Dynamical Topology Analysis of VANET Based on Complex Networks Theory

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1 BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volue 14, Special Issue Sofia 014 Print ISSN: ; Online ISSN: DOI: /cait Dynaical Topology Analysis of VANET Based on Coplex Networks Theory Hong Zhang, Jie Li School of Civil Engineering and Mechanics Huazhong University of Science and Technology, Wuhan , China Eail: Abstract A Vehicular Ad hoc NETwork (VANET) is a special subset of ulti-hop Mobile Ad hoc Networks, in which the vehicles wireless interfaces can counicate with each other, as well as with fixed equipents alongside city roads or highways. Vehicular obility dynaic characteristics, including high speed, predictable, restricted obility pattern significantly affect the perforance of routing protocols in a real VANET. Based on the existing studies, here we propose a testing network according to the preferential attachent on the degree of nodes and analyze VANET odel characteristics for finding out the dynaic topology fro the instantaneous degree distribution, instantaneous clustering coefficient and average path length. Analysis and siulation results deonstrate that VANET has a sall world network features and is characterized by a truncated scale-free degree distribution with power-law degree distribution. The dynaic topology analysis indicates a possible echanis of VANET, which ight be helpful in the traffic congestion, safety and anageent. Keywords: VANET, dynaic topology, coplex network, instantaneous degree distribution, clustering coefficient. 1. Introduction With the developent of econoy and China city urbanization, cars are increasing in failies, which akes the traffic conditions in the city ore coplex. In order to solve this proble, Vehicular Ad hoc NETworks (VANET) eerge as the tie requires it. 17

2 Recent years have seen a lot of advances in wireless counication technology. VANET as a special application has becoe a proising approach for facilitating the traffic safety, traffic anageent, environental protection and vehicular counication [1]. Safety applications are iportant to reduce the nuber of accidents on city roads and highways, including all driver assistance applications, i.e., overtaking the support, eergency braking notification, accident inforation, traffic ja warning, optial route selection, and security distances, etc., in order to avoid accidents and proote road safety. VANET assists drivers while providing inforation about the traffic conditions on the road so that it akes their journey safe. It also provides inforation about the particular traffic conditions with the ultiate goal to avoid road congestion for the sooth flow of traffic and cofort, internet-connectivity, and entertainent of on-road passengers and drivers. Moreover, a parking navigation syste [], digital billboards for VANET [3], business activities through on-road streaing [4] are all exaples under the category of t delivery applications. In VANET, due to its dynaic characteristics, the counication between vehicles can be exchanged quickly. Vehicles are oving at high speed, the otion trajectory is liited on the road, the topology is rapidly changing, so that vehicles pay ore attention to the road traffic ahead. The high speed oving is one of the key factors that lead to the decline of the network perforance and network expansion. VANET is a wireless counication technology for vehicle counications in Ad-hoc networks. Reliable counication can provide relevant inforation and valuable security to the vehicles and drivers, and provide data of the traffic anageent syste. With the popularization and iproveent of VANET, it will becoe one of the ost iportant ways to solve the traffic ja, quickly handle traffic accidents and optiize the traffic flow. VANET can provide a ore intelligent counication way, e.g., different city ITS counications, vehicles counication, and different kinds of inforation platfor counications, etc. Through these interactions, the vehicle can choose a ore reasonable travel route before a trip. To avoid possible traffic jas in the travel, VANET can upload relevant traffic inforation. As a result, the network topology analysis is an iportant issue, which should be helpful in the transportation infrastructure. VANET can be deployed through integration of governent authorities and network service providers to address three vehicular scenarios, i.e., highway, urban and rural [5]. In recent years, a coplex networks theory provides a new viewpoint and ethod for studying the coplex systes. The finding of a sall-world network and scale-free network akes a revolution in network science, since it attracted a great deal of researches of coplex networks. The network structure can decide the network function. Urban traffic network affects VANET, which is a typical coplex network. It is a base research that connects the coplexity of the topological structure of VANET with coplex network theory. Through the research on network topology, we can find out the inner acting force in the network and the driving force of the external one, interpret the echanis and regular pattern of VANET on a acro scale. These researches will be dedicated to the traffic congestion alleviation and 173

3 prevention, the spatial-teporal structure planning of a city, disasters prevention and response, reliability iproveent of VANET. This paper cobines the coplex network theory with traffic flow theory and concentrates on the topology and reliability of VANET, spatial-teporal coplexity of VANET and the influence of the traffic network structure on VANET.. Related works and background With the increase of the vehicles in the city, traffic congestion has becoe an iportant proble. It is difficult to eet the growing traffic deand, relying on a new road or expansion of the network scale. Intelligent Transportation Systes (ITS) put forward soe fundaental solution to these probles. VANET is one of key technologies in ITS and the Internet of Things, aiing to increase the traffic safety and cofort. The core idea of the syste is to apply the advanced data counication, positioning, sensor, electronic control and other related inforation technology to transportation. With the developent of Intelligent Transportation, VANET has gradually attracted the attention of researchers. On one hand, the vehicle obile odel is suarized and classified in [6]. The authors in [7] introduce a VANET odel generation tool VanetMobiSi, siilar to the real vehicle environent that is widely used in Ad Hoc Networks. On the other hand, the scholars pay ore attention to the real scene siulation of Vehicular Ad Hoc Networks. The authors in [8] use real vehicle trajectory obility odels to test VANET routing protocol perforance. In [9] Shanhai Vehicle Ad Hoc Network is constructed through the floating data and analysis of its routing protocol perforance..1. Coplex networks theory Many of the real-world networks have been described by coplex networks theory which was put forward by Erdos and Renyi in 1960-ies, such as the scientific collaboration network, coputer network, transportation network, electric power networks, interpersonal relationship network, and so on. Strongatz [10], S t r o n g a t z and W a t t [11] and N e w a n [14] proposed a WS sall-world network odel in 1998 which realized the transition fro a regular network to a rando network. WS odel describes the sall-world property successfully. However, the nodes degree distribution for WS odel does not confor to realworld network. Then B a r a b á s i and A l b e r t [13] proposed the BA scale-free network odel, constructing in 1999 a network with power-law distribution of nodes degree. The coefficient of BA odel is sall for large-size networks, indicating that BA odel does not show a significant sall-world property. Many natural systes can be exained by odels of coplex networks. Studying real-world networks indicated that ost networks showed a sall-world property which eans the network has a high degree of clustering coefficient and a sall average path length, or has a power-law distribution. 174

4 .. VANET characteristics In practical applications, due to price factors, in a transportation syste it is difficult to equip all vehicles with an On BoarD unit (OBD). VANET should be given priority to public transport vehicles, such as taxi, and further construct a city public traffic vehicle ad hoc network. VANET has the following characteristics: i. Mobility. VANET is coposed of obile nodes and fixed nodes. The obile nodes geographical location ay change at any tie based on variable speed oving. So the topology of the network changes, but does not affect the overall operation of the network. In fact, this is the biggest difference between VANET and a fixed structure network. ii. Wireless. The wireless channel is not stable, vulnerable to interference and onitoring, security has becoe an iportant research topic. iii. Multi hop. Due to the fact that the wireless transit power and signal coverage is liited, while counicating with other nodes outside the coverage, it ust be ulti hop to coplete with an interediate point. iv. Self-organization. Each node oves quickly, independent of the network coposition. All nodes are coordinated according to the distributed algorith. This is the iportant reason VANET to have good prospects for application. v. High dynaics. The obile nodes can open and close the network according to their own needs when the network is affected by antenna coverage. VANET topology also changes quickly. The difference between VANET and other wireless network is shown in Table 1. Table 1. The difference between VANET and a wireless network Content The traditional cellular wireless network VANET Topology Fixed Dynaic, flexible Infrastructure Yes Little Safety and quality of service Better Poor Configuration speed Slowly Quickly Cost High Low Survival tie Long Short Route selection and aintenance Easy Difficult Network robustness Low High Relay equipent Basic station and wired backbone network Backbone network characteristics 3. Methodology and odel High speed, reliable Wireless nodes and wireless backbone network Low capacity, high error In this paper the coplex network is a new ethod to study VANET dynaical topology in currently available ethods. The process is as follows: it analyzes the network characteristics and describes the network odels that shape the testing 175

5 network; introduces the paraeters concept defined to apply to the network we would ake use; later the results of siulation and theoretical value on the testing networks are shown Network backbone Each node has a counication and coputing device that can transit inforation. The obile nodes counicating with each other copose a selforganizing network. As shown in Fig. 1, it reflects the real-life network infrastructure. 176 Fig. 1. VANET doains in reference architecture VANET syste structure consists of two parts: one is the counication between the vehicle and the fixed infrastructure, the counication of the road and vehicle (RVC), vehicle and the fixed infrastructure (VI). The fixed infrastructure ainly refers to the RoadSide Unit (RSU); on the other hand is the counication between vehicles, i.e. the vehicle counication (IVC) or vehicle to vehicle counication (VV). The On-Board Unit (OBU) includes a vehicle state paraeters acquisition odule, GPS positioning odule, input and output devices and a counication odule. The vehicle state paraeters odule collects the data and inverts to an analog signal and a digital signal by input and output devices. GPS odule acquires the positioning inforation fro a satellite. The vehicle counication odule realizes the counication between the vehicle and RSU infrastructure. The input and output devices provide VANET platfor for the driver. The driver can input inforation to the network, warning inforation through the audio output device and gain the VANET vehicle situation through the video output equipent. RSU, installed along the road, is responsible for the counication; on one hand it counicates with OBU, reports the traffic inforation within the coverage region to the control center, at the sae tie it provides a feedback fro the control center to vehicles. The control center connects

6 with all roadside units, suarizes and analyzes the vehicle status inforation by onitoring, anages the traffic. The passengers can use a obile phone connected to OBD and RSU by a wireless network. They also obtain related inforation as shown in Fig.. Fig.. VANET architecture In a icrocosic odel, the Rando WayPoint (RWP) is one of Ad Hoc Network coon odels. The nodes rando oveent in RWP cannot objectively reflect the oving characteristics in VANET because the vehicles are affected by the traffic lights, traffic signs and traffic arking that akes the difference between the. IDM_IM and IDM_LC are closer to the reality scenes. They use an intelligent driver odel to generate the vehicle trajectory and increase the crossroads and ulti lane, so that siulation of the whole traffic network is not suitable. In the syste, the vehicle is equipped with a sensor, the sensors of all vehicles constitute a obile ad hoc network to share the road conditions, traffic and weather inforation. In addition, the roadside units are static nodes. The location of the static nodes is fixed. As shown in Fig. 3, the roadside units will send the liited inforation to the vehicle which is convenient for the vehicle to prepare in advance. Fig. 3. A case of roadside units 177

7 3.. Network backbone Consider an acyclic directed graph G = (V, E) where V is the set of vertices connected by a set of unit capacity edges E. These vertices and edges sybolize the nodes and channels of a wireless counication syste as shown in Fig 4; where the nodes that transit data packets into the network are source nodes (V1 and M), and the nodes that ultiately receive essages are called receiver nodes (V3 and M3) for a particular ulticast session. Due to the liitation of the transission range, the data packets have to pass through interediate nodes that act as relay nodes between the sources and receivers. The nodes V and M are in the transission range of the source nodes V3 and M3, respectively. 178 Fig. 4. Illustration of a wireless network in ulticast session Based on the analysis above ade, VANET, having coplex characteristics, is a typical coplex network. Our strategy is given the initial network G0 with nodes N0 and M0 links. According to certain rules insert soe odular to produce a new network, at that the ost faous ethod is the sall-world network and the scalefree network. A coplex network can describe the statistical properties of the systes based on a graph. There are serial basic statistical paraeters, including the degree distribution, the clustering coefficient, the average shortest path length, etc. in a coplex network. WS sall-world network odel (WS odel) eans that it has a high degree clustering coefficient and a sall average path length. WS odel lies between regular networks to rando networks. In WS odel the clustering coefficient is high; however, the degree distribution of the nodes does not confor with the real networks. The classic research on a coplex network indicated that ost networks showed power-law degree distribution, defined as BA scale-free network odel. Due to the growth and preferential attachent they are proxiate to the growth of any network systes in real world. We propose the BA scale-free network odel as the network orphology of the new network odel in this paper. In a real network, there are usually three cases of connection between the nodes that are fully connected and randoly connected or falling in between. Following the Freeway obility odel [15], the siulations are carried out for a 3-lane highway (depicting one side of the highway) by a length of 10 k and a width of 5 per a lane. In all siulations, with a transission range of 50, each obile node speed is taken as 100 k/h. Each counication scenario consisting of five obile nodes (V1, V, V3, V4 and V5) has been taken into account in a way that V1 and V4 are within the counication range of each other, as well as V and V3 and V5 are within a counication range of each other, as shown in

8 Fig. 5a. It is assued that each node has knowledge of its own location, as well as of its one-hop neighboring nodes. The vehicles are fully connected within the scope of coverage, which is fully connected as shown in Fig. 5b. Based on the above description, for any given t 0, N(t) is expressed as the total nuber of the network changes. If N(t) is a rando process, G(t)=(V(t), E(t)) is called a coplex network. Note that N(t)= V(t), M(t)= E(t), li E N( t) = N, t where E N( t) express the node average at t oent in VANET. (a) (b) Fig. 5. VANET siulation layout with a Freeway obility odel 3.3. Method description In VANET the nodes are divided into two categories, fixed nodes and obile nodes. Fixed nodes refer to RSU, and obile nodes refer to the oving vehicles on the road. In this paper the nodes refer to the oving nodes in the following text. Fig. 6 shows that V1 and V4 connect each other, as well as V and V4, in addition V, V3, and V5 connect together at this tie. In the initial network, the nuber of nodes is n 0 = 5, and the nuber of edges is 0 = 5. At each tie step, a odule coposed of several nodes is added to the network. When the tie step t is large enough, so that the network size is large, new nodes are chosen based on the echanis of preferential attachent. The new nodes would be connected to the existing nodes of the network with a larger degree priority, and the nuber of connections is ( 0 ) [16]. We assue that in the rewiring probability k i (), t the node i was chosen in the network depending on the degree k i ( t) at t oent with probability p(t) of the triangle connected. Ω ( i) represents the node i neighbor set, and ki ( t) ki () t = = t (1) ki () t kj, j (( )( ( )) ) ( ) ( ) ()() t Ω i 1 ki () t = 1 1 p t p t ki () t =. k () t k () t k ()() t k () t As can be seen, k rate of change is proportional to ( ), ( ) 0 ) t, k i (t i ) =. Then i i j, j Ω i i i i i k i t ki t ( + i 179

9 ( 0 t + ) () ki () t =. t i In VANET the nodes ove in unpredictable ways and different speed, and appear or disappear without certain regularity. The nodes oveent leads to links frequently and disconnections between nodes, which cause a change of the network topology. At this point, VANET and the wired network have a significant difference. In the references, the vehicle obility odel is usually divided into a acroscopic odel and a icroscopic odel [17]. Each vehicle has its own characteristics. There are a lot of factors to affect the vehicle trajectory, for exaple, the topological structure of the road, soe of the city streets and highways restrictions on the vehicle oveent, the road speed liit, overtaking and rules of safe driving, traffic signs. 4. Network properties analysis 4.1. Instantaneous degree distribution The node degree k is the nuber of nodes it is directly linked to, and its strength can be viewed as an indication of its centrality. The average k is express as k, and p(k) describes its degree distribution. A randoly selected node degree is exactly the probability of k, also equal to the degree nuber k of nodes in the total nuber of network nodes. Traditionally, for a network G, the degree distribution could be N k denoted as ( ), p k = where N k is the node nuber of degree k; N is the nuber N of nodes in the network. The value of p(k) is between [0, 1]. Usually another representation ethod is used, that is cuulative degree distribution. Its eaning is the probability distribution of the node degree over k, then p( k) p( k ). { i ( )}, = If there are li p{ ki( t) = k} = pi( k), k=0, 1,,, and pi ( k) t k = k k = 0 = 1, p k the node i expresses steady-state degree distribution. As shown in Fig. 5, the nodes V degree is 3, and the node X degree is 4 at t oent. In VANET each node degree distribution is instantaneously changing. There is a corresponding structure in the network odel proposed; the transient average degree distribution is proposed to describe the real tie degree distribution in a network. According to N e w a n, S t r o g a t z and W a t t s study [18] the instantaneous degree distribution is expressed as 1 (3) p( t, k) = { i () }. () p k t = k E N t i V() t 180

10 If there are li p( t, k) = p( k), k=0, 1,,, and p ( k) = 1, { ( k) } t k = 0 p the node i is called instantaneous degree distribution. When t E[ N K () t ] ( t + 0 ) p( k). For the network odel proposed and (), we can write ( 0 + ) (4) p{ ki() t < k} = p ti > t. k 1 The probability density function of tie t i can be written as p( t i ) =. Then 0 + t the probability will be obtained, which would be repeated ties. Equation (4) can be written as ( 0+ ) ( 0+ ) t (5) p ti > t = 1. k ( t+ 0 ) k Then ( 0 + ) p 0 { ki ( t) < k} ( ) t (6) p( k) = = k. k + t ( ) ( 0 + ) 0 3 When t p ( k ) ~ k. Fro (6), p(k) is related to t,, 0 and k, which obeys a power-law distribution with an exponent γ = 0 + 3, where the value of γ depends on 0 and. We have fixed = 5, 0 = 5, relevant paraeters N=10000, n 0 = 5, then we can obtain γ = 5 that is irrelevant with t, as shown in Fig. 6; p(k) has the sae trend at different t t=1 t= p(k) k Fig. 6. Degree distribution with t = 1 and t = 5 fro analytical results 181

11 4.. Instantaneous clustering coefficient In VANET network the clustering coefficient C i (t) [19] of the node i (the degree k i (t)) is defined as the ratio of between the actual nuber of edges aong the given neighbor nodes and the theoretical nuber of edges at t oent. There are actually E i (t) edges aong the selected node i and k i (t) neighbours, linked to each other. Then the instantaneous clustering coefficient of node i is Ei ( t) (7) Ci () t =. ki() t ( ki() t 1) The instantaneous clustering coefficient C(t) of the network with E[N(t)] nodes is the average of C i (t). It is expressed as 1 (8) C() t = i (). () C t E N t i V() t F r o n c z a k et al [19] give the equations of C i (t) and C(t) ( 1) 4 (9) Ci() t = ln t+ ln t, i 8( t + t i ) ( 1) ( 1) 16 ( + 1) t t (10) C() t = ln t+ ln ζ ln, + 4t ( 1) t t + 1 where ζ ( 1, t ). When t ( ) (11) C() t = ln t+ ln ζ ln +. 4t ( 1) + 1 So that: (1) ( ) ( ) ( ) ln t ln t ln < C() t < ln t t 4.3. Average path length The distance between two nodes i and j in a network d ij is defined as the edges nuber of the shortest path of connecting two nodes. The diaeter of the network is the axiu distance between two nodes, D = ax d ij. The network average path length L is defined as the average distance between all nodes: (13) L= dij. N( N 1) i, j G, i j N e w a n, S t r o g a t z and W a t t s [18] gave the average path length using a heuristic ethod. In it A, B and C are constant, L = Aln( N B) + C. Bollobás ln ( N ) and Riordan proved that the average path length of BA odel is L ~. ln ln N ( ) 18

12 5. Siulations and discussions 5.1. Siulation experients The theoretical analysis is verified by siulation experients. In view of the taxonoy of VANET siulation software, in M a r t i n e z et al. [1] have divided the into three categories, i.e., realistic obility generators (or traffic siulators), network siulators, and VANET siulators. Table. Siulation Paraeters Paraeter Value Siulation tool OMNet++, Matlab Siulation tie s Mobility odel Freeway or linear obility odel Topology size 10 k 30 Nuber of lanes 3 Lane width 5 Node density 10 Source nodes (data flows) 4 Nodes speed 15-0 k/h Transission range 50 The ethod above proposed is siulated in this section. In light of the coplexity of the coputing instantaneous degree distribution, the clustering coefficient and path length of a network, we first set up one basic network to evaluate the validity of our ethod. 5.. Discussion In Figs 7-10 the siulation screenshots in MATLAB are presented. The degree distributions clearly show the characteristics of a scale-free network at the iddle section. When the node degree k is sall, p (k) has distribution increasingly siilar to the sall-world network odel in Fig. 7a (loglog axis) and then decreases after the peak. Therefore, p (k) obeys the power-law distribution since the node degree k is large in Fig. 7b. In Fig. 8 with N increasing, the clustering coefficient reains at a high level with = 0, 3, 5, 10, 15, 0 respectively, which indicates that the network shows a sall-world network property. When the network size for this case is about 5000 and ore, the clustering coefficient reains essentially unchanged. In Figs 8 and 9 the instantaneous clustering coefficient is increasing with the value of. In Fig. 10 with N increasing and = 3, 5, 10, 15 respectively, the average path length increases slowly. For a large nuber of network nodes, the average path length is short. This indicates that the network proposed also shows a sall-world property. In conclusion, the value of N does significantly change both the clustering coefficient and the average path length. 183

13 10 0 Siulation results 10-1 p(k) k (a) (b) Fig. 7. The p (k) of siulation results with 0 = 3, = 3 (a); dependences of p (k) on k with 0 = 6, = 3 (b); + arks represent the siulation results; arks denote the nuerical results =0 =3 =5 =10 =15 =0 = C N/10 4 Fig. 8. The clustering coefficient results, using our ethod with = 0, 3, 5, 10, 15, 0, 30 respectively C Fig. 9. The clustering coefficient results, using our ethod with N =

14 =3 =5 =10 =15 6 L N Fig. 10. The path length results, using our ethod with = 3, 5, 10, 15 respectively 6. Conclusions In this paper we focus on the dynaical topology with the application of the coplex network theory. In the viewpoint of the ean field theory, the concept of a sall-world network and a scale-free network is first defined, and VANET odel is then proposed for siulating and coputing the instantaneous degree distribution, instantaneous clustering coefficient and average path length; Methods of iproving the coplex network paraeters are also discussed in this paper, such as developing the instantaneous degree distribution, and increasing the factors. Aong the, the instantaneous degree distribution and the clustering coefficient are the ost direct and efficient paraeters to analyze the dynaical topology. A nuerical siulation is carried out with the proposed ethod, the results being better related to the analytical results, so that the analysis is strengthened. As seen fro the analysis results, the instantaneous degree distribution shows the characteristics of the WS sall-world network for a sall node degree k and a BA scale-free network with a power-law distribution as the network scale increases. The clustering coefficient reains at a high level with = 0, 3, 5, 10, 15, 0 respectively and increases with the value of. The average path length is short that shows that the sall-world property is affected little by the network size. The BA odel characteristics are preferential attachent and growth, and the growth is infinite. However, the life of any networks in reality is liited, as WWW network alost every tie has a new webpage entering the syste and an old webpage leaving. In VANET, when the nodes arrive to the destination, they would exit the syste. Therefore, we will study the topology of the network and the edges exit probability after the syste goes into a saturation state in the future. Acknowledgents: The research is sponsored by the National Natural Science Foundation of China (Grant No ). This research is also sponsored in part supported by the Education Science and the 1th five-year Plan of Hubei province (No 01B433) 185

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