Performance evaluation of link metrics in vehicle networks: a study from the Cologne case

Performance evaluation of lin metrics in vehicle networs: a study from the Cologne case Jun Zhang Telecom Paristech, University of Paris-Saclay jun.zhang@telecomparistech.fr Meng Ying Ren Telecom Paristech, University of Paris-Saclay University of Technology of Troyes mengying.ren@telecomparistech.fr Houda Labiod Telecom Paristech, University of Paris-Saclay labiod@telecomparistech.fr ABSTRACT In vehicle ad hoc networs, the lin duration is an important concept for clustering and dissemination. Many lin metrics are proposed to predict it based on the vehicles velocities and distance between vehicles. However, there is a lac of comparison of these metrics under the same framewor. In this paper, we compare several common adopted lin metrics, LLT (lin life time), (spatial locality similarity), and (similarity function), in the performance of lin duration prediction, according to the vehicular mobility trace of the city of Cologne, Germany. We find that i) the impact of velocity prediction has different impact on different lin metrics; ii) and perform well in selecting long-lived lins; iv) LLT performs well in filtering out short-lived lins. We also show that, by combining and LLT intelligently, it is possible to create a lin metric that performs well in both selecting long-lived lins and filtering out short-lived lins. Keywords lin metric, vehicle networ 1. INTRODUCTION Due to the high mobility and scalability, traditional routing schemes for wireless networs do not perform well in vehicle ad hoc networs (VANETs). Instead, data forwarding/dissemination is suggested to replace routing in VANETs to reduce the protocol overhead, and prevent frequent lin breas. To scale down the complexity in data forwarding, clustering is one promising solution. The connections between clustering head (CH) and clustering members (CMs) remain stable in a certain period, so that data forwarding only needs to focus on the lin breas between CHs. The ey component of clustering algorithms in VANETs is the design of the lin metric. The lin metric should Permission to mae digital or hard copies of all or part of this wor for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this wor owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. c 16 ACM. ISBN 978-1-43-2138-9. DOI:1.114/123 reveal how long the connection between two vehicles will last. Because of randomness of the vehicles mobility, the lin duration between vehicles cannot be nown in advance. Therefore, a lot of schemes utilize current status of vehicles to predict the future, while distance between vehicles and difference of velocities of two vehicles are the two most adopted parameters. There are different ways to combine distance and difference of velocities to form the metric. The lin life time (LLT) [9] [11] defines the metric as the ratio between the distance that one vehicle goes out of the transmission range of anther one and the difference of velocity. The spatial locality similarity () [4] defines the metric as a normalized value, such that the distance and the difference of velocities play similar roles. The similar function () suggested by [2] used the sum of the current distance and predicted future distance to indicate the lin duration between vehicle pairs. We would lie to figure out what ind of combination of these two parameters will lead to a more accurate prediction of lin duration. To reach this goal, we study the performance of these lin metrics according to the vehicular mobility trace of the city of Cologne, Germany [1]. We compare these metrics in three aspects: correlation with the actual lin duration, the performance of the top lins according to the lin metrics, and the performance of the last lins according to the lin metrics. The paper below is organized as follows. In the Section 2 we review the related wors on the lin metrics based on distance and difference of velocities. In the Section 3 we compare the performance of LLT,,, and compare them with the distance based, and difference of velocity based benchmar approaches. In the Section 4 we propose a new lin metric based on the analysis of shortcoming and benefit of previous lin metrics. In the Section we conclude the paper. 2. RELATED WORK In the literature, there are many lin metrics proposed to predict the lin quality of vehicle pairs in vehicle networs. Because the distance between vehicles is the dominate factor in determining the lin quality, these lin metrics are required to reveal the length of lin duration, i.e., how long two vehicles are within a certain distance to each other. Intuitively, the lin between two vehicles which are at a large distance to each other, and have a large difference in velocity are expected to have a short lin duration, and that between

two vehicles which are close to each other, and have similar velocity are expected to have a long one. Hence, the distance between two vehicles and velocity of each vehicles become the fundamental parameters in designing lin metrics. In the following, we will review several typical lin metrics that are based on distance and velocity. For the purpose of coherence, in Table 1 we give all necessary variables for the definition of following lin metrics. Table 1: Variables used for the definition of different lin metrics Variables Meaning l i = (x i,y i) vehicle i s location v i vehicle i s velocity vector θ i vehicle i s direction in the polar coordinate system z i,j,z = {l,x,v} z i z j z,z {l,x,v} Norm of z r maximal transmission range maximal velocity (scalar) v max 2.1 Lin life time Lin life time (LLT) utilizes the predicted lin duration as the lin metric. The wor in [9] gave the equations to compute LLT, given the current locations and velocities of two vehicles. Let v i and v j be the velocities of two vehicles i and j, the direction of velocities of these two vehicles in the polar coordinator system are θ i and θ j respectively. The coordinations of these two vehicles are (x i,y i) and (x j,y j) respectively. Let a = v i cos(θ i) v j cos(θ j) b = x i x j c = v i sin(θ i) v j sin(θ j) d = y i y j. The lin life time, that is, the time duration that these two vehicles are within the distance r is then computed as LLT ij = (ab+cd)+ (a 2 +c 2 )r 2 (ad bc) 2 a 2 +c 2. (1) When the two vehicles move in the same or opposite direction, the above equation can be simplified as LLT ij = as suggested in [11]. vij lij + vij r ( v ij) 2, (2) 2.2 Spatial locality similarity The wor in [4] proposed to use spatial locality similarity () as one part of lin metric. The intuition is to use normalized ratio of distance and difference of velocities to obtain a normalized value that indicates how long the lin can last. A higher indicates two vehicles moves in a similar manner and stays in the similar region, which implies a longer lin duration. Formally, spatial locality similarity is defined as 1 ij =. (3) 1+( l ij ) r 2 +( v ij 2v max ) 2 2.3 Similarity function In [7], [2] an affinity propagation based clustering algorithm is proposed to reduce the overhead in establishing clusters. The lin metric suggested in [2] is called similarity function (). It uses the sum of the current distance and predicted future distance at t seconds later between two vehicles to predicate the closeness of two vehicles in the future. Formally, it is defined as ij = l ij (l i +t v i) (l j +t v j). (4) 3. PERFOANCE COMPARISON OF LINK METRICS In this section, we compare the performance of different lin metrics according to the vehicle trace file from TAPAS- Cologne project [1]. The setting of scenarios, and lins metrics in comparison are described in Section 3.1, 3.2 respectively/ An analysis of the lin duration distribution is conducted in Section 3.3. After that, we evaluate lin metrics in the following aspects: 1. correlation between lin metrics and actual lin duration (Section 3.4), 2. average lin duration of the top and bottom lins selected by lin metrics (Section 3.). 3.1 Scenario settings We use the vehicle mobility trace from the TAPASCologne project [1] for the purpose of the analysis of lin metrics. This trace file records more than 7 individual car trips in the city of Cologne covers a region of square ilometers. According to the suggestion from their web site [1], we extract the the location and velocity of vehicles between 6am and8am. Wesubtracttypicalcases outofthis2hours trace. In each case, we determine a starting time t c, where c is the index for cases, and select vehicles (called central vehicles) that are moving in the city at that moment. For each selected central vehicle, we also select its nearby vehicles (called neighboring vehicles) that are within meters and move in the same direction as the central vehicle. Here meters is defined to be the threshold to decide whether two vehicles can communicate or not. Then we record the following information of these vehicles: 1. location and velocity, 2. lin metrics between each (central vehicle, neighboring vehicle) pair calculated at the starting time t c, 3. and lin duration calculated from the starting time t c, i.e., the duration of time that two vehicles are within a distance of meters. The statistics of the five testing cases is shown in Table. 2. v c specifies the mean velocity of central vehicles (in the unit of meters per second), and v nb specifies the mean velocity of neighboring vehicles. v c v nb specifies the mean difference in velocity of the central vehicles and their neighboring vehicles when they move in the same direction. Density specifies the mean number of neighboring vehicles around the central vehicle. All of the above properties are measured at the starting time. These five cases can be classified by the velocity of the central vehicle, the difference of the velocity between the central vehicle and neighboring vehicle, and the vehicle density, which is shown in Table 3.

Table 2: Setting of mobility trace Case v c v nb v c v nb Density 1 12 1 2 7 2 7 7 14 3 7 6 1 2 4 12 3 9 74 4 3 1 1 Table 3: Classification of testing cases Cases Criteria high middle low v c 1, 4 2, 3 v c v nb 4-1,2,3, Density 4, 2,3 1 3.2 Lin metrics in comparison Lin metrics are calculated based on distance and velocity at the starting time t c, where c is the index of the case. We consider two ind of velocities: instant velocity and average velocity. The instant velocity for each vehicle is given by the trace file at each case at the time t c. The average velocity for each vehicle i is the one in the last t seconds, which is calculated as l i(t c) l i(t c T). () T In our simulation, we set T as 1 seconds. The lin metrics in comparison include: 1. lin life time by instant velocity () 2. lin life time by average velocity () 3. spatial locality similarity by instant velocity ((I)) 4. spatial locality similarity by average velocity ((A)). similarity function by instant velocity with 1 second distance prediction ((I,1)) 6. similarity function by average velocity with 1 second distance prediction ((A,1)) 7. similarity function by instant velocity with 1 seconds distance prediction ((I,1)) 8. similarity function by average velocity with 1 seconds distance prediction ((A,1)) In addition, we consider the distance, and difference in velocities () as two benchmar lin metrics. 3.3 Lin duration distribution We plot the distribution of lin duration between central vehicles and neighboring vehicles in the five testing cases in the Fig. 1. Lin duration is measured in the unit of seconds. From this figure, we have two observations: 1. mean linduration increasesas the max( v c, v nb ) decreases: when the velocity is high (Fig. 1(a)-Fig. 1(d)), more than half of lins have lin duration less than seconds; while when the velocity is low (Fig. 1(e)), the median lin duration can be up to 1 seconds. 2. v c v nb plays marginal role in the lin duration distribution: there is no big difference in the case 1 and 4, while the velocity different in the latter is much large; in contrast, the lin duration distribution is quite different, while the velocity difference is similar in case 2 and. The reason for the first observation is because the maximal value of the instant velocities of two neighboring vehicles indicates how fast the lin between them will be lost in the worst case. For example, for two vehicles of distance 1 meters and at the velocities of 12m/s, their lin can brea in 1 seconds if one vehicle braes. On the other hand, for same vehicles at the velocities of 4m/s, it will tae up to seconds if one vehicle braes. The reason for the second observation is because the velocity of vehicles may change rapidly. So a large difference in the instant velocities of two vehicles does not necessarily indicate a large difference in the average velocities. Lin duration (seconds) Lin duration (seconds) 2 18 16 1 1 1 8 6 3.2.4.6 26 2 2 18 16 1 1 1 8 6.1.2.3.4 Lin duration (seconds) 6 3 1 Lin duration (seconds) Lin duration (seconds) 3 2 1 1.1.2.3.4 3 3 2 1 1.1.2.3.2.4.6 Figure 1: The lin duration distribution between central vehicles and neighboring vehicles in the five testing cases 3.4 Correlation analysis We study the correlation between lin metrics and actual lin duration to see how well each lin metric predict how long each lin last. Two inds of correlation is considered,

global correlation and local correlation. The global correlation regards all lins in each case as a whole group, and computes the correlation between lin metrics and actual lin duration on these lins. The local correlation regards all lins attached to the same central vehicle in each case as a whole group, computes the correlation for each group, and taes the mean correlation of all groups in the same case. For the correlation coefficients, two inds of correlation coefficients are considered: correlation based on value, and ran correlation. The first one quantifies the extent of linear dependency between the values of two groups of data, and the second quantifies the extent of linear dependency between the orders of two groups of data. For the correlation coefficient based on value, we choose the commonly adopted approach: Pearson product-moment correlation coefficient [6]. It is the division between the covariance of two random variables and the product of the standard deviation of these two variables. For two groups of associated data(a 1,a 2,,a n), and (b 1,b 2,,b n), their Pearson product-moment correlation coefficient is p(a,b) = n n i=1 (aibi) n n i=1 ai i=1 bi n n i=1 a2 i ( n i=1 ai)2 n n i=1 b2 i ( n i=1 bi)2. (6) is always between -1 and 1. When it is close to -1 and 1, it infers that these two groups of data has a strong linear dependency, either negatively, or positively. When it is, it infers that these two groups of data is independent. For the ran correlation, we choose the Kendall s tau coefficient [3]. It measures the similarity of the ordering of two groups of data. Let (a 1,a 2,,a n), and (b 1,b 2,,b n) be the two groups of data in concern. A pair of tuples of value (a i,a j) and (b i,b j), where i j, is said to be concordant if both a i > a j and b i > b j, or both a i < a j and b i < b j. This pair is said to be disconcordant if both a i > a j and b i < b j, or a i < a j and b i < b j. When a i = a j, or b i = b j, this pair is neither concordant nor disconcordant. The Kendall s tau coefficient, in the τ b format, is defined as n c n d τ B(a,b) =, (7) n n 1 n n 2 wheren c isthenumberofconcordantpairs, n d is thenumber of disconcordant pairs, n = n(n 1)/2, n 1 = (t i(t i 1))/2, and n 2 = (µ j(µ j 1))/2. Here t i is the number of tied values of the i th group of ties for the first quantity, and µ j is the number of tied values of the j th group of ties for the second quantity. The Kendall s tau coefficient is ranged between -1 and 1. The coefficient 1 indicates the ran of these two groups are same, and -1 indicts a totally reversed order between these two groups. The closer Kendall s tau coefficient is to 1, the more similarity in order is between these two groups. Fig. 2 and Fig. 3 plot the global correlation and local correlation for the five testing cases. For both global and local correlation, we can see that: 1. Correlation coefficient between lin metrics and actual lin duration is usually between.2 and.4, showing a wea positive correlation. In some cases, certain lin metrics have zero correlation, showing the incapability to ran or evaluate the actual lin duration. The Pearson coefficient and Kendall s tau coefficient in certain scenarios can be quite different, especially for LLT, showing that there exists large mismatch between actual lin duration and predicted lin duration. 2. The correlation by LLT is similar to that by the difference of velocity. In contrast, the correlation by and is similar to that by distance. In all cases, the global correlation and local correlation can be quite different. This is because neighboring vehicles move in a similar mobility pattern. Therefore, difference of velocities plays a more important role in global correlation, and distance plays a more important role in local correlation, except that there exists a large gap in velocity between central vehicles and neighboring vehicles (case 4). 3. The impact of the difference in instant velocity and average velocity on LLT is much significantly compared with and. There is nearly no difference in the performance of (I) and (A), while there is no consistent order of performance by (I,1), (I,1), (A,1), (A,1). The special findings on the global correlation are as follows: 1. When the mean velocity in the networ is low, distance, and so does and, has a higher correlation with the lin duration. 2. When the mean velocity is not low, difference in velocities has a higher correlation with lin duration among all lin metrics. For the local correlation, we can see that 1. When the difference of velocities between central vehicle and neighboring vehicle is small, distance has a higher correlation with the lin duration among different lin metrics; 2. In general, the correlation between vehicle s velocities with lin duration does not outperform other lin metrics, unless there is a large difference in the velocity between central vehicles and neighboring vehicles. Overall, we can see that, there is no winning lin metrics for all cases. In general, the maximal value of the correlation coefficient between distance and lin duration, or that between difference in velocities and lin duration determine the upper bound of correlations of all lin metrics in comparison. The leading lin metrics and dominating parameters (distance or velocity) in different conditions is summarized in the Table 4. 3. Top and Bottom lins In the problem of forwarder selection and cluster-head cluster-member association, it is important to select reliable candidates that have better lin metrics. On the other hand, the computation of the node metrics for the election of cluster heads is usually based on the aggregation of lin metrics for lins attached to the same vehicle. For the purpose of accurate prediction, lins with worse lin metrics should be filtered out in the early stage to avoid polluting the calculation. Therefore, the lin duration of the top or the bottom

Table 4: Summarization of the correlation between lin metrics and lin duration Condition Leading lin metrics Dominating parameters Global correlation Small mean velocity LLT distance Large mean velocity, Local correlation Similar group velocity, distance Different group velocity LLT (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I).2.4.6 Correlation with lin duration.2.3.4. Correlation with lin duration.2.3.4 Correlation with lin duration.1.2.3.4 Correlation with lin duration (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I).1.2.3.4 Correlation with lin duration.2.3.4..6 Correlation with lin duration.2.3.4. Correlation with lin duration.1.2.3.4. Correlation with lin duration (A,1) (I,1) (A,1) (I,1) (A) (I) (A,1) (I,1) (A,1) (I,1) (A) (I).2.4.6 Correlation with lin duration.2.4.6 Correlation with lin duration Figure 2: The global correlation between different lin metric and actual lin duration in the five testing cases Figure 3: The local correlation between different lin metric and actual lin duration in the five testing cases lins selected by lin metrics is also an important criteria in evaluation. Weplottheaveragelindurationbottom andtop lins bydifferentlinmetrics inthefivetestingcases infig. 4and Fig. (in the unit of seconds). As reflected in the section 3.4, whether using instant velocity or average velocity as the input has a marginal impact on the performance of. In addition, the performance of (I,1), (A,1), (I, 1) and (A, 1) is similar and does not have a consistent ordering in different cases. Therefore, for and, we simply use (I,1) and (I,1) to represent the performance of lin metrics in those families. In Fig. 4, we can see that: 1.,,, is not good in identifying short-lived lins, i.e., many lins with large difference in velocities, or small,, still have a large lin duration. 2. in general selects the most short-lived lins among all lin metrics for the first five or first ten bottom lins, i.e., when is very low, there is a higher lielihood that this lin s lin duration is short. 3. Although distance is not able to identifying very shortlived lins, it is possible to detect relative short-lived lins. This is because when the neighboring vehicles have similar mobility pattern, a vehicle that is farther

away from the central vehicle is expected to move out sooner. In Fig., we can see the curves of, and distance form one group, and LLT and form another. The average lin duration of the top lins by lin metrics in the firstgroupingeneral islargerthanthanbythesecondgroup. This is because distance has a higher local correlation with the actual lin duration, as mentioned in the Fig. 3 before. Overall, we can see that, there is no lin metric both achieve good performance in accurately selecting lins with long lin duration and filtering out short-lived lins. Average lin duration of bottom lins Average lin duration of bottom lins 3 2 Lin duration 1 1 2 4 6 8 1 4 3 3 2 1 1 Lin duration Average lin duration of bottom lins Average lin duration of bottom lins 3 3 2 1 1 Lin duration 4 3 3 2 1 1 Lin duration Average lin duration of top lins Average lin duration of top lins 8 7 6 3 2 4 6 8 1 1 9 8 7 6 Lin duration 3 Average lin duration of top lins Lin duration 3 3 2 Average lin duration of top lins Average lin duration of top lins 1 1 1 8 6 Lin duration 1 1 1 Lin duration Lin duration Figure : The top lins selected by different lin metrics Average lin duration of bottom lins 1 1 1 8 6 Lin duration Figure 4: The bottom lins selected by different lin metrics 4. A NEW LINK METRIC 4.1 definition From the discussion in the Section 3 we can see that previous distance and velocity based lin metrics can be classified into two categories: distance oriented (, ) and velocity oriented (LLT). The lin metrics in the first categories tends to achieve better performance in selecting lins with long duration, and that in the second categories tends to achieve better performance in filtering out lins with short duration. In terms of correlation with the actual lin duration, lin metrics in both categories may have low correlations with the lin duration in certain cases. To overcome the drawbac of these previous lin metrics, we propose to combine distance oriented lin metrics and velocity oriented lin metrics together to form a new one. The intuition is as follows. The new lin metric is based on distance oriented schemes, so as to have better prediction on long-lived lins. In addition, a velocity oriented module is added to this metric, so as to be sensible to lins with short duration. We choose (I) as the basic distance oriented module, and as the basic velocity oriented module. Because both of them are positive and easy to be computed. The new lin () metric is computed as { ij, if LLT ij t th ij = ij LLT ij t th, otherwise When LLT ij is very small, this new lin metric should also besmall as its valueis scaled downwith thefraction between LLT ij and t th. When LLT ij is sufficiently large, this new lin metric becomes ij. We fix t th as 1 seconds in default. 4.2 evaluation (8)

As shown in Fig. 6, the correlation between this new lin metric and the actual lin duration is always larger than.3, for both correlation coefficients. Compared with the performance of other lin metrics in Fig. 2 and Fig. 3, this new lin metric always achieve a performance close to the best one. Fig. 7 and Fig. 8 shows the comparison between the proposed new lin metric () in selecting top duration lins and bottom duration lins with other previous lin metrics. For the ease of display, we remove the curves by the lin metrics that have been shown to not perform well. We can see that, the proposed new lin metric achieves nearly the best performance in all cases, thans to the capability in identifying very short-lived lins by, and in identifying long-lived lins by (I). Case 4 3 2 1.2.4.6 Correlation with lin duration (a) Global correlation Case 4 3 2 1.2.4.6 Correlation with lin duration (b) Local correlation Figure 6: Correlation between proposed lin metrics and actual lin duration 4.3 application 4.3.1 Forwarder selection The proposed new lin metric can be applied to select a forwarder that rests in the communication range for a relative long time. In order to now how reliable the suggestion given by this new lin metric is, we use a conditional probability to quantify its effect. We define P b(ld(a) > LD(b) nl(a) > nl(b) + δ) as the conditional probability that lin a s lin duration is larger than that of lin b, given that the new lin metric of the lin a is larger than that of lin b by δ. Fig. 9 shows this conditional probability in the five testing cases. We can see that, as long as the new lin metric of one lin is larger than anther by.2, there is nearly 8% probability that this lin s duration is larger. In practise, such a property is very helpful in distinguishing long-lived lins and short-lived lins with a high confidence. In addition, we can see from Fig. 9 that such a probability increases when the velocities of vehicles decreases. 4.3.2 Cluster head election The proposed new lin metric can be used to form the metric for cluster head election. In the literature, the metric for each cluster head candidate can be simply -based, such as the Lowest- scheme in [], or based on the relative mobility () of neighboring nodes, i.e., the standard deviation of the change of distance between node pairs [8]. Another common approach is to aggregate lins metrics, i.e., to tae the mean lin metric of lins between the cluster candidate and its neighbors. We compare our metric with,,,,, in cluster head election of the five testing cases under the above Average lin duration of bottom lins Average lin duration of bottom lins 3 3 2 Lin duration 1 1 2 4 6 8 1 6 3 1 Lin duration Average lin duration of bottom lins 1 1 Average lin duration of bottom lins Average lin duration of bottom lins 6 3 Lin duration 1 8 7 6 3 1 Lin duration Lin duration Figure 7: The bottom lins selected by the proposed new lin metric metric aggregation approach. In addition, we also compare the relative mobility approach, Lowest- approach, and the optimal approach that use lin duration as the metric. In order to compare different cluster head election metric fairly, we consider the following evaluation criteria. Each central vehicle i selects s neighbors with the best lin metrics (except and Lowest-), and set its cluster head candidate metric m i as the mean value of these lin metrics. Considering the scalability, s is set as s = max(1,nb(i)/1), where NB(i) is the number of i s neighbors. The mean lin duration of these s lins attached to the vehicle i is denoted as LD(i). Top five central vehicles is selected based on the cluster head candidate metric. The corresponding performance criteria is the mean lin duration of the s lins attached to these five central vehicles. As shown in Fig. 1, in most cases (except case 3), is the one that has the closest performance to the optimal one. Even in the case 3, its performance is close to the best benchmar metrics in comparison. Therefore, is effectively in predicting cluster heads that maintains stable connection with their neighbors.. CONCLUSION In this paper, we studied lin metrics in vehicles networs

Average lin duration of top lins 8 7 6 3 Lin duration 2 4 6 8 1 Average lin duration of top lins 1 1 1 8 6 Lin duration Mean lin duration (seconds) 6 8 Mean lin duration (seconds) Average lin duration of top lins 1 9 8 7 6 Lin duration 3 Average lin duration of top lins 1 1 Lin duration 1 Mean lin duration (seconds) 1 Mean lin duration (seconds) Average lin duration of top lins 3 3 3 28 26 2 2 Lin duration 1 3 Mean lin duration (seconds) Figure 8: The top lins selected by the proposed new lin metric Figure 1: The mean lin duration of selected lins attached to the central vehicle Pb(LD(a)>LD(b) nl(a)>nl(b)+δ) 1.9.9.8.8.7.7.6 Case 1 Case 2 Case 3 Case 4 Case.6. 1 δ Figure 9: Conditional probability that the lin duration of one lin a is larger than anther lin b, given that nl(a) > nl(b)+δ that based on distance and velocities, including lin life time, spatial locality similarity and similar function, according to the real vehicle mobility trace in the city Cologne. We compare these lin metrics in terms of correlation with the actual duration, and average lin duration of top and bottom lins selected by these lin metrics. We reveal that, these lin metrics have either a performance close to the distancebased approach, or velocity-based approach. There is no winning lin metrics that performs the best in all cases. By analyzing these lin metrics, we proposed a new lin met- ric that combines the benefit or distance-based approach and velocity-based approach. The new lin metric performs well in both correlation with the actual lin duration, and the capability in selecting long-lived lins and filtering out short-lived lins. In the future, we will extend our analysis to other real mobility data, such as Madrid trace [?], to see whether our conclusion is generic. 6. REFERENCES [1] TAPASCologne project. http://olntrace.project.citi-lab.fr/. [2] M. Bhaumi, S. DasGupta, and S. Saha. Affinity based clustering routing protocol for vehicular ad hoc networs. Procedia Engineering, 38:673 679, 12. [3] M. G. Kendall. A new measure of ran correlation. Biometria, 3(1/2):81 93, 1938. [4] Y. Li, M. Zhao, and W. Wang. Internode mobility correlation for group detection and analysis in vanets. Vehicular Technology, IEEE Transactions on, 62(9):49 461, 13. [] C. R. Lin and M. Gerla. Adaptive clustering for mobile wireless networs. Selected Areas in Communications, IEEE Journal on, 1(7):126 127, 1997. [6] K. Pearson. Note on regression and inheritance in the

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