Degree of Node Proximity: A Spatial Mobility Metric for MANETs Elmano Ramalho Cavalcanti

Marco Aurélio Spohn

Computing and Systems Department Federal University of Campina Grande, Brazil

Computing and Systems Department Federal University of Campina Grande, Brazil

[email protected]

[email protected]

ABSTRACT Spatial mobility metrics are used in several areas in mobile ad hoc networks (MANETs), such as protocol evaluation, and the design of clustering algorithms. We show that current spatial mobility metrics do not take into account spatial dependence in the absence of node movement. In order to provide a better understanding of spatial dependence, we propose a more comprehensive mobility metric, Degree of Node Proximity (DNP), based on the average distance among mobile nodes. Through simulation, we compared our metric against other well-known spatial metric over an extensive set of mobility models. DNP is shown able to capture spatial dependence in scenarios with different levels of node pause time. Besides that, DNP is not biased towards node speed, being able to distinguish group-based mobility models from others. As an additional contribution, we proposed several regression models for predicting DNP for all the mobility models under consideration in this paper.

Categories and Subject Descriptors C.2.1 [Computer-Communication Networks]: Network Architecture and Design—Wireless communication ; C.4 [Performance of Systems]: [Measurement techniques]

during simulation. The movement pattern has a direct impact on protocol performance [1, 4, 6, 18], topology and network connectivity [5, 12, 26], data replication [14], and security [9]. As for the performance itself, it can vary drastically depending on the adopted mobility model [4]. Mobility models can be classified into four categories: random, temporal-based, spatial-based (or group-based), and with geographic restriction [3]. Mobility metrics aim at measuring quantitatively and qualitatively mobility models. Bai et al. [4] proposed a framework to analyze the impact of mobility on performance of routing protocols for MANETs. They proposed a mobility metric to quantify the spatial dependence of mobile nodes (Section 2), called degree of spatial dependence, DSD. Since then, DSD has been used for many purposes: design and evaluation of routing protocols [21, 27, 28], mobility model design [22], validation [29] and evaluation [20, 30], performance analysis of routing protocols [4, 21], mobility-aware routing protocol analysis [11], and design of clustering algorithms [31]. However, we show that DSD has a critical drawback (Section 2.1). As our main contribution, we introduce a novel spatial metric, called Degree of Node Proximity (DNP), which overcomes DSD limitations (Section 3). In order to evaluate the proposed metric, we conducted extensive simulations using four well-known mobility models (Section 4), performing a comprehensive analysis of metrics behavior (Section 4.1).

General Terms

2.

Measurement

Since a mobile node may move according to other node’s movement, it is opportune thinking about mobility metrics that measure this relationship. Related to this statement, Bai et al. [4] proposed the degree of spatial dependence (DSD), which indicates the similarity between the velocities of two nodes that are not too far apart (less than 2R). DSD is high when the velocities (magnitude and direction) of two nodes are similar, what normally occurs when the movement of a node depends on the other’s. Thus, when applied to the whole wireless network, this metric reveals when nodes move in a group manner, no matter if they represent aero-vehicles, people, or even small animals. DSD is based on the cosine similarity between the velocities of nodes. Let ~v (i, t) be the velocity of node i at time t, Cos(i, j, t) be the cosine of angle between the velocities of nodes i,j, and SR(i, j, t) be the speed ratio between the minimum and maximum of |~v (i, t)| and |~v (j, t)|. Then, the degree of spatial dependence between nodes i,j at time t, DSD(i, j, t), is defined according to Equation 1.

Keywords mobility metric, spatial dependence, mobility model, ad hoc network

1. INTRODUCTION Mobile ad hoc Network (MANET) simulators usually employ synthetic mobility models to guide node movements

Permission to make digital or hard copies of all or part of this work 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. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. MobiWac’11, October 31–November 4, 2011, Miami, Florida, USA. Copyright 2011 ACM 978-1-4503-0901-1/11/10 ...$10.00.

RELATED WORK

DSD(i, j, t) = Cos(i, j, t) × SR(i, j, t)

(1)

Therefore, the average degree of spatial dependence (DSD) is computed as the average between all pairs of nodes distant by 2R1 . The formula for computing DSD for a group of N mobile nodes is given by Equation 2, where P is the amount of node pairs distant by 2R, and T is the time interval considered. Group-based mobility models (e.g., RPGM [13]) are expected to present high values for DSD. DSD =

N N T 1 X X X DSD(i, j, t) P i=1 j=i+1 t=0

(2)

Based on the work by Bai et al. [4], Zhang et al. [31] extended and developed the concept of a similar spatial mobility metric, called linear distance based spatial dependency (LDSD), which is also based on the cosine angle between the nodes’ velocities. The authors used LDSD in the design of a distributed group mobility adaptive clustering algorithm [31]. However, both DSD and LDSD present the same limitation, which is described in next section.

2.1 Limitations on Previous Metrics The main limitation on DSD and LDSD is that they do not consider spatial correlation (dependence) during periods of absence of node movement. While any of two nodes i, j are pausing, their correlation is always zero, what is not necessarily true, because nodes i and j might have paused (i.e., switched to velocity zero) just because there is some dependence between them. Figure 1 shows the state transition diagram between the velocities of two nodes. There are exactly three states: the first when both nodes are moving, the second when both are pausing, and the third when one is moving and the other is pausing. As discussed below, DSD captures spatial dependence only during the first state. Let us consider a common square group mobility scenario, where both width, X, and length, Y , are 500 m, and transmission range is set to 50 m. Let P3 represent the position of node P at t = 3, and P5..7 that node P does not move from t = 5 to t = 7. Then consider two mobile nodes, B and C, which are moving in accordance to their leader, node A (Figure 2). At time t0 , node A starts moving until t = 10, and then stops for 10 seconds (A10..20 ). Nodes B and C have different reaction times; i.e., the time to perceive their leader movement and starting moving accordingly (2 and 3 seconds, respectively). As a result, B and C try to keep themselves inside node A’s transmission range. For this group mobility scenario, the DSD metric just captures the correlation when at least two nodes are moving at the same time (i.e., from t2 to t11 ), while the correlation is considered null during pause times (Table 1). There is a clear spatial dependence among nodes during pause times, but it is not captured by DSD. From t0 to t1 , the total degree of spatial dependence is zero. From t3 to t9 , DSD is 0.747 since all nodes are moving. However, the average degree of node dependence, from t = 0 to t = 19, is just 0.296. Therefore, due to node pause time, the use of cosine similarity alone is not a good indicator of spatial dependence among nodes. Another limitation on DSD is that it is biased by the average node speed. Hence, a group of people running to1

If two nodes i, j are distant more than two units of the transmission range (R) in the time step t, then DSD(i, j, t) = 0 is always true.

Figure 1: State transition diagram between the velocities of two nodes.

Figure 2: Example of a group mobility scenario.

Table 1: Variation of degree of spatial dependence over time. Time Nodes A,B A,C B,C Mean

t0..1 0 0 0 0

t2

t3..9 t10..11 DSD(i,j,t) .851 .851 0 0 .776 0 0 .613 .613 .284 .747 .204 DSD = .296

t12..19 0 0 0 0

Figure 3: Example of Maximum Average Distance (MAD). gether would mostly exhibit higher DSD values than the same group would in case they were just walking together. However, this behavior is obviously inconsistent. This and the other aforementioned limitation of DSD is shown in Section 4.1. Before that, in the following section we present a novel spatial mobility metric for mobile ad hoc networks.

3. DEGREE OF NODE PROXIMITY We propose a spatial mobility metric based on the distance between pairs of nodes, called Degree of Node Proximity (DNP). Let N be the number of mobile nodes, T the network simulation time, and D(i, j, t) the Euclidean distance between nodes i, j at time t. Instead of using the absolute distance, we consider the relative distance between nodes as the method of measuring the distance. It is achieved by using the transmission range (R) as the distance unit [16]. Thus, the average distance between nodes i, j from time 0 to T , AD(i, j), is defined according to equation 3. PT t=1 D(i, j, t)/R (3) AD(i, j) = T Since the number of pairs of nodes in the network is N (N − 1)/2, the average distance between all nodes from time 0 to T (AD) is computed as follows: AD =

1 N (N − 1)/2

N N X X

AD(i, j)

(4)

i=1 j=i+1

In order to normalize the values of AD into the same range of the DSD values (i.e., [-1,+1]), we divide AD by the maximum average distance (M AD) of the scenario, which is the half of the maximum possible distance between two points in the scenario. M AD is also measured in units of transmission range, and is computed as follows: √ X2 + Y 2 (5) M AD = 2R To illustrate an example, suppose a scenario where X = 600 m and Y = 800 m, and node transmission range, R, is set to 100 m. Then, the maximum average distance, M AD, is given by 5R (i.e., 500 m). Figure 3 illustrates this situation.

Figure 4: Variation of Degree of Spatial Dependence and Degree of Node Proximity for the mobility example scenario (Figure 2). The proportion of AD and M AD gives a notion about the degree of mobility dependence. When the average distance among nodes is constantly low, then this probably means that nodes follow some sort of group-mobility pattern. For this reason, we define our spatial mobility metric DNP as expressed in Equation 6. AD (6) M AD DN P values range from −1 to 1. We have that DN P = −1 when all nodes are always distant by 2*M AD (i.e., the maximum distance between two points in the scenario). On the other hand, the smaller the distance between all nodes, the closer DN P is to 1. It is expected that group-based mobility models (e.g., RPGM [13] and CMM [25]) present high DN P values, while other models present lower values. Figure 4 shows the variations of the spatial metrics for the scenario presented in the previous section. There is a clear fluctuation on DSD due to nodes’ pause time periods, particularly at the beginning and at the end of the simulation. We note a slight variation on DN P since nodes B and C follow their leader’s movements (i.e., node A). Next, we present results regarding extensive simulations for comparing the performance of DSD and DNP over a heterogeneous set of mobility models. DN P = 1 −

4.

SIMULATION

To check the ability that our proposed mobility metric have to capture spatial dependence among mobile nodes, we have selected the following mobility models: • Random Waypoint (RWP) [8]: is one of the simplest yet most used mobility model in MANET simulationbased studies [16]. It has just three configuration parameters: minimum and maximum speed, and maximum pause time. Figure 5(a) shows an illustration of this model. • Reference Point Group Mobility (RPGM) [13]: is a group-based model where the movement of the leader of a group influences the movement of all its members (Figure 5(b)). The distance between the leader and its members should not be greater than a threshold, called maximum distance from center. RPGM is more

Table 2: Mobility models selected for simulation. Feature RWP RPGM GM MAN Randomness X Group-based X Temporal X Grid-based X applicable for battle field or rescue operations scenarios. • Gauss-Markov (GM) [19]: in this model the velocity of mobile node is assumed to be correlated over time and modelled as a Gauss-Markov stochastic process. GM is a temporally dependent mobility model whereas the degree of dependency is determined by the level of one of its input parameters.

Table 4: Correlation matrix between parameters and mobility metrics. Metric Model R s S|AS MPT NG RWP .18 .00 -.64 .25 DSD RPGM -.33 -.09 -.16 -.58 .38 GM -.07 .08 MAN .16 .02 -.66 -.06 RWP .00 -.06 -.12 -.82 DNP RPGM .24 .01 -.03 -.29 .77 GM .00 -.22 MAN .00 -.00 .36 .69

The results presented in this article depend on some assumptions which are mandatory for computing mobility metrics. First, the communication between nodes is always bidirectional during the simulation. Second, the transmission range, R, is constant and equal for all nodes. Third, the total number of nodes is constant during the simulation. Lastly, the simulation scenario has a two-dimensional rectangular geometry. Table 2 summarizes the main characteristics of the selected mobility models. RPGM and MAN models are classified as having moderate randomness. The former, because the movements of regular nodes are limited to their leader’s movements, while in the latter node movements are limited due to obstacles spread over the scenario (e.g., city blocks). Gauss-Markov (GM) presents variable randomness, since it depends on the value of memory parameter α. The BonnMotion tool [2] was employed for mobility scenario generation, producing the synthetic traces for the mobility models. For all scenarios, 100 nodes moved for a period of 900 seconds over an area of 1000 x 1000 meters. Transmission range was set to 100, 150, and 200 meters. For the RPGM model, the number of mobile nodes per group (N G) was set to 10, 25, and 50, which represent scenarios with 2, 4, and 10 groups of nodes. Memory parameter and maximum pause time (MPT) were set to a large range of values (see Table 3), in order to explore various mobility scenarios. All graphs present results with a confidence level of 99%, based on 10 repetitions for each one of the 1, 404 generated scenarios. In some situations, the interval length is smaller than the graph dots, making it barely visible.

the variation of maximum node pause time, M P T , causes on DSD in the RPGM model with 2, 4, and 10 groups of 50, 25, and 10 mobile nodes, respectively. As expected, DSD increases for larger groups, due to the threshold maximum distance of 2R units for every pair of nodes. However, DSD considerably decreases when the maximum pause time increases3 . The same situation occurred for all RPGM scenarios with different number of groups. The strong impact that pause time causes in DSD is due to the moderately high negative correlation between them (−0.58, see Table 4). On the other hand, node pause time has little impact on degree of node proximity (Figure 6). Thus, DNP is shown more suitable for characterizing spatial dependence among mobile nodes in a larger set of mobility environments. Figure 7 shows the effect of pause time on DNP for two other mobility models, Random Waypoint and Manhattan. In the RWP model, DNP presented a moderate reduction for M P T = 100 s, after what it kept approximately constant. Overall, pause time had little impact on DNP in the Manhattan model. Another problem related to the DSD metric is that it is affected by node speed as shown in Figure 8. In the RPGM model, DSD also drops when the node speed increases, independently of the number of nodes per group. When node speed is three times higher, DSD is almost cut by half. On the other hand, DNP is not affected by node speed as shown in Figure 8. This is crucial since the level of spatial correlation (dependence) between a group of mobile nodes should be independent of the nodes’ velocities. The dependence level between a group of people walking somewhere should be as high (or low) than between some vehicles. As well as DSD, DNP can clearly distinguish a spatial dependency mobility model (i.e., RPGM) from others (Figure 9). However, whereas non-group-based models present DSD values close to zero, the same models present positive values for DNP (Table 5). Thereby, besides the ability to properly distinguish group-based models from others, DNP may also be used as a generic measure for characterizing overall mobility in wireless ad hoc networks.

4.1 Analysis

4.2

• Manhattan (MAN) [4]: is a grid-based model where nodes follow specific paths (e.g., streets) distributed in a rectangular grid (Figure 5(c)). It is suitable for modeling the movement of vehicular wireless networks.

We investigate the impact of pause time and average speed2 on DSD and DNP. Afterwards, we show that DNP is able to differentiate among mobility models taken into account in this work, without being impacted by node pause time. As stated in Section 2.1, DSD does not capture spatial dependence during pause states. Figure 6 shows the effect that

Regression Analysis

Multiple linear regression is one of the most used techniques for predicting the value of one dependent variable (i.e., response variable) from a set of independent variables (i.e., predictors) [23]. This technique has already been used for predicting mobility metrics from mobility model’s input parameters [10, 17, 24]. There are at least two main pur-

2

Since in both RWP and RPGM model the speed follows an uniform distribution, the average speed is the mean between the minimum and maximum speed.

3 In the RPGM model, the pause time presents an uniform distribution; i.e., the average pause time is exactly M P T /2.

(a) Random Waypoint mobility model.

(b) RPGM mobility model.

(c) Manhattan mobility model.

Figure 5: Illustrations for the RWP, RPGM and Manhattan mobility models. Table 3: Node speed and node pause time configuration used for simulation. Parameter - unit GM RWP RPGM MAN Minimum speed (s) - m/s 1, 3, 5 1, 3, 5 1, 3, 5 Maximum speed (S) - m/s 10, 20, 30 10, 20, 30 10, 20, 30 Average speed (AS) - m/s f(S)a 6, 11, 16 Speed standard deviation f(S,AS) b f(s,AS) c Maximum pause time (MPT) - s 0, 100, 200, 300, 400, 500, 600, 700, 800, 900 s d Nodes per group (NG) 10, 25, 50 Memory Parameter 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 Number of rows/columns 10 / 10 Number of experiments 2,700 540 8,100 2,700 a It depends on S. b It depends on AS and S. c It depends on AS and s. d For RWP, RPGM, and Manhattan models.

Table 5: Descriptive statistics for the Metric Model Mean Std. Min RWP .007 .005 -.008 DSD RPGM .117 .126 .005 GM .001 .005 -.012 MAN .013 .012 -.004 RWP .299 .044 .245 DNP RPGM .560 .080 .374 GM .271 .023 .261 MAN .268 .023 .223

metrics. Max .029 .805 .017 .058 .415 .744 .337 .321

poses for this approach. First, to allow researchers specifying rigorous and standard MANET simulation scenarios for protocol evaluation [17, 24]. Second, to support designing mobility-adaptive protocols [10]. For the regression analysis, DNP is chosen as the response variable. For predictors selection, two possible sets of variables are considered. The first contains the mobility models’ input parameters (e.g., number of nodes or node pause time). As we have shown that node speed does not impact DNP, this parameter was discarded from the first set. The second set contains derived parameters, which are a combination of two or more input parameters (e.g., area = X ∗Y ). We tried various possible subsets of predictor variables to find one that gives significant parameters and explains a high percentage of the observed metric value variation. Thus, three derived parameters are used for predicting DNP (as used by Cavalcanti and Spohn [10]): i. area: is given by the product X.Y . The area unit is expressed in terms of the transmission range (i.e., R2 ).

ii. Number of Groups (N G): is defined as the ratio between the number of nodes (N) and the number of nodes per group (NNG) (i.e., N G = N/N N G). It is suitable for group-based mobility models (e.g., RPGM). iii. Number of Blocks (N B): is the product of the number of rows and the number of columns. This derived input parameter is applicable for grid-based models (e.g., Manhattan), where N B can represent the number of city blocks. The values of the predictor variables used in the regression analysis are shown in Table 6. The simulation time was set to 1000 seconds and the node transmission range was defined as 250 meters. We set a wide range of values for the predictors in order to accurately detect its relationship to the DNP metric (e.g., linear, logarithmic) through scatter plots analysis. In order to create the regression model for DN P , we check all the most-required regression assumptions [15, 23]: i. Linearity between predictors and response variables. To ensure this assumption we made nonlinear transformations in several predictors variables. ii. Normality of residuals (i.e., the residuals are normally distributed). Residual is calculated as the difference between the observed value of the variable and the value suggested by the regression model. The normality of residuals assumption is checked through the Normal QQ plot, and the measures of skewness and kurtosis of the residual distribution. iii. Absence of multicollinearity between selected predictors

Table 6: Configuration of the predictors for regression analysis. Predictor Values Number of nodes (N) 50, 75, 100, 125, 150 Simulation area (A) 8, 16, 24, 32, 40 Number of groups (NG) 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 20, 25, 30 Number of blocks (NB) 50, 100, 200, 250, 500 Maximum pause time (MPT) 0, 250, 500, 750, 1000

(a) RPGM with 2 groups of 50 nodes

Figure 7: Effect of pause time on DNP for several mobility models (s = 5 m/s, S = 30 m/s, R = 100 m). variables4 . We set the variance inflation factor (V IF = 5) as the threshold for disregarding a predictor from the regression model. iv. Homoscedasticity (i.e., the variance of the residuals is homogeneous). We ensure this property through visual check of the residual plots. v. Treatment of outliers. We use Mahalanobis and Cook’s distance for detecting outliers [7].

(b) RPGM with 4 groups of 25 nodes

The predictive models of DNP for the Random Waypoint, RPGM, and Manhattan models are given by Equations 7 to 9. As expected, node pause time causes little effect on DNP, corroborating the results shown previously (Figure 7). √ P (7) ln(ΦRW DN P ) = .113 ln(A) − .002 M P T − 1.705 √ GM ln(ΦRP DN P ) = .587/N G − .15 ln(A) − .004 M P T − .21 (8) √ M AN ln(ΦDN P ) = .158 ln(A) + .055 ln N B + .003 M P T − 2.212 (9)

(c) RPGM with 10 groups of 10 nodes Figure 6: Effect of node pause time on DSD and DNP in RPGM with 2, 4, and 10 groups (s = 3 m/s, S = 20 m/s, R = 150 m).

The coefficient of determination (R2 ) and its standard error for the regression models are shown in Table 7. The standard errors and confidence interval for the predictor’s coefficients are detailed in Table 8. The results show that the regression models provide substantial precision for determining the degree of node proximity among nodes. The RPGM model presented the best accuracy predictive model, whereas more than 85% of the variation of DNP is counted by the variation of the predictors area, number of groups and node pause time. 4 Multicollinearity exists when two or more predictor variables in a multiple regression model are highly correlated.

(a) RPGM with 2 groups of 50 nodes

Figure 9: Degree of Node Proximity (DNP) histograms.

(b) RPGM with 4 groups of 25 nodes

(c) RPGM with 10 groups of 10 nodes Figure 8: Effect of node average speed on DSD in RPGM with 2, 4, and 10 groups (M P T = 200 s, R = 200 m).

Table 7: Regression models’ summary. Model RWP RPGM Manhattan

R2 adj. .792 .852 .825

Std. Error .02311 .04025 .03393

Table 8: Lower and upper bound of coefficients’ values with 99% confidence interval. Equation Predictor Std. Error βlower βupper β0 -1.705 .023 -.1765 -1.646 Eq. 7 ln(N G) .113 .007 .095 .130 √ MP T -.002 .000 -.003 -.002 β0 -.210 .018 -.257 -.164 Eq. 8 1/N G .587 .016 .545 .628 ln(area) -.150 .005 -.163 -.136 √ MP T -.004 .000 -.005 -.003 β0 -2.212 .018 -2.260 -2.165 Eq. 9 ln(area) .158 .004 .147 .170 ln N B .055 .002 .049 .060 √ MP T .003 .000 .002 .004

5. CONCLUSION We have demonstrated that the cosine similarity metric, used to model the degree of spatial dependence (DSD), a spatial mobility metric from the well-known IMPORTANT framework [4], cannot capture spatial dependence among nodes in the absence of node movement. We proposed the Degree of Node Proximity (DNP), a novel spatial mobility metric based on the average distance among nodes. DNP is shown to be more realistic than DSD at capturing the spatial dependence in scenarios having different pause timing levels. Moreover, DNP is not biased towards node speed. In addition to that, we have presented DNP prediction equations for Random Waypoint, RPGM, and Manhattan mobility models. As future work, we intend to investigate how to design better adaptive-protocols by employing the DNP prediction equations derived in this work.

6. REFERENCES [1] W. Alasmary and W. Zhuang. Mobility impact in ieee 802.11p infrastructureless vehicular networks. Ad Hoc Networks, In Press, Corrected Proof:–, 2010. [2] N. Aschenbruck, R. Ernst, E. Gerhards-Padilla, and M. Schwamborn. Bonnmotion: a mobility scenario generation and analysis tool. In Proc. of the 3rd ICST, SIMUTools ’10, p. 51:1–51:10, June 2010. [3] F. Bai and A. Helmy. Wireless Ad Hoc and Sensor Networks, chapter A Survey of Mobility Modeling and Analysis in Wireless Adhoc Networks. Kluwer Academic Publishers, June 2004. [4] F. Bai, N. Sadagopan, and A. Helmy. IMPORTANT: A framework to systematically analyze the impact of mobility on performance of routing protocols for adhoc networks. In IEEE INFOCOM, p. 825–835, 2003. [5] C. Bettstetter. On the connectivity of ad hoc networks. The Computer Journal, 47(4):432–447, July 2004. [6] J. Boleng, W. Navidi, and T. Camp. Metrics to enable adaptive protocols for mobile ad hoc networks. In ICWN, p. 293–298, Las Vegas, Nev, USA, 2002. [7] K. A. Bollen and R. Jackman. Modern Methods of Data Analysis, chapter Regression diagnostics: An expository treatment of outliers and influential case, p. 257–91. Sage Publications, 1990. [8] J. Bronch, D. Maltz, D. Johnson, Y.-C. Hu, and J. Jetcheva. A performance comparison of multi-hop wireless ad hoc network routing protocols. In Proc. 4th Mobicom, p. 85–97. ACM/IEEE, 1998. [9] S. Capkun, J.-P. Hubaux, and L. Buttyan. Mobility helps peer-to-peer security. IEEE Transactions on Mobile Computing, 5(1):43–51, January 2006. [10] E. Cavalcanti and M. Spohn. Predicting mobility metrics through regression analysis for random, group, and grid-based mobility models in MANETS. In ISCC, p. 443–448, Riccione, Italy, June 2010. [11] J. Ghosh, S. J. Philip, and C. Qiao. Sociological orbit aware location approximation and routing (SOLAR) in manet. Ad Hoc Networks, 5(2):189–209, 2007. [12] M. Grossglause and D. Tse. Mobility increases the capacity of ad-hoc wireless networks. IEEE/ACM Transactions on Networking, 10(4):477–486, 2001.

[13] X. Hong, M. Gerla, G. Pei, and C.-C. Chiang. A group mobility model for ad hoc wireless networks. In Proc. 2nd MSWiM, p. 53–60, Seattle, Washington, 1999. [14] J. L. Huang and M. S. Chen. On the effect of group mobility to data replication in ad hoc networks. IEEE Trans. on Mobile Computing, 5(5):492–507, 2006. [15] R. K. Jain. The Art of Computer Systems Performance Analysis. Wiley-Interscience, New York, NY, USA, May 1991. [16] S. Kurkowski. Credible Mobile Ad Hoc Network Simulation-Based Studies. PhD thesis, Colorado School of Mines, 2006. [17] S. Kurkowski, W. Navidi, and T. Camp. Constructing manet simulation scenarios that meet standards. In IEEE MASS, p. 1–9, October 2007. [18] V. Lenders, J. Wagner, and M. May. Analyzing the impact of mobility in ad hoc networks. In 2nd REALMAN , p. 39–46, Florence, Italy, 2006. ACM. [19] B. Liang and Z. Haas. Predictive distance-based mobility management for pcs networks. In Proc. of 18th IEEE INFOCOM, p. 1377–1384, April 1999. [20] Y. Lu, H. Lin, Y. Gu, and A. Helmy. Towards mobility-rich analysis in ad hoc networks: Using contraction, expansion and hybrid models. In Proc. of IEEE ICC, p. 4346–4351, 2004. [21] Y. Lu, H. Lin, Y. Gu, and A. Helmy. Towards mobility-rich performance analysis of routing protocols in ad hoc networks: Using contraction, expansion and hybrid models. In IEEE ICC, p. 4346–4351, June 2004. [22] K. Maeda, K. Sato, K. Konishi, A. Yamasaki, et al.. Urban pedestrian mobility for mobile wireless network simulation. Ad Hoc Networks, 7(1):153–170, 2009. [23] D. Montgomery and G. Runger. Applied Statistics and Probability for Engineers. Wiley, 3 edition, 2002. [24] A. Munjal, T. Camp, and W. Navidi. Constructing rigorous manet simulation scenarios with realistic mobility. In European Wireless Conference (EW), p. 817–824, 2010. [25] M. Musolesi and C. Mascolo. Designing mobility models based on social network theory. MC2R, 11(3):59–70, 2007. [26] P. Santi. Topology Control in Wireless Ad Hoc and Sensor Networks. Wiley, first edition, 2005. [27] C. Shete, S. Sawhney, S. Hervvadkar, V. Mehandru, and A. Helmy. Analysis of the effects of mobility on the grid location service in ad hoc networks. In IEEE ICC, p. 4341–4345, June 2004. [28] D. Son, A. Helmy, and B. Krishnamachari. The effect of mobility-induced location errors on geographic routingin mobile ad hoc and sensor networks: Analysis and improvement using mobility prediction. IEEE Trans. on Mobile Computing, 3(3):233–245, 2004. [29] C. Tuduce and T. Gross. A mobility model based on wlan traces and its validation. In IEEE INFOCOM, p. 664–674. IEEE, 2005. [30] S. Williams and D. Hua. A group force mobility model. Simulation Series, 38(2):333–340, 2006. [31] Y. Zhang, J. Ng, and C. Low. A distributed group mobility adaptive clustering algorithm for mobile ad hoc networks. Computer Communication, 32(1):189–202, 2009.