	0.400	0.00
Beacon Interval (seconds)	17 min, 5 sec	37 min, 26 sec
Reboots	0	0
CPU Power	0.377	0.357
LPM Power	0.152	0.153
Listen Power	0.448	0.404
Transmit Power	0.091	0.052
Power	1.067	0.966
On-time	16 min, 49 sec	22 min, 39 sec
Listen Duty Cycle	0.746	0.674
Transmit Duty Cycle	0.171	0.099
Avg Inter-packet Time (seconds)	0 min, 58 sec	0 min, 59 sec
Min Inter-packet Time (seconds)	0 min, 08 sec	0 min, 05 sec
Max Inter-packet Time (seconds)	95.66667	95.66667

5 Proposed methodology 1

5.1 Scalability of TGO topology

The main objective is to design a novel scalable, flexible, simple, understandable network. Requirements in designing proposed topology is an optimal incremental network model for star topology with low power and less battery consumption [16]. Network formation was initiated from clustering phase where all nodes are deployed randomly then all clustering nodes will form different groups based on parameters like distance, similarity etc.By location and battery power cluster head will be selected. After these above phases, proposed topology were explained by algorithm with the notations in Table 3 and flow chart in Fig. 4 followed by implantation details and simulation results.

5.2 Algorithm for proposed models

5.3 Implementation

In proposed topology formation, inputs are sensor devices like receiver, router and transmitter. Network formations start at deployment of receiver at the center. In the next level of formation all routers are connected to receiver will form a star topology which is common structure for all three networks. Based on required output, networks connections will be established on router and transmitter.

Number of receivers added to each router will obtain by count generator from number of transmitter divided by routers. Suppose if star of star was selected then transmitters are added to each router based on count. If TGO of TGO selected then routers and receivers will form TGO topology [17]. Similarly, if wheel of wheel was selected then routers and receivers will form wheel topology. The proposed methodology 1 results are displayed at Fig. 5.

5.4 Experimental setup 1

In this phase, experiments are conducted using cupcarbon simulator. Results are generated by fixing following parameters.

Simulation parameters: - time 8640s, speed 150 ms, arrow speed 50 ms.

Radio parameters: - standard 802.15.4.

Device parameters: - sensor radius 20, energy max 19460, UART/Rate 9600.

6 Proposed methodology 2

6.1. Survivability of TGO topology

In IOT communication technologies most of the applications are using the star topology. If an edge was removed from star topology then node also lost connection and it becomes orphan. The key consideration in topology design of a network is fault tolerant, survivability, optimality. Solution suggested by researchers for survivability is K-node connectivity. To overcome such situation a better edge survivable topology is needed [18]. In this paper we are presenting a novel design for generating K- edge connected network with optimal links using TGO topology. In the proposed model it can survive even edge is lost from a sector.TGO topology has more than two paths in a network. The comparison was done between hexogen and TGO by using COOJA simulator [19]. TGO network was generating better results mainly in power consumption of networks.

6.2 Objectives

Design a survivable minimum edge connected network 2-edge connected.

Link failures have to be tolerated and 2 paths at least should be presented from every node,

Design a special mesh has its own Security and scalability [20].

6.3 Requirements

Need an optimal incremental network to increase the network performance parameters like Delay, Jitter, packet loss etc.,

Network should have Affordability, Availability, and Security.

Need low power consumption networks topologies with 2-edge survivability [21].

6.4 Implementation

In proposed topology formation, input is six sensors and the output will be deployed hexagon structure and TGO structures. The above two structures are 2-edge survivable networks are displayed in Fig. 7. In hexagon all nodes are connected with node degree 2. In TGO all connected to single node with degree 4 and remaining alternated edges are connected with node degree 2.

6.5 Experimental setup 2

In this experiment six number of motes, one hour simulation time,sky motes, Contiki process was Collect View-Shell and radio medium is Unit Disk Graph Medium(UDGM):Distance Loss for all three networks are considered [22]. Results are displayed in Fig. 8 and tabulated in Table 5.

7 Simulation analysis

After conducting different experiments on various quality of service parameters by NS2, Cooja and cupcarbon simulators these results are obtained. In the below discussed topologies are listed in Fig. 3. Power consumption of star, TGO is lesser than wheel, semi-complete and complete topologies. Power consumption by semi-compete and complete topology are almost equal and high. Star and TGO topologies are optimal because of less number of edges or connections. Similarly, battery consumption of star, TGO is less than the other topologies because of less power consumption.

Fig.3

Explores all possible ways of hub networks.

Bandwidth, capacity and throughput are high for complete and semi-complete topologies, moderate for TGO and wheel. Low for star topology. Network life time is long for star and TGO, moderate for wheel and less life time for semi-complete, complete topologies. Flow of duplicate messages in a network is less for star and TGO topologies, medium for wheel and semi-complet,more for complete topology. In Fig. 6 two topologies are considered they are hexagon and TGO. After conducting several experiments on these topologies with cupcarbon simulator the following results are obtained. Power consumption and battery power of both topologies are almost same but the merit we observed in TGO is having more capacity for transferring packets in a network than hexagon.

Fig.4

Flow Chart for Topology formation in Proposed model.

Fig.5

Battery level for star of star at transmitter (S7), Router (S2), Receiver (S1). b) Power Consumption for star of star at transmitter (S7), Router (S2), Receiver (S1). c) Battery level for TGO of TGO at transmitter (S7), Router (S2), Receiver (S1). d) Power Consumption for TGO of TGO at transmitter (S7), Router (S2), Receiver (S1). e) Battery level for wheel of wheel at transmitter (S7), Router (S2), Receiver (S1). f) Power Consumption for wheel of wheel at transmitter (S7), Router (S2), Receiver (S1).

Fig.6

a) TGO of TGO receives more packets than star of star but less than wheel of wheel. b) Consolidate Power Consumption at transmitter (S7), Router (S2), Receiver (S1) by three networks. c) Consolidate Battery Consumption at transmitter (S7), Router (S2), Receiver (S1) by three networks.

Fig.7

a) Hexagon structure. b) TGO structure.

Fig.8

Graphical Comparison of Hexagon and TGO topologies. a) TGO received more packets than hexagon. b) TGO do not have packets lost. c) TGO has less hops than hexagon. d) TGO has less Rtmetric than hexagon. e) TGO has more ETX than hexagon. f) No Chrun for TGO. g) TGO has more beacon interval. h) Listen and transmit duty cycle are slightly less for TGO. i) Avg inter packet times and max inter packet time are almost sago is slightly low. j) TGO consumes less power than Hexagon.

8 Application of TGO topology

8.1 Loon inter balloon communication

Project Loon is a research project developed by Google and its main desire is to provide internet to the interior and rural places of the world. High-altitude balloon network was created with the help of balloons above the stratosphere. For better communication a small group of balloon is connected to big balloon which will form a star topology. As the balloons are movable star topology is not feasible option because of no edge suvivablity.Alternative topologies are TGO and Wheel topologies because of 1-edge survivability and 2-edge survivability respectively.

8.2 Wireless sensor network

In WSN, much popular routing protocol are designed one among them is LEACH. In LEACH mechanism Nodes are randomly places and based on some process clusters and cluster heads are selected which results star of star network (optimal design 1) [23].In this network there is no edge survivability and inter node communication directly. To overcome these problems an incremental method can be created by converting star of star network to TGO of TGO network which is 2 edge survivability network with inter node communication [24].

8.3 Data center network topologies

As the number of system is increasing day by day new problems like scalability, security was emerged. To handle these problems since 1953 on wards different network topologies was introduced. Some of them are Fat tree, random network, Google flat tree, dcell, Bcube etc. [25, 26]. In this paper we have addressed scalability problem by novel networks which can address scalability and security [27].

9 Conclusion

The basic principles in designing an IOT communication networks are to obtain maximum scalability and survivability. In this paper, Mathematical concept like graph theory based star, TGO and wheel networks are studied and analysis of TGO topology was done with popular graphs of graph theory. After conducting separate experiments for scalability and survivability of TGO topology, In both the experiments TGO consumes less power than other networks. In scalability experiment TGO results lie in between star and mesh networks. Similarly, in survival experiment, all most in all parameters TGO is showing better results over hexagon. These experiments and results are generated by using cupcarbon for scalilablity experiment and Cooja simulator with Contiki OS for survivability experiment. Comparison was taken place between basic topologies like a star, TGO, wheel with different simulation times. TGO was tested on different simulators and result analysis was explained on QoS parameters in section 7 and various applications of TGO topology are identified. Finally from the above results TGO is a better scalable and survival network for IOT communications Technology.

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