A Graph Structure Approach to Improving Message

Wireless Networks manuscript No. (will be inserted by the editor)

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks Romeu Monteiro · Wantanee Viriyasitavat · Susana Sargento · Ozan K. Tonguz

Received: date / Accepted: date

Abstract Efficient message dissemination in vehicular ad-hoc networks (VANETs) is crucial for supporting communication among vehicles and also between users and the Internet, with minimal delay and overhead but maximum reachability. To improve the message dissemination in these networks, we show the need to study the graph-theoretic properties of VANETs, since they neither follow the small-world nor the scale-free network characteristics often found in large self-organized networks. We consider 3 fundamental properties: connectivity, node degree, and clustering coefficient. For each property, we develop and validate analytical models for both the urban and highway scenarios, building an extensive graph structure perspective on VANETs. With this, we see how connectivity changes with network density, that VANETs exhibit truncated Gaussian node degree distributions, and that network clusR. Monteiro Instituto de Telecomunicacoes, Universidade de Aveiro, Campo Universitario de Santiago, 3810-193 Aveiro, Portugal and Electrical & Computer Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. E-mail: [email protected] W. Viriyasiatavat Electrical & Computer Engineering Department, Carnegie Mellon University, Pitsburgh, PA 15213, USA. E-mail: [email protected] Present address: Faculty of Information and Communication Technology, Mahidol University, Bangkok, Thailand 10400. S. Sargento Instituto de Telecomunicacoes, Universidade de Aveiro, Campo Universitario de Santiago, 3810-193 Aveiro, Portugal. E-mail: [email protected] O. K. Tonguz Electrical & Computer Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. E-mail: [email protected]

tering coefficients do not depend on the network’s size or density. We then show how these results can be used to generate individual behavior favorable to the whole network using local information. The usefulness of this new approach is demonstrated by proposing new mechanisms to enhance the urban vehicular broadcasting protocol UV-CAST. Our results show that these new mechanisms lead to excellent performance while reducing the overhead in the UV-CAST protocol. Keywords Protocol Architecture · Routing Protocols · Wireless Communications

1 Introduction Developing efficient protocols for message dissemination in Vehicular Ad-Hoc Networks (VANETs) is an important and challenging task. These protocols are absolutely essential for enabling communication between vehicles as well as between vehicles and the Internet, thus creating an infrastructure supporting applications from infotainment to traffic safety. Such communications must strive to maximize reachability and minimize delay, while also minimizing the use of the limited channel bandwidth. This is a daunting task in VANETs for a number of reasons: the high speeds of the nodes, the rapidly changing propagation characteristics, the connections from the mobile nodes to fixed Access Points (APs), the variability of vehicle densities, and roadway scenarios from interregional highways to urban Manhattan grids, among others. In order to build efficient protocols that address VANET’s unique characteristics, it is necessary to describe their properties. Several works have studied the properties of VANETs with a focus on the mobility of the nodes and time-dependent properties of the links.

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Works such as [1],[2],[3],[4],[24] study connectivity in VANETs in terms of the frequency and duration of the contacts between vehicles and between vehicles and infrastructure, the inter-arrival times, the inter-vehicle spacing, the re-healing times and the vehicle traffic volume. These are very important indicators; however, there are other important indicators which have not been explored, namely the properties related with the topological or graph structure of VANETs. In this work we study VANETs from that perspective, and refer to this approach as network science and graph-theoretical interchangeably. Two groups of complex networks with specific network graph properties stand out from the others: smallworld and scale-free networks. Many ad-hoc networks including biological networks, computer networks and even the human social networks [5] are small-world and scale-free networks. Their graph properties make travelling between their nodes fast and simple. Thus, it is crucial to study the graph properties of VANETs to evaluate if their structure suits the simple dissemination strategies of scale-free and small-world networks, before setting out to design more complex protocols. More specifically, we focus on 3 network properties we believe to be relevant in studying the structure of VANETs: 1) network connectivity, 2) node degree distribution, and 3) clustering coefficient. The first and second properties will lead to observations on connectivity at global and local scales, thus enabling one to bridge both properties so that nodes can work with little local information in a way that is favorable to the network as a whole. Furthermore, the study of the clustering coefficient - the frequency at which a node’s neighbors are also neighbors of each other - will provide insight into the grouping structure of local communities of nodes, so that protocols can consider an adequate level of redundancy using minimal local information. We provide a study of these properties in both urban and highway VANETs, using real life data as well as analytical models. In order to exemplify the application of the principles derived from the study of these properties, we design mechanisms to improve the performance of the recently developed urban vehicular broadcast protocol (UV-CAST) [6]. These mechanisms reduce the overhead of dissemination while maintaining the message dissemination performance. Therefore, knowing the network properties can indeed lead to a better protocol design. In [7] we started exploring these possibilities by measuring parameters such as network connectivity, average shortest path length, clustering coefficient and node degree distribution from urban and highway VANETs. We then used these measurements to suggest mecha-

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nisms for improving VANET routing protocols, which we exemplified in practice with UV-CAST. In this paper we build upon this earlier work by extending it substantially, with the following key contributions: 1. Developing analytical models that predict these network parameters on urban and highway scenarios with different sizes and densities, whose accuracy we prove through validation against real-world data. 2. Tuning the additional mechanisms proposed for UVCAST, and demonstrating how our proposal informs the maximum number of vehicles, while also increasing the distance between vehicles and the message source when they are informed, with much smaller and scalable network overhead than flooding and UV-CAST protocols. 3. Proving that graph structure can and should be applied to VANETs, as it provides further insight into how to design and improve protocols specific for VANETs. The remainder of the paper is organized as follows. Section 2 presents the related work, while Section 3 summarizes the information on the data used to emulate real world data. In Section 4 we present the network definitions and notation used to develop analytical models in the following section. Taking real life data, Section 5 explores if VANETs are small-world or scalefree networks. Section 6 analyzes the connectivity, node degree distribution and clustering coefficient of urban and highway VANETs, through analytical models compared with real data. Section 7 elaborates on possible uses for the data and conclusions obtained in Section 6, and exemplifies with a proposal to improve the UVCAST [6] protocol. Finally, Section 8 summarizes this paper’s main contributions and formulates topics for future work.

2 Related Work As noted in Section 1, most studies on the properties of VANETs describe these networks in terms of connection times and the vehicles’ mobility properties. In [1] the size and duration of vehicle chains is studied, and a simulation model of highway VANETs that replicates the properties of these chains is designed, so as to allow for a better study and simulation of VANETs. The works in [2],[3],[4],[24] describe VANETs in terms of different properties: the number of periods in which pairs of nodes are connected, the duration of these periods of connection and disconnection, the statistical description of inter-arrival times between vehicles and the inter-spacing between them. These works observe real traffic data or simulate vehicular mobility

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks

and thus produce results that are not easily obtainable from any analytical model. One of the most significant aspects is the way in which traffic patterns change with vehicle density and how it affects the statistics. In spite of this, a statistical description of the network graphs created by VANETs at each moment in time is still missing. As for the study of connectivity, it should be noted that there are several different ways to define connectivity. The simplest way is binary: defining a connected network as a network where all nodes are connected through single-hop or multi-hop paths. This is the definition used in works such as [29] which studies the probability of having a connected network in idealized highway VANETs taking into account temporal properties and transitions. This is a sensible approach when there is a mandatory need for full connectivity. A definition of connectivity very frequently found in the scientific literature is the one commonly known as kconnectivity, which is the probability that the network remains connected after the removal of any k − 1 number of nodes [8]. This type of connectivity study can be found in multiple works, such as [8],[9],[28] which developed mathematical models for this type of connectivity. These approaches are appropriate when the main requirement is full connectivity with redundancy. However, studying full connectivity in a strict sense even considering different levels of redundancy lacks nuance: it does not distinguish variable amounts of disruption, even though disruptions are a common issue in VANETs. Other works study different aspects of connectivity, such as the probability of the network having at most a certain number of clusters [10]. While there are several works on VANET connectivity of 1D/highway networks, very few studies exist for 2D/urban VANETs. Incidentally, such definitions of connectivity do not allow one to easily estimate the fraction of network nodes accessible to some node at a given time, as this will depend on the size of the network and on border effects which significantly increase the difficulty of this problem. A significant number of protocols to broadcast messages in VANETs has been proposed, but we will focus on some examples closer to our work. In [21] a Direction-aware Function-Driven Feedback augmented Store and Forward Diffusion (DFD-FSFD) scheme is presented. Each message contains a propagation function which encodes target areas and preferred routing as in a gravitational field. In disconnected situations, messages are stored and carried forward. In [22], AckPBSM (Acknowledged Parameterless Broadcast in Static to highly Mobile protocol) is proposed. For broadcast in

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well-connected networks, this protocol uses the concept of Connecting Dominating Set (CDS). In disconnected networks, messages are relayed through reception acknowledgments embedded in periodic hello messages. Message latency depends on the hello messages interval time, which might cause significant additional delay for large hello interval times. In [25] and [26] a probabilistic broadcasting method for highway VANETs named Irresponsible Forwarding (IF) is proposed and evaluated. IF aims to spread messages as fast as possible while reducing collisions, by having all vehicles rebroadcast with a probability proportional to the probability that there is no other vehicle downstream able to rebroadcast. Then [27] proposes CAREFOR, an enhancement to IF based on 2 ideas: 1) allowing different communication ranges for source and receiving vehicles to be considered for calculating rebroadcast suitability, 2) estimating a probability of collision at each vehicle and restricting rebroadcast to vehicles with collision probability below a given threshold dependent on the density of vehicles. IF and CAREFOR are designed for the highway (not urban) scenario and do not carry-andforward messages to support moments and regions of disconnection. The works in [31],[32],[33] propose cross-layer algorithms which select relaying nodes for broadcast by coordinating with the MAC layer and in some cases using information from the physical layer. The work in [31] considers a broadcast handshake scheme (BRTS/BCTS) followed by a countdown timer that has nodes rebroadcasting messages with a delay that is a function of node position, relative velocities of the vehicles and channel conditions given by SNR and PER. The work in [32] suggests building a virtual backbone infrastructure that will be used to quickly forward messages using a Dynamic Backbone-Assisted MAC (DBA-MAC) protocol. The backbone is created through distributed clustering based on the distance between vehicles and the estimated lifetime of the wireless connections. In [33] a binary partition strategy is pursued in order to find the farthest node capable of retransmitting: nodes emit consecutive black-bursts according to their location in the near or far segment (and sub-segment, and so on) and remove themselves each time they listen to a node in a farther segment. However, besides requiring more information than that usually available at the routing layer, these 3 protocols are designed solely for 1D vehicular networks. An inclusive message dissemination protocol should support both 1D and 2D VANETs, since vehicles move both in highway scenarios as in urban scenarios.

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In [6] an urban VANET broadcasting protocol, called UV-CAST, is designed and tested. In this paper, we will consider this to be our reference protocol for message dissemination in urban environments since it is a lightweight infrastructureless protocol which overcomes the limitations existent in the protocols previously presented. We describe UV-CAST in Section 7. We will add mechanisms based on the graph structure properties of urban VANETs which are not studied and considered in the original UV-CAST protocol. As for network approaches based on graph structure itself, some of the most relevant studies in the subject include the celebrated work of Watts & Strotgatz [11] on small-world networks, and the well known work of Albert & Barabasi [12] exploring scale-free networks. Watts & Strotgatz’s work shows that, in many kinds of large self-organized networks, one can go from one node to any other through a small number of hops. While the size of the network might grow significantly, the average shortest path length will increase just slightly. These researchers also presented a model for these networks as intermediates between lattice-like networks and random networks. Albert & Barabasi studied a subset of smallworld networks which they called scale-free networks, where the structure of the network remains the same regardless of the scale used to observe it. These networks have a small number of nodes with many edges and many nodes with few edges. Kleinberg’s research [13], building upon these earlier works, shows that smallworld networks that exhibit a clustering exponent equal to the number of lattice dimensions can easily be navigated using a distributed greedy algorithm with a very short delivery time bounded by O((logN )2 ). Despite the aforementioned studies, an extensive analysis of the characteristics of both urban and highway VANET from a graph-theoretical perspective is not available in the literature. These characteristics include the study of connectivity, defined as the fraction of network users a node can connect to, node degree distribution and clustering coefficient in VANETs. Furthermore, the concepts of small-world and scale-free networks have not been tested on VANETs, despite the possibility of applying a pre-existent body of network research to VANETs if the networks are similar. Research such as [30] recognizes the importance of studying VANETs from a graph-theoretic approach and applying the concepts of small-world and scale-free networks. In fact, [30] claims that VANETs display smallworld and scale-free properties. However, what this work provides is an attempt to build a scale-free highway VANET through the preferential attachment growth model, and then observes some properties which in some cases may resemble a scale-free network. We argue that

Romeu Monteiro et al.

VANETs cannot be built artificially - vehicles and links are either available or not - but only partially destroyed through the removal of nodes and/or links in order to fit the above mentioned properties. Even though that might make routing simpler, it comes at the expense of creating disruptions and/or longer paths, which in turn runs contrary to the research goals and is not addressed in [30]. The correct approach is thus to study the properties of actual existing VANETs in order to create better methods for data dissemination. In this work we propose the study of VANETs from an unexplored graph-theoretical perspective in order to gain further insight into the behavior of VANETs and their similarities/differences to other types of selforganized networks already studied from this perspective. For the specific purpose of efficient message dissemination, the establishment of a mathematical model relating connectivity with node degree distribution via node density will allow protocol designers to make nodes adapt their individual behaviour through a local indicator (node degree) to suit the global state of the network (connectivity). Furthermore, the study of the clustering coefficient will inform us about the amount of existing redundancy. 3 Real life data In this work, we collect and analyze sets of data for both urban and highway VANETs in order to develop a graph-theoretic formulation of these networks. These data sets contain the positions of the vehicles in different time moments, approximating real life traffic data. All data sets and Matlab files used in this work are available online [23]. In the case of urban VANETs, we use data generated by the Cellular Automata (CA) model presented in [14], which emulates real vehicle patterns of movement in a Manhattan grid shaped urban scenario with 125 m x 125 m sized blocks. We consider that 1-hop communication can be established between vehicles at either a line-of-sight distance rLOS = 250 m or non-line-of-sight distance rN LOS = 140 m (we consider only buildings as obstacles to LOS). As for highway VANETs, we use samples measured by the Berkeley Highway Laboratory regarding highway I80 [15], which provide information about the time and speed of the vehicles passing through certain points of the highway, which we extrapolate assuming that the vehicles’ speeds are constant. For highway VANETs we consider line-of-sight at all times with a communication distance rLOS = 250 m. From this data, we look at instantaneous snapshots in both urban and highway VANETs, and study the underlying graph where nodes are vehicles and edges exist between those vehicles that

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks

Table 1: Density vs. Connectivity for Urban and Highway Scenarios

Table 2: Network Definitions and Notation

Definition Highway (25 km of length) Set of Network Nodes Density Conn. Time of Day Set of Nodes in the Same Cluster 10 vh/km2 ≈ 2% 3.9 vh/km ≈3% 01:00-03:00 as Node n 60 vh/km2 ≈ 47% 26.0 vh/km ≈ 68 % 10:00-12:00 Average Shortest Path Length 80 vh/km2 ≈ 90% 84.9 vh/km ≈ 99 % 15:00-17:00 Node Degree Average Max for Disconnected Network Min for Well Connected Network can establish 1-hop communication. For each scenario, Planar Network Vehicle Density Linear Network Vehicle Density we consider 3 connectivity regimes - high, medium and Clustering Coefficient low connectivity - and the corresponding vehicle densiConnectivity ties. For urban VANETs this means changing the numArea ber of vehicles in the CA model, while in highway VANETs of Urban Grid Length it means collecting data from different times of the day. of Total Road in Tx Range This information is summarized in Table 1. of Parallel Rd in Tx Range of Orthogonal Rd in Tx Range of Parallel Segment i of Orthogonal Segment i 4 Definitions and Notation of City Blocks of Side of Manhattan Grid In order to design analytical models for the parameters of Total (Highway) Road considered, let us first define the variables and the notaof (Highway) Rd in Tx Range Distance tion used. We start by defining the set of vehicles/nodes to Closest Intersection in the VANET as N = {n1 , . . . , n|N | }. This way, |N | Transmission (Tx) Range will represent the number of vehicles in the VANET. Line-Of-Sight We also consider the clusters within the VANET, which Non-Line-Of-Sight Probab. Allowing Rebroadcasts are the groups of vehicles connected through single- or Minimum multi-hop links. In our model we also need to consider, Probab. Supressing Rebroadcasts for each node n, the set of nodes in that node’s clusMinimum Urban (4 km2 of area) Density Conn.

ter: Mn = {mn1 , . . . , mn|Mn | }. This paper’s notation is summarized in Table 2. We also define the main concepts considered in this work:

Node degree distribution - the degree of a node is the amount of links connecting a given node to other network nodes. The node degree distribution is the frequency of occurrences of the different node degree values in a given network. Connectivity - this parameter’s goal is to quantify the availability of connecting paths between nodes. For Urban VANETs we study connectivity by studying the probability that the minimum node degree in the network is dmin . For Highway VANETs, we consider that connectivity is represented by the fraction of pairs of nodes in the network connected by at least one singlehop or multi-hop path. Clustering coefficient - the clustering coefficient of node n is defined as the fraction of pairs of nodes directly connected (i.e. through a single-hop) to node n that are directly connected to each other. The cluster-

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Notation N = {n1 , . . . , n|N | } Mn = {mn1 , . . . , mn|Mn | } L ∈ [1; +∞[ k ∈ N0 kmed k− k+ σ ∈ R+ λ ∈ R+ C ∈ [0; 1] V ∈ [0; 1] A ∈ R+ Agrid l ∈ R+ ltot lpar lort lpi l oi lbl lgr lroad ltr d ∈ R+ dci r ∈ R+ rLOS rN LOS p ∈ [0; 1] pmin s ∈ [0; 1] smin

ing coefficient of a network is the probability that, for two network nodes directly connected to a third common node, there is also a direct connection between each other.

5 VANETs: Small-World or Scale-Free? This section analyses if VANETs are small-world or scale-free networks. Such information should be taken into account when designing protocols for message dissemination, since these network structures are some of the most frequently found in different types of networks, and provide fundamental insight into how to propagate messages along the network. More specifically, smallworld networks provide short paths between any two nodes through a combination of regular short links and random large links, while scale-free networks provide short paths through their hierarchical structure. A small-world network is a network with a very small average shortest path length between its nodes compared to the number of nodes. This is objectively

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L(|N |) ∝ log(|N |)

(1)

Examples of different types of small-world networks can be found in [16],[17]. A particular subset of smallworld networks are scale-free networks [18]. The structure of such networks remains the same regardless of the observation scale [17]. Most of the nodes in these networks have very low degrees while a very small number of nodes has large degrees. A scale-free network displays a node degree distribution which is described by a power law [12] as in (2): PK (k) ∝ k −γ

(2)

where γ is a constant parameter dependent on the specific distribution and k is the degree of the node. First, we will compare VANETs with small-world networks. Thus, we need to identify if the relationship between the size of the network and its average shortest path length abides by equation (1). Second, we will compare VANETs with scale-free networks. For urban VANETs, one could expect some closeness to scale-free networks due to the possibility that nodes at intersections could work as major hubs due to their long ranges of communication in multiple directions. 5.1 Are VANETs Small World Networks? In order to determine whether VANETs are small-world networks we will focus on the Average Shortest Path Length. This parameter represents the average minimum number of hops between all possible pairs of connected nodes in a network. In this subsection we plot the results obtained with real life data and make a comparison with the best logarithmic fit according to equation (3). L(Agr ) = a · log(Agr ) + c

(3)

5.1.1 Urban VANETs We start by obtaining data using the Cellular Automata (CA) model and plot the average shortest path length against the network area Agr . It should be noted that this area is proportional to the number of nodes in the network for each density. Adding the logarithmic fit function (3), where a and c are constants optimized in order to find the best fit, we get the curves in Figure 1 with the parameters in Table 3. We observe that there are significant mismatches

Best log curves L(Area) = a*log(Area)+c 25

L − Average Shortest Path Length

quantified by having an average shortest path length L which grows proportionally to the logarithm of the number of nodes |N | of the network [11]:

20

15

dens = 10 vh/km2 dens = 60 vh/km2 dens = 80 vh/km2

10

fit − 10 vh/km2 fit − 60 vh/km2

5

fit − 80 vh/km2

0 0

2

4

6

8

10

12

14

16

Area (km2)

Fig. 1: Average shortest path length vs. vehicle density and network area in an urban scenario, and best logarithmic fits. Table 3: Parameters for Best Logarithmic Fits for Average Shortest Path Lengths in Urban VANETs Density 2

10 vh/km 60 vh/km2 80 vh/km2

a

c

R-square

SSE

0.08554 6.312 6.073

1.162 2.889 4.052

0.9594 0.9359 0.9664

0.001801 15.89 7.472

for high and medium densities; in spite of that, the fit is very good for the low density. This is illustrated by the SSE in Table 3. Both SSE and R-square measure the goodness of fit, where SSE denotes the Sum of Squares due to Error, and R-square is the square of the correlation between the data points and the corresponding values estimated by the fit. The mismatches result from the increased geographical spreading of the nodes as the network size increases through the increase in the area of the network. Without edges that work as geographical shortcuts, the ”VANET world” effectively grows and cannot be a small-world. For the low density there seems to be a good match, but actually the average shortest path length stabilizes as the area increases above a certain point. This happens because the number of nodes increases proportionally to the geographical area of the network, but the network breaks regularly into smaller groups of connected vehicles due to the sparsity of vehicles, and thus the paths in the clusters of vehicles cannot grow more than a certain threshold. This disconnectedness prevents low density networks from being small-world, since it invalidates the small-world principle that most pairs of nodes are connected through a small number of hops. Since for medium and high densities the average shortest path length does not grow with the logarithm

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks

Table 5: Parameters for Best Truncated Gaussian Fits for Node Degree Distributions in Urban VANETs

L − Average Shortest Path Length

Best log curves L(Length) = a*log(Length)+c

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dens = 3.9 vh/km dens = 26.0 vh/km

14

dens = 84.9 vh/km fit − 3.9 vh/km

12

fit − 26.0 vh/km fit − 84.9 vh/km

10

7

8

Density

a

b

c

R-square

SSE

10 vh/km2 60 vh/km2 80 vh/km2

0.5315 0.1932 0.1627

-0.174 3.728 5.098

1.74 2.924 3.467

0.9999 0.9941 0.9944

0.000023 0.000755 0.000593

6 4 2 0

0

5

10

15

20 Length (km)

25

30

35

40

Fig. 2: Average shortest path lengths vs. network area and vehicle density in a highway scenario, and best logarithmic fits. Table 4: Parameters for Best Logarithmic Fits for Average Shortest Path Lengths in Highway VANETs Density

a

c

R-square

SSE

3.9 vh/km 26.0 vh/km 84.9 vh/km

0.1046 0.8121 6.827

1.337 3.342 -9.183

0.6093 0.7131 0.9751

0.0197 0.7468 3.3489

of the number of vehicles, these networks are not smallworld networks. Lower density urban VANETs have an average shortest path length that is small and stable, but this happens through lack of paths between pairs of nodes which goes against the small-world definition. 5.1.2 Highway VANETs For highway VANETs, a similar study is performed. The fit using a logarithmic function similar to (3) with the highway length lroad instead of the network area Agr also yields poor results, as can be observed in Figure 2 and Table 4. In this case, the very high connectivity of the networks with highest density provides for an average shortest path length that increases significantly with the highway length. This happens because far away nodes have paths connecting them and these paths grow in number of hops with the physical distance between the nodes, which in turn grows with the highway length. In spite of this, the average shortest path length for the highest density does not grow with a logarithmic curve, and for lower densities there is a stabilization of this value since the network is disconnected. Since the average shortest path length in highway VANETs of high and medium densities does not grow with the logarithm of the size of the network, these highway VANETs are

not small-world networks. For highways with low vehicle densities we can see the stabilization of the lengths of the paths at the expense of connectivity. The degree of disconnectedness means the low density networks are not small-world, since there are no paths (thus no short paths) between most nodes of the network. In conclusion, we have seen in both scenarios that VANETs are not small-world networks. For such reasons, we cannot replicate methods developed for smallworld networks on VANETs, such as those by Kleinberg [13], for instance. It is necessary to develop protocols that take into account the specific network properties of VANETs.

5.2 Are VANETs Scale Free? In order to find out if VANETs are scale-free networks we will focus on the Node Degree Distribution. When studying the properties of a network graph, a node’s degree is the number of edges connecting it to other nodes. In this paper, we consider these edges to exist between any two vehicles within transmission range of each other. Thus, for VANETs, the node degree distribution represents the probability distribution of the number of vehicles within 1-hop distance from each vehicle. 5.2.1 Urban VANETs In Figure 3 we observe the node degree distributions for urban VANETs of different densities in a squared region of 4 km2 . We also see the truncated Gaussian curves that best fit the distributions. These fits are parameterized by the values given in Table 5 according to equation (4) : P (k) = a · e−(

k−b 2 c )

, k≥0

(4)

where the constants a, b and c define these truncated Gaussian distributions. Please note that this formula is only valid for node degree k ≥ 0 , in contrast with the standard Gaussian distribution. A careful inspection of the results in Figure 3 and Table 5, one can see that the truncated Gaussian curves

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Romeu Monteiro et al. Degree distribution in Urban VANET 2

dens = 10 vh/km

P(k)

0.5

Table 6: Parameters for Best Truncated Gaussian Fits for Node Degree Distributions in Highway VANETs

dens = 60 vh/km2

0.4

dens = 80 vh/km2 fit − 60 vh/km2

Density

a

b

c

R-square

SSE

0.3

fit − 80 vh/km2

3.9 vh/km 26.0 vh/km 84.9 vh/km

0.2902 0.0985 0.0296

1.604 12.73 45.20

2.036 5.591 18.58

0.9953 0.9904 0.9826

0.0009475 0.000561 0.0001861

fit − 10 vh/km2 0.2 0.1 0 0

2

4

6

8

10

12

14

k

Fig. 3: Node degree distributions for urban VANETs of different densities and corresponding best truncated Gaussian fits. Degree distribution in highway VANET 0.3 dens = 3.9 vh/km 0.25

dens = 26.0 vh/km

in scale-free networks, it is not true that the large majority of vehicles has a very small number of links, since the vehicles tend to have a moderate number of links (i.e., the probability that a node has a certain number of links does not increase at all times as the number of links decreases, as in scale-free networks). This situation provides increased path redundancy, but it takes away advantages of scale-free networks such as shorter paths and easier routing optimization.

dens = 84.9 vh/km

0.2 P(k)

fit − 3.9 vh/km 0.15

fit − 26.0 vh/km

5.3 Summary

fit − 84.9 vh/km 0.1 0.05 0 0

10

20

30

40

50

60

70

k

Fig. 4: Node degree distributions of highway VANETs with different vehicle densities and their respective truncated Gaussian fits.

fit very well with the data for urban VANETs. We also computed the best fits for other famous distributions (including exponential, power-law, and Rayleigh) but none showed to fit better than the truncated Gaussian. Since the distributions are approximately Gaussian and do not follow a power law, we conclude that urban VANETs are not scale-free. 5.2.2 Highway VANETs

In Subsections 5.1 and 5.2 we saw that VANETs are neither small-world nor scale-free since their average shortest path lengths do not grow with the logarithm of the number of nodes nor do their node degree distributions follow power-law distributions. This implies that it is not possible to use the body of knowledge developed for small-word and scale-free networks to solve VANET problems. In spite of this, we will use the information on node degree distribution to build appropriate message dissemination protocols, since this information allows us to bridge local information (node degree) with global information (connectivity) through the parameter of vehicle density. The relationship between vehicle density and network connectivity is explored in Subsection 6.1.

6 Network Parameters

Figure 4 depicts the node degree distributions for the To complement the study of small-world and scale-free highway scenario together with the truncated Gaussian networks, we study several parameters important for curves that fit best the distributions. Other famous disnetwork graph analysis in VANETs: connectivity, node tributions didn’t show best fits better than the trundegree distribution and clustering coefficient. Furthercated Gaussian. These fits are parameterized according more, we present analytical models for these parameters to (4) by the values in Table 6. and compare them with results obtained from real life data. The goals of this study are: 1) to relate global conAgain, the fits based on a truncated Gaussian model work very well, and also demonstrate that highway VANETsnectivity with the local node degree, through the study are not scale-free. We had hypothesized that urban VANETsof each of these parameters as functions of vehicle density; 2) to understand how vehicles in VANETs group might be scale-free networks due to hub nodes at inthemselves into communities of neighbors, through the tersections. While it is true that in urban VANETs a clustering coefficient. The results obtained will allow us small number of nodes has a large number of links, as

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks Connectivity vs Vehice Density

Probability of Minimum Node Degree vs. Density 1

1 Analytical P(dmin>=1) Analytical P(d

min

Area = 4km2

>=2)

0.8

0.6

Simulated P(dmin>=1)

0.4

Simulated P(dmin>=2)

Connectivity

Probabilty

0.8

0.2 0

9

0

20

40

60

80

0.6 0.4 0.2

2

Density (vh/km )

Fig. 5: Probability of having a Urban VANET with minimum node degree dmin for different vehicle densities. to develop ideas on how to generate desired global behaviors from local interactions, as well as on how to optimize the redundancy of the dissemination of messages between neighboring vehicles. Note that the definitions for connectivity and clustering coefficient have been presented in Section 4.

6.1 Connectivity 6.1.1 Urban VANETs In order to analyze the connectivity of Urban VANETs, we will use the metric of Probability of Minimum Node Degree, measuring the probability that all nodes in the VANET are connected to at least other dmin nodes. We choose this metric because it is used frequently to evaluate the connectivity of 2D network graphs, for its simplicity and relation with the probability of kconnectivity. As has been proven in [9], the probability of k-connectivity for a homogeneous ad-hoc network is similar to the probability of minimum node degree k when this probability is almost 1. Urban VANETs are not homogeneous networks, thus this approximation does not hold for their case. For that reason, we will limit our analysis to the probability of minimum node degree. First, we present our analytical model for the probability that a network’s minimum node degree dmin is at least n0 . We calculate the probability that all |N | = σA nodes in the network have more than n0 − 1 links using the probabilities from the network’s node degree distribution PK (k) as calculated in Section 6.2.1 and in (16), assuming independence between the degrees of the nodes:

P (dmin ≥ n0 ) = [1 −

nX 0 −1 k=0

PK (k)]σA

(5)

0 0

20

40 60 Density (vh/km2)

80

Fig. 6: Connectivity vs. vehicle density for an urban scenario of 2 km x 2 km, with 95% confidence intervals. Afterwards, we compare these with the values obtained for the Urban VANETs simulated with the CA model for a standard Manhattan grid with 4 km2 . Since the border effect can have a very strong impact in the minimum node degree of a network, we do not consider the node degree of nodes less than rLOS from the border. Figure 5 shows the analytical and simulated probabilities of minimum node degree for minimal degrees of 1 and 2. As expected, these probabilities increase as the vehicle density gets higher. Furthermore, the trace based simulation values validate our analytical model. Through simulation with the CA model, we can obtain the connectivity in terms of the average fraction of network nodes each node will be able to connect with at each point in time. This information complements the results on the nodes with less links provided by the probabilities of minimum node degree. In Figure 6, we observe that, for a density lower than 40 vh/km2 , the connectivity is generally smaller than 10%, while from 80 vh/km2 upwards, it will be larger than 90%. Furthermore, there is a steep increase between those points. We can also observe the relationship between vehicle density and connectivity for urban VANETs of a standard area. In Section 7, we will use the information in Figure 6 to establish the densities which correspond to regions of low, intermediate, and high connectivity. 6.1.2 Highway VANETs For highway VANETs we develop a model to estimate the connectivity as a function of the linear vehicle density λ and the length lroad of the highway stretch, which we will then compare with real life data. First, we assume the probability of having |N | vehicles in a section of road with length lroad can be approximated by a Poisson process. In a highway environment

10

Romeu Monteiro et al.

we believe that will generally be the case, as there are no traffic lights and vehicles usually do not interfere with each other’s movements, except for rare moments of congestion. (λlroad )|N | e−λlroad P|N | (|N |, λ, lroad ) = |N |!

(6)

< |M | > V (|N |, λ, lroad ) = = |N | − 1 |N |

1 1 X · < |Mi | > (7) |N | − 1 |N | i=1

where: < |M | > is the average number of vehicles a vehicle in the set of |N | consecutive vehicles can connect to; i is the index of the vehicle from 1 to |N |. Now, the average number < |Mi | > of vehicles that a vehicle in the #i position can connect to is given by the average of the number |Mi | of vehicles in the chain of consecutively connected vehicles, where vehicle i is included without counting vehicle i:

|N | |N |−1 X X 1 [k · |N |(|N | − 1) i=1 k=0

min(i−1,k)

X

{g(j, i − 1)·

j=k−min(|N |−i,k)

(10)

with, g(m, n) =

( (1 − e−λrLOS )m e−λrLOS , −λrLOS m

(1 − e

) ,

0≤m 2rLOS (20)

(ltr λ)k −ltr λ ·e k!

(21)

Replacing (20) and (21) in (18), one gets: PK (k) = Z 2rLOS (ltr λ)k −ltr λ 2 e · dltr + k! l road rLOS 2rLOS (2rLOS λ)k −2rLOS λ )( e )= lroad k! 2λk ∂ e−2rLOS λ ∂ e−rLOS λ [( )k −( )k ]+ lroad (k!) ∂(−λ) −λ ∂(−λ) −λ 2rLOS (2rLOS λ)k −2rLOS λ (1 − )( e ) (22) lroad k!

(1 −

which makes it possible to compute PK (k) from the inputs λ, lroad and rLOS . In Figure 11 one can see the statistics obtained from the expanded data from highway I-80, for a 20 km long highway section, regarding the node degree distribution

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks

Assuming a uniform probability distribution of the vehicles’ positioning throughout the open area, one can easily compute the probabilistic distribution of the distance d to the common vehicle:

Degree distribution in highway VANET 0.3

dens = 3.9 vh/km fit − 3.9 vh/km

0.25

13

dens = 26.0 vh/km fit − 26.0 vh/km

P(k)

0.2

dens = 84.9 vh/km fit − 84.9 vh/km

0.15

FD (d) =

πd2 , for 0 ≤ d ≤ rLOS 2 πrLOS

(23)

fD (d) =

2d d[FD (d)] = 2 , for 0 ≤ d ≤ rLOS dd rLOS

(24)

analytical = 3.9 vh/km analytical = 26.0 vh/km analytical = 84.9 vh/km

0.1

0.05

0 0

10

20

30

40

50

60

70

k

Fig. 11: Node degree distributions for highway VANETs including 95% confidence intervals and comparison with analytical values.

and its comparison with the results from the analytical model. Here one can also observe that there is a very good match for the two lowest densities, and some mismatch for the highest vehicle density. The latter is due to the fact that, in situations of heavy traffic on highways, the traffic pattern changes severely with a strong impact on inter-vehicle distances [20]. This will make the vehicles start to group with each other and lose part of the randomness in the inter-vehicular distances, thus increasing the number of vehicles in each vehicle’s surroundings. In spite of this, with this model we can establish a very accurate relationship between the node degree distribution and vehicle density (and, thus, connectivity) for low and medium density highway VANETs, and an approximate one for high density highway VANETs. This way, vehicles can use local information to estimate the global connectivity and run protocols optimized according to the connectivity of the network.

6.3 Clustering coefficient 6.3.1 Urban VANETs So as to estimate the clustering coefficient of urban networks, let us consider a vehicle positioned in an open area and connected to other vehicles located less than rLOS meters away. We assume an infinite area and thus no border effect. The clustering coefficient is the probability that 2 vehicles connected to a common vehicle are also connected among themselves. Therefore, for 2 vehicles which are less than rLOS meters away from a common vehicle, the clustering coefficient is the probability that they are separated by less than rLOS meters.

The probability of these 2 vehicles being connected is given by the average fraction of the area common to the communication range of one of the vehicles and the communication range of the common vehicle. This common area is given by: I(d) = 2rLOS cos−1 (

d 2rLOS

)−

q d 2 4rLOS − d2 , 2 for 0 ≤ d ≤ rLOS

(25)

To get the clustering coefficient C, we weigh the common area as a fraction of the total area within rLOS meters with the probability distribution of the distance between one of the vehicles and the common vehicle: Z rLOS I(x) C= fD (x) · 2 dx = πrLOS 0 Z rLOS x x cos−1 ( )dx 2rLOS 0 Z rLOS q 1 2 − x2 dx = 0.5865 (26) − 2 x2 4rLOS πrLOS 0 Analyzing the data from the CA model in Figure 12 and the theoretical value, we observe that they are similar, as the clustering coefficient is around 0.53 while the theoretical value is 0.5865. Lower densities seem to exhibit a lower clustering coefficient than higher densities. Such deviations from the theoretical value and larger confidence intervals are due to the limited number of vehicles, particularly in cases of smaller areas and lower vehicle densities. In VANETs, the clustering coefficient estimates the probability that 2 vehicles within communication range of a common vehicle are also within each other’s communication range. For a clustering coefficient close to 0.5 this means that, if vehicle A has received a specific broadcast message from vehicle B (1-hop communication), there is a 50% chance that the vehicles within communication range of vehicle A have received the same message from vehicle B. This way, if vehicle A rebroadcasts immediately, an average of more than 50% of its neighbors will get a redundant message (these neighbors might have already received the same message from a source other than vehicle A and B). Note that this only depends on the positioning of A and

14

Romeu Monteiro et al. Clustering Coefficient vs Vehicle Density

C - Clustering Coefficient

Clustering Coefficient vs Vehicle Density

C - Clustering Coefficient

1

0.8

0.6 Area = 1km2

0.4

Area = 4km2 Area = 9km2

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Fig. 12: Clustering coefficient vs. network area and vehicle density in an urban scenario with 95% confidence intervals.

B and their communication ranges compared to each other and other vehicles, i.e. the distribution of the vehicles in space, not density. 6.3.2 Highway VANETs Performing derivations for a 1D case similar to those made for the 2D urban scenario, we get an estimate for the average clustering coefficient in highway VANETs: FD (d) =

2d d = , for 0 ≤ d ≤ rLOS 2rLOS rLOS

(27)

fD (d) =

1 d[FD (d)] = , for 0 ≤ d ≤ rLOS dd rLOS

(28)

I(d) = 2rLOS − d, for 0 ≤ d ≤ rLOS

0

0.6

0

0

Z

0.8

0

Area = 16km 2 Analytical C = 0.5865

C=

1

rLOS

I(x) fD (x) · dx = 2rLOS Z rLOS 1 2rLOS − x · dx = 0.75 r 2rLOS LOS 0

(29)

(30)

Comparing the values obtained for the data from highway I-80 in Figure 13 and our theoretical value of 0.75, we observe a very good match. From the theoretical model, we observe that there is no dependency on any parameter except for the 1D vs. 2D geometry.

7 Applications 7.1 General Applications From the study on the graph properties of VANETs in Section 6, we propose new methods for improving

Fig. 13: Clustering coefficient vs. highway length and vehicle density in a highway scenario with 95% confidence intervals.

VANET dissemination protocols. In particular, based on periodic beaconing, a vehicle can correlate overall vehicle density with its node degree. Since the vehicle can estimate the number of neighbors at each moment in time, it can also estimate the node degree distribution, assuming that the number of nodes with a degree k is proportional to the time the node spends with k neighbors. With this information, the vehicle can either adopt different behaviors at each point in time, as it believes it is one of the nodes with largest or smallest degree in the network, or it can simply compute the vehicle density corresponding to its average node degree or node degree distribution, as studied in Subsection 6.2. Then, by considering the relationship between vehicle density and the connectivity of the network, which can be approximated using the results in Subsection 6.1, the nodes are aware of the global network connectivity and can behave accordingly. In practice, this means that a node that obtains a small average node degree will estimate a low connectivity, and thus might change its behavior in order to increase the number of broadcasted messages to increase reachability. The clustering coefficient as studied in Subsection 6.3 describes how vehicles are grouped into communities. A higher clustering coefficient will increase the number of common neighbors between two vehicles broadcasting consecutively. Thus, a higher clustering coefficient should force the vehicle to reduce the number of broadcast messages and to find additional information to better select which nodes will rebroadcast. The results obtained in Subsection 6.3 provide information on redundancy (although averaged throughout the network) which relies only on the geometry of the network. It is interesting to see how the results of the network property analysis presented in this paper can be used to improve and/or optimize VANET routing protocols. To exemplify this

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks IDLE New message arrives NO

NO

In ROI? YES Is assigned the SCF task?

Disconnected regime YES In ROI?

Rebroadcast

YES

NO With prob. 1-s

S With prob. s

With prob. P 1-p Receives With redudant prob. Compute wait time message p With prob. 1-p

P

Received hello message from an uninformed neighbor

Wait time expires With prob. p

15

gorithm allows one to estimate the upper-bounds for both average received distance and reachability. Observe that the UV-CAST performance is very close to these boundaries. In spite of this, the overhead in terms of average number of messages transmitted per vehicle for UV-CAST is similar to that of the flooding algorithm, whereas one would expect a reduction in the number of messages transmitted per vehicle as the density increases and more vehicles can be informed with each transmitted message.

Wait for new Uninformed neighbors

Rebroadcast

7.2.1 Proposal to improve the UV-CAST protocol

Well-connected regime

Fig. 14: Operational flowchart for the UV-CAST protocol with additional P and S mechanisms in gold. (Abbrv: ROI-Region of Interest, SCF-Store-carry-forward mechanism) [6].

concept, an urban broadcast routing protocol, known as UV-CAST, is used as an illustration.

7.2 Improvement of the UV-CAST protocol The Urban Vehicular Broadcast (UV-CAST) [6] protocol is presented for message dissemination in urban scenarios, with the goal of delivering safety messages to all vehicles inside a certain Region of Interest (ROI). This protocol addresses problems both in well-connected and sparse networks (i.e., broadcast storm and disconnected network problems). As shown in Figure 14, a vehicle may operate in one of two modes: well-connected or disconnected. In the well-connected regime, a broadcast suppression technique is implemented: based on its distance from the previous relay and location (e.g., whether it is at the intersection), a vehicle computes the waiting time and only rebroadcasts the message if no redundant message is received before the timer expires. Vehicles which are not in a well-connected regime may be assigned the Store-Carry-Forward (SCF) task. Additional details can be found in [6]. This picture also shows in gold the P and S mechanisms (that we will introduce later on in the paper) and their influence on the decision flow. While the UV-CAST protocol is shown to yield very good results, we believe that there is still room for improvement. Figure 15 shows the performance (through the indicators of average received distance and reachability) as well as the overhead (through the number of average transmitted/received messages per vehicle) of different broadcasting algorithms for a simulated Manhattan grid scenario. The flooding al-

We set out to improve the UV-CAST protocol as a demonstration of how network graph properties and the analytical model relating them can be used to design better protocols. The core of our approach lies in adopting local node behaviors to suit global network connectivity by directly measuring node degrees and then relating those observations with network connectivity through the analytical model. Furthermore, we use the observations regarding the clustering coefficient as indicators of redundancy, thus informing our definition of boundaries for allowing and suppressing message retransmission. Considering the performance of UV-CAST without our modifications, our idea for improving UV-CAST is to add two mechanisms that are activated in networks of very high and very low connectivity in order to reduce overhead while keeping maximum performance quality. The main challenge is that connectivity is a global property not measurable by each node. However, nodes have access to local information such as node degree. This is where our analytical model comes into action by relating connectivity with vehicular density, and vehicular density with node degree. This will allow for an adaptation of individual behaviors in a way that is favorable to the larger network state. We will introduce the ”p” mechanism, which suppresses the number of transmissions in higly connected networks by a factor of p, and the ”s” mechanism which allows for more transmissions in disconnected networks by a factor of s. We start by defining a disconnected network as one with less than 15% of connectivity, while a well-connected network has more than 50% of connectivity. We now need to obtain the corresponding average node degree values. The relationship between network connectivity and vehicle density can be obtained from Subsection 6.1.1, while the subsequent relationship between vehicle density and node degree is described in 6.2.1. The average node degree will correspond to approximately

We call this the ”s” mechanism. In the next section we test the usefulness of these mechanisms through simulation and compare them with the performance of the standard UV-CAST and a flooding algorithm.

Average number Average received distance (m) of msg received

We call this the ”p” mechanism. This way, each time the waiting time expires, the message is rebroadcasted with probability p; furthermore, when a vehicle fulfills the requirements to become an SCF agent, it will become such an agent with probability p. From the analysis of the clustering coefficient in urban VANETs in Subsection 6.3, we expect that on average a vehicle which receives a rebroadcasted message will also have received the broadcast that preceded with a 50% chance. Since this might happen with several neighbors, as broadcasts might follow several paths in parallel, we select a bound which is lower than 50%, so that the suppression of broadcasts is aggressive for larger densities. Thus, the variable p is lower-bounded by pmin which we set to pmin = 0.25. In the case of low density networks, where the decision whether or not to rebroadcast has very strong effects, we will show that the ”p” mechanism introduces a slight loss in reachability, which is an undesirable outcome (see Figure 15). Thus, to compensate for this loss, we increase the probability of retransmission. Therefore, we propose that a vehicle in the well-connected regime, despite receiving a redundant message, still rebroadcasts (after the waiting time expires) with probability 1 − s. This rebroadcast probability should be larger as the vehicle density decreases while being limited by a maximum of 75% probability (since, even though rebroadcasts are crucial at such low densities, for 50% of the vehicles on average, the message is likely to be redundant, according to the average clustering coefficient). We design this scheme such that this probability decreases for higher densities and is activated only for nodes in disconnected regions. We set smin = 0.25 to limit the maximum rebroadcast probability to 75%. ( smin + (1 − smin ) kkmed , if kmed < k− − s= (32) 1, otherwise

Average number of msg transmitted

k− = 3 (at 15% connectivity) and k+ = 4 (at 50% connectivity). In order to reduce the amount of messages exchanged in highly dense networks, we propose a mechanism to reduce the number of Store-carry-forward (SCF) agents (in the disconnected regime) and number of message rebroadcasts (in the well-connected regime). Note that, according to (31), the value of p decreases with the vehicle density: ( 1−pmin pmin + kmed −k+ +1 , if kmed > k+ p= (31) 1, otherwise

Romeu Monteiro et al.

Reachability

16 1 0.9 0.8 20

40

500

60

Density (veh/km2)

80

100

80

100

80

100

80

100

400 300 20

40

60 2

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10 5 0 20

40

60 2

Density (veh/km ) 0.9 0.8 0.7 20

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Density (veh/km ) Flooding UVCast UVCast with p only UVCast with p and s

Fig. 15: Comparison of the results regarding performance and overhead of the flooding algorithm, UVCAST and UV-CAST with the new mechanisms.

7.2.2 Experiments & Results The proposed mechanisms to improve the performance of the UV-CAST protocol are tested in this section. For comparison purposes, we also test the standard UVCAST protocol and a flooding algorithm. The simulation environment is similar to that reported in [6]: a 1 km x 1 km Region Of Interest is considered around an accident scene in a Manhattan grid scenario, and the simulation runs for 120 seconds after the moment of the accident. The source of the message is the accident scene, in the center, and the source broadcasts 1 single time. Note that parameter kmed is calculated through an exponential moving average of the vehicle’s node degree. In Figure 15, we observe the results for different combinations of these mechanisms, as they are evaluated using four different metrics: reachability - the fraction of vehicles in the ROI that are informed by

A Graph Structure Approach to Improving Message Dissemination in Vehicular Networks

the end of the simulation; average received distance the average distance to the accident scene when the vehicles receive the warning message; average number of received messages per vehicle; and average number of transmitted messages per vehicle. First, we look at the metrics which measure how fast and how many vehicles are informed. These metrics are represented in the first and second plots in Figure 15. Observe that these results are very similar in either the UV-CAST protocol, the flooding algorithm and UV-CAST with our ”p” and ”s” mechanisms. This is the desired outcome, as all algorithms perform very closely to the upper bounds shown by the flooding algorithm. Then, in the third and fourth plots we observe the overhead in terms of average number of received and transmitted messages per vehicle. As for the number of received messages, the standard and extended UV-CAST show a similar performance, both with stable rates of received messages as the density increases, whereas the flooding algorithm seems to linearly increase the rate with the density. Regarding the rate of messages transmitted per vehicle, observe that, while both UV-CAST and the flooding algorithm increase and then stabilize their rates with increasing densities, the addition of our mechanisms to UV-CAST creates a very significant reduction in this overhead measurement as the density increases, thus alleviating the congestion in highly concentrated networks. It should be noted that UV-CAST with ”p” and ”s” is able to reduce the number of messages transmitted while keeping the number of messages received by helping assigning the rebroadcasts to vehicles which can inform more neighbors. These results clearly show that the proposed ”p” and ”s” mechanisms represent significant improvements, as they decrease the overhead while maintaining the maximum performance quality.

17

mechanisms through extensive simulations, which resulted in strong reductions in the network overhead while maintaining the excellent performance in terms of reachability and average received distance. Our results have proven that graph properties can and should be applied to VANETs, as it provides further insight into how to design and improve protocols specific for VANETs. As for future research, it would be important to find a way to include mobility information in the proposed approach. Realism could also be improved by using probabilistic models for the links between nodes as a function of distance, as well as different penetration rates. Furthermore, there might still be room for reduction of overhead in message dissemination. Acknowledgements The authors wish to thank Andre Cardote for providing us with semi-processed data and useful code for the expansion of the data collected by the Berkeley Highway Lab on the traffic in highway I-80. This work was funded in part by the Portuguese Foundation for Science and Technology under the Carnegie Mellon — Portugal program (grant SFRH/BD/51633/2011).

References

1. A. Cardote, S. Sargento, and P. Steenkiste, ”On the connection availability between relay nodes in a vanet,” in Proceedings of the IEEE Globecom 2010, Miami, Florida, USA, 2010. 2. N. Wisitpongphan, O. Tonguz, F. Bai, P. Mudalige, and V. Sadekar, ”On the Routing Problem in Disconnected Vehicular Networks”, in INFOCOM Minisymposia 2007, Anchorage, Alaska, USA, May 2007. 3. W. Viriyasitavat, F. Bai, and O. K. Tonguz, ”Dynamics of Urban Connectivity in Urban Vehicular Networks,” in IEEE Journal On Selected Areas in Communications, vol. 29, No. 3, March 2011. 4. W. Viriyasitavat, O.K. Tonguz and F. Bai ”Network Con8 Conclusion nectivity of VANETs in Urban Areas,” in SECON’09 Proceedings of the 6th Annual IEEE Communications Society In this work, we have studied urban and highway VANETs Conference on Sensor, Mesh and Ad-Hoc Communications and Networks, pp. 646-654, 2009. from a network graph structure perspective by focus5. M. Kas, S. Appala, C. Wang, K.M. Carley, L.R. Carley, ing on a set of parameters: connectivity, node degree and O.K. Tonguz, ”What if wireless routers were social? distribution and clustering coefficient. In addition to Approaching wireless mesh network from a social network describing a set of VANETs through these indicators, perspective,” in IEEE Wireless Communications, Vol. 19, Issue 6, December 2012 we have also designed and evaluated models of these 6. W. Viriyasitavat, F. Bai, and O. Tonguz, ”UV-CAST: An indicators for VANETs of different types, sizes, and urban vehicular broadcast protocol,” in Proceedings of the densities. We have shown that it is possible to bridge IEEE Vehicular Networking Conference (VNC), Dec. 2010, local and global connectivity properties, so that inpp. 25 32. dividual behavior generates positive outcomes for the 7. R. Monteiro, W. Viriyasitavat, S. Sargento, and O.K. Tonguz, ”Improving VANET protocols via network sciglobal network. Furthermore, we combined this with ence,” in IEEE Vehicular Networking Conference (VNC), a clustering coefficient dependent on geometry so as to November 2012. work with minimal information about the node’s neigh8. Q. Ling, and Z. Tian, ”Minimum Node Degree and kbors, and we designed mechanisms to improve an existConnectivity of a Wireless Multihop Network in Bounded Area” in IEEE GLOBECOM 2007 Proceedings, 2007. ing VANET broadcasting protocol. We validated these

18 9. M. Penrose, ”On k-connectivity for a geometric random graph” in Random Structures and Algorithms. 15:145-164, 1999. 10. A. Ghasemi, and S. Nader-Esfahani, ”Exact Probability of Connectivity in One-Dimensional Ad-Hoc Wireless Networks” IEEE Communications Letters, Vol. 10, No. 4, April 2006. 11. D. J. Watts & Steven H. Strotgatz, ”Collective dynamics of ’small-world’ networks,” Nature, vol. 393, June 1998. 12. A. Barabasi and R. Albert, ”Emergence of Scaling in Random Networks,” Science, vol. 286, October 1999. 13. J. M. Kleinberg, ”Navigation in a small world,” in Nature, Vol. 406 (24 August 2000). 14. O. K. Tonguz, W. Viriyasitavat, and F. Bai. ”Modeling urban traffic: a cellular automata approach,” IEEE Communications Magazine, Topics in Automotive Networking, 47(5):142-150, May 2009. 15. Berkeley Highway Lab (BHL), http://sprocket.ccit. berkeley.edu/bhl. 16. L. A. N. Amaral, A. Scala, M. Barthlmy, and H. E. Stanley, ”Classes of Small World Networks,” in Proc. of the National Academy of Sciences, Vol. 97, No. 21. (10 October 2000), pp. 11149-11152. 17. X. F. Wang and G. Chen, ”Complex Networks: SmallWorld, Scale-Free and Beyond,” in IEEE Circuits and Systems Magazine, First Quarter 2003. 18. S. H. Strotgatz, ”Exploring complex networks,” Nature, Vol. 410 (8 March 2010). 19. N. Wisitpongphan, F. Bai, P. Mudalige, V. Sadekar, and O. Tonguz. ”Routing in Sparse Vehicular Ad-Hoc Networks,” IEEE Journal on Selected Areas in Communications, 25(8):1538-1556, Oct. 2007. 20. O. Tonguz, N. Wisitpongphan, F. Bai, P. Mudalige, and V. Sadekar, ”Broadcasting in VANET,” in INFOCOM MOVE Workshop 2007, Anchorage, Alaska, USA, May 2007. 21. P. Costa, D. Frey, M. Migliavacca, and L. Mottola. ”Towards lightweight information dissemination in intervehicular networks,” in ACM workshop on Vehicular adhoc networks (VANET), pages 2029, 2006. 22. F. J. Ros, P. M. Ruiz, and I. Stojmenovic. ”Reliable and Efficient Broadcasting in Vehicular Ad-Hoc Networks,” in IEEE Vehicular Technology Conference (VTC), April 2009. 23. R. Monteiro, http://nap.av.it.pt/rmonteiro 24. Y. Li, D. Jin, Z. Wang, L. Zeng, and S. Chen, ”Exponential and Power Law Distribution of Contact Duration in Urban Vehicular Ad-Hoc Networks,” in IEEE Signal Processing Letters, Vol. 20, No. 1, January 2013. 25. S. Busanelli, G. Ferrari, and S. Panichpapiboon, ”Efficient Broadcasting in IEEE 802.11 Networks through Irresponsible Forwarding,” in Proceedings of IEEE ”GLOBECOM” 2009. 26. S. Panichpapiboon, and L. Cheng, ”Irresponsible forwarding under real inter-vehicle spacing distribution,” IEEE Trans. Veh. Technol. 62 (2013) 2264-2272. 27. A. Mostafa, A.M. Vegni, and D.P. Agrawal, ”A probabilistic routing by using multi-hop retransmission forecast with packet collisionaware constraints in vehicular networks,” in Ad Hoc Networks. 14 (2014), pp: 118-129. 28. Z. Yan, H. Jiang, Z. Shen, Y. Change, and L. Huang,”kconnectivity analysis of one-dimensional linear VANETs” in IEEE Trans. Vehicular Technology, vol. 61, no. 1, 2012, pp: 426-433. 29. Y. Zhang, H. Zhang, W. Sun, and Cheng Pan, ”Connectivity analysis for vehicular ad hoc network based on the Exponential Random Geometric Graphs,” in Intelligent Vehicles Symposium Proceedings, 2014 IEEE, pp.993-998, 8-11 June 2014.

Romeu Monteiro et al. 30. H. Zhang, and J. Li, ”Topology analysis of VANET based on complex network” LISS 2014. Springer Berlin Heidelberg, 2015. pp. 1143-1148. 31. Y. Bi, L. Cai, X. Shen, and H. Zhao, ”Efficient and Reliable Broadcast in Intervehicle Communication Networks: A Cross-Layer Approach” in IEEE Transactions on Vehicular Technology, Vol. 59, No. 5, June 2010, pp. 2404-2417. 32. L. Bononi, and M. Felice, ”A Cross Layered MAC and Clustering Scheme for Efficient Broadcast in VANETs” in IEEE International Conference on Mobile Adhoc and Sensor Systems, 2007, pp 1-8. 33. J. Sahoo, E. Wu, P. Sahu, and M. Gerla, ”BinaryPartition-Assisted MAC-Layer Broadcast for Emergency Message Dissemination in VANETs” in IEEE Transactions on Intelligent Transportation Systems, Vol. 2, No. 3, September 2011, pp. 757-770.