1. Introduction

Rcently, with the rapid delevepment of wireless communications and mobile wireless devices, such as PDAs and smart phones, a novel network, mobile opportunistic network (MON) is designed and widely used, in which mobile devices carried by humans could exploit the intermittent contacts for data communication or content sharing. In a MON, a stable end-to-end path from a source to a destination does not exist, and thus a store-carry-forward paradigm is applied, which is shown to be the only applicable communication method in many extreme scenarios, such as deep space communications, disaster recovery, and battlefield[1][2]. Moreover, the increasing density of mobile wireless devices populates the edge of the Internet, and raises the question of the efficient cooperative use of these vast space of resources by leveraging on the spontaneous communication capacity offered for free by “mobile clouds [3]” of edge devices, e.g., for offloading mobile data, data caching and sharing, etc [4][5]. Therefore, mobile opportunistic networks pave the way to a pervasive and universal communication environment in which the store-carry-forward communication can play an important role due to its capacity of freeing users from infrastructure dependence. Unlike infrastructure-based counterparts, mobile opportunistic networks highly depend on the mobility patterns of wireless device carriers, i.e., human mobility. Accordingly, analyzing and modeling human mobility are essential in performance evaluation of MONs.

A lot of mobility models have been proposed [6]—generic high level models that aim to produce movement accurate enough with statistical measures, and models that describe incidental scenarios, hoping for a more accurate depiction of single devices. Random Waypoint (RWP), one of the high level models, assumes that all nodes move independently without any inter-nodal correlation, while people are often related with each other through a complex social network resulting in a highly clustered phenomenon in real life [7]. In addition, through the analysis of real traces gathered from real-life experiments, it has been observed that the typical distributions of contact duration, inter-contact time and contacts number. Especially, inter-contact time was showed that it follows a power-law distribution with a dichotomy: a power law at the first interval and ending with a truncated exponential cut-off [8][9]. Conversely, RWP is proved to yield exponential inter-contact time distribution [10]. Therefore, RWP is not so good to simulate human mobility and more realistic models are in need for MONs. On the other hand, working day movement model [11] is one of the delegations of models that describe incidental scenarios. It simulates the everyday life of people that go to their workplaces in the morning, spend their day at work and go back to their homes at evenings. The synthetic data they generate match well the distributions of inter-contact time and contact duration of real traces. But complex configurations of parameters and simulation areas result that it is not widely used as expected especially in large-scale scenarios. There are two typical characteristics in large-scale scenarios: high node density and long duration. Therefore, more simple but accurate enough mobility models are essential for simulations.

In this paper, we propose a social motivation-aware mobility model (SMAM) for mobile opportunistic networks and the main contributions of our work are listed as follows:

The rest of the paper is organized as follows: Section 2 briefly reviews the previous work relevant to mobility modeling; Section 3 introduces a new geographical partition; Section 4 presents SMAM in detail; Section 5 shows experimentally the better performance of SMAM by presenting the main characteristics of human mobility and accurately evaluating the social routing algorithms like BUBBLE’s performance; in Section 6, we make some concluding remarks.

2. Related Work

In the last few years, there have been a considerable number of papers on designing a mobility model for human mobility. Inter-contact times, contact durations, contacts number are typical metrics for characterizing mobility in MONs. An inter-contact time is the time interval between contacts for a node pair. It is defined as the time interval a node pair is not in contact with each other. The contact duration is the time a contact between a pair mobile nodes lasts. Contacts number is the total number of encounters between two mobile nodes. Inter-contact time corresponds to how often nodes meet and have the opportunity to send messages to each other, and contact durations limit the amount of data that can be sent, while contacts number reflects the strength of social ties between mobile nodes. Usually, inter-contact time distributions, contact duration distributions and contacts number distributions are used in comparisons.

[12] shows that simple mobility models have very different properties in inter-contact time and contact durations compared to real user traces. [13] shows that the inter-contact times are only power-law distributed up to 12 hours and have an exponential cut-off after that. A possible cause for the phenomenon is the daily routines people have. [14] shows the power-law exponential dichotomy of inter-contact time that have observed in the real-life experiments. They also propose SWIM, a simple mobility model, to generate traces that have the similar statistical properties of real-traces. [15] proposes a model that can generates movement traces similar to random walk except the flight lengths and the wait time in destinations are generated based on Levy Walks—with power law distribution. The model produces inter-contact time distributions similar to real world traces. However, since every node moves independently, the model does not generate any social structure in the network. [16] proposes a modification of Levy Walks, SLAW (Self-similar Least-Action Walk), which considers more statistical features of human mobility traces than Levy Walks: the self-similar nature of people’s destinations (i.e., people have a bounded mobility area in daily life) and people’s preference to a closer destination. It has proved that it matched well the inter-contact time distribution of real traces, but no results are presented in terms of contact duration and contact number distributions. In [11], the authors present a working day movement model that simulates the everyday life of people, i.e., go to their workplaces in the morning, spend their day at work and go back to their homes at evenings. [17] proposes a flexible mobility pattern, where the sequence of inter-contact times are modeled as Semi-Markov Modulated Process. It generates traces featuring predictable probability distributions in both individual node level and aggregate level. [18] proposes a simple parametric mobility model STEPS, which abstracts the fundamental spatio-temporal behaviors of human mobility, i.e., preferential attachment and attractors, by using a power law to drive nodes movement. But it doesn’t take full account of human’s sociality such as social ties between people, which will cause a loss in accuracy of depicting human mobility.

Even though some of these existing mobility models did a good job to present the statistical features of human mobility, there still doesn’t exist a mobility model that can be widely used because of the following limitations: a) Not accurate to simulate the statistical properties of human mobility; b) Too complicated to configure the parameters or simulation map; c) Not suitable for large-scale scenarios. Therefore, we propose a social motivation-aware mobility model to avoid these limitations mentioned above.

3. Geographic functional cells

To avoid the complicated configurations of simulation map and form a widely-used mechanism, we introduce a novel concept of geographic functional cells. In real life, our world is split by walls, roads, mountains, rivers or something else into many irregular regions of varied sizes. But it can be observed that the city human live in usually takes lattice design. Therefore, if we assume a city is composed of many lattices, each cell can be viewed as a geographic functional area playing a main role of this area such as a hospital, a residence community.

Inspired by the characteristics of the real geographic partition, we divide the simulation area into geographic functional cells, which are squared cells with a side length l and assigned with specific functions respectively. As is shown in Fig. 1, under a city-based scenario, each cell may take a function like residence, school, park and so on. While under a campus-based scenario, each cell may take canteen, dormitory, teaching building, etc. The functions of cells are defined according to the social needs under different scenarios. We define a geographical function set (GFS) corresponding to social needs and the size of GFS shouldn’t be less than the number of social needs. If not, the needs of nodes can’t be satisfied and that will cause an error in simulations. In SMAM, we assume that GFS is in one-to-one correspondence to social needs set. Each squared cell is assigned with a certain function in GFS randomly, to ensure that each function should be assigned to at least one cell.

Fig. 1.An example of geographic partition

As is shown in Fig. 1, there are usually some cells with the same geographical function. To distinguish these cells with the same function, we assume every node has an independent popularity for each cell, and each node has a full map of these functional cells with an attachment of initial popularity evaluation Pinit.

As we all know that the popularity of a supermarket always changes because of many factors such as the service quality, goods price, the quantity of customers and the evaluation of other people, the popularity of a cell for each nodes may also change. The most direct reflection of popularity in one’s mind is the number of people one can meet there. Hence, we denote the number of nodes that node ni encountered in cell C at the last time as Seen(C), which approximately reflects the visiting frequency of cell C. Generally, as we go more and more frequently to one place, its popularity will be larger and less influenced by external factors. That is to say, the popularity grows with the times nodes have been there, and as a node goes more and more frequently to one cell, the cell’s popularity tends to be an approximation to 1. The popularity can be calculated by Eq. (1), where n presents the times node ni has ever been C. As is definitely larger than 1, the th power of which is larger than 1 as well, then Pni(C) is less than 1. Besides, all the parameters are greater than zero, so Pni(C) is located in [0, 1].

Besides, the popularity of cells can be transitive by means of individuals’ interaction through social ties. We use encounters between pair nodes to estimate the strength of social ties between them. Recommendation from one who has a stronger tie will have a deeper impact on the node’s evaluation of the popularity of cells. To this end, the popularity for each node will be influenced to different degrees by others according to the strength of social ties between them. In SMAM, we assume two nodes in contact are friends of each other and they will share their own popularity of cells with friends. That is to say, if node ni encounters node nj, ni and nj are friends, and they will update the popularity information as showed in Eq. (2). In Eq. (2), Encounters(ni,nj) refers to the number of contacts between node ni and node nj, and Encounters(ni) refers to the total encounters of node ni. The formula implies that the more frequency the pair nodes encounter, the stronger effect it has on the popularity recommendation to the other node.

As we can see in Eq. (2), Pni(C) will get its lower limit zero when Pni(C)OLD = Pnj(C) = 0. On the other hand, the maximum value of Pni(C) won’t be greater than 1 because Pnj(C) - Pni(C)OLD is no more than zero when Pni(C)OLD equals to 1. Consequently, Eq. (2) can ensure Pni(C) is located in [0, 1].

4. Social motivation-aware mobility model

We believe that an ideal human mobility model should have the following features:

To meet these requirements mentioned above simultaneously, we propose a new mobility model, social motivation-aware mobility model (SMAM). In SMAM, we take the influence of geographical constraints and social motivation-aware of human mobility into consideration to accurately depict the main characteristics of human mobility and enable to simulate varied-scale scenarios.

4.1 Social motivation-aware of human mobility

Psychologically, social motivation is obtained from learning and experience in social life on the basis of people’s need of social culture. It is the direct drive and internal power of individual’s activities to achieve a certain purpose. In this paper, we take full account of the social motivations to explain the basic laws of human mobility.

In social life, it is observed that people have a wide variety of essential needs to maintain their life. Accordingly, the basic law of human mobility in SMAM can be summarized as shown in Fig. 2.

Fig. 2.The basic law of human mobility in SMAM

4.1.1 Expectancy value theory

In psychology, a lot of researches related to motivation depend on expectancy value theory (EVT). As one of the most influential theories in psychology, the theory assumes that the motivation of individual tasks is determined by two variables: individuals’ expectations for success and the subjective task value [19]. The expectancies of individuals have shaped their behaviors as well as the choices they make. The subjective task value can be thought of the motivation that allows an individual to answer the question “Do I want to do this activity and why?” With this perspective, EVT reflects the rules in making individual’s behavioral choices and the influence of identity on motivated actions.

In Eq. (3), EVT defines two kinds of achievement motivation (Mach): the motivation to succeed (Mas) and the motivation to avoid failure (Maf). Atkinson used the probability of success (Ps) and the probability of failure (Pf) to define expectancy, by assuming Ps+Pf=1. Besides, it also considers the inducement of success (Is) and failure (If).

In this paper, we apply EVT to illustrate the basic laws of human mobility. First, individuals move to finish tasks, like meeting the social needs, by developing a belief about the tasks. If a belief already exists, it can and most likely will be modified by new information. Second, individuals assign a value to each attribute such as the popularity of the destinations and distance to the destination, which a belief is based on. Third, an expectation is created or modified by the results of a calculation based on beliefs and values. I(C) is the movement intention of individuals to a random cell C, which can be calculated by the following equation.

In Eq. (4), li(t) refers to the current location of node ni, and distance(lni(t),C) is a function that decays with the distance between the current location of node ni and the center location of cell C, as shown in Eq. (5). Pni(C) implies the popularity of cell C for node ni. The influence factor α is a constant in [0, 1], and the larger α is, the more the decisions depend on proximity. Conversely, the smaller is α, the more the decisions depend on popularity.

where ║·║ is the Euclidean distance, the current location of ni is (xi,yi) and the center of cell C is (cx,cy), then

In Eq. (5), r is the node’s communication radius and s is the maximum side length of simulation world size, the ratio of which can be viewed as a scaling factor, while the world size is set 250m×250m and the communication range is 10m in Section 5. Obviously, the value of distance(lni(t),C) is located in [0, 1] because the denominator is definitely bigger than one.

4.1.2 Affiliation motivation of human mobility

In psychology, people are found to be fearful of loneliness and have a psychological tendency to stay with other people, which we call affiliation motivation. Affinity is a kind of gregarious behaviors and the lowest level of interpersonal attraction. Meanwhile, it is the embodiment of the human’s sociality. To present the affiliation motivation and raise the clustered phenomenon in social life, we take individuals’ interaction through social ties into consideration. In SMAM, that means nodes can share the popularity of cells with other nodes through social ties, to indirectly influence other nodal choice of destination and raise a phenomenon of aggregation. This is in line with the law of our daily life. In real life, the recommendation from a more intimate friend will have a greater impact on our decisions. In contrast, the recommendation from a general friend might be only a reference to our decisions. Accordingly, in SMAM, we use encounters between pair nodes to describe the strength of social ties between them. A stronger social tie has a stronger influence on the popularity of cells for each node. The popularity of a certain cell for pair nodes, the higher popularity will be influenced by the lower and becomes smaller, and the lower popularity will be influenced by the higher and becomes larger, as shown in Eq. (2). Gradually, nodes’ recognition of each cell shows a gregarious tendency.

4.2 The model in details

More in detail, each node has a so called home which is randomly and uniformly distributed in several certain cells which may take the geographic function like residence communities. However, every node may not stay at home at the beginning of simulation and we set the probability p for the node staying at home, or the node in (1 - p) choose randomly one point over the network area as its starting point.

Before a node decides where to go, it generates a new social need which we call it a task. Then it will put all the cells with the corresponding function into a candidate destination set (CDS), and we define a variable Tc, as shown in Eq. (7).

Then combined with Eq. (4), we can calculate the whole movement intentions of each cell by the following Eq. (8).

Consequently, individuals will move to the cell with max{MI(C)}.

Table 1.Notation

Upon reaching the destination, the node will stay a time interval in [0, Tmax]. Based on the observations that people stay for a long time only in a few places, whereas for most places one stays for a short period of time, we let the distribution of wait-time follows a truncated Levy distribution in [0, Tmax]. Eq. (9) defines a Levy distribution with a scaling factor c and exponent α in terms of a Fourier transformation. It is validated in our simulations that when α was set to 0.75, the curves are closer to human traces. In Fig. 3(a), the probability density distribution of wait time is shown that it follows Levy distribution with the parameters setup α = 0.75 and c = 4. Fig. 3 (b) shows the CCDF of wait time.

Fig. 3.(a) Levy Distribution of wait time where α = 0.75 and c = 4. (b) CCDF of Levy Distribution of wait time where α = 0.75 and c = 4.

For α = 1, it reduces to a Cauchy distribution and for α = 2, a Gaussian with . Asymptotically, for α < 2, f(x) can be approximately by [11].

5. Simulation and validation

5.1 Statistical properties of SMAM

In this section, we simulate three real scenarios whose traces were gathered from mobile devices carried by people, referred as Infocom 05 [23], Cambridge 06 [24] and MIT Reality Traces [20][25], as shown in Table 2. Then we compare and analyze the complementary cumulative distribution function (CCDF) of inter-contact time, contact duration, and the number of contacts for each pair of nodes in RWP, Levy Walks, SLAW, SMAM and real traces. We use the Opportunistic Network Environment (ONE) simulator.

Table 2.Three experimental parameters extracted from real traces

All these datasets are well-known experimental traces. Infocom 05 and Cambridge 06 used the same device Intel iMote while MIT Reality Traces used Smart phones. But all of them utilized Bluetooth, whose communication radius is about 10 meters, to communicate between pair nodes. For another, the duration of Infocom 05 is the shortest about 3 days and Cambridge 06 lasts for 8 days longer, while MIT Reality Traces has the longest duration about 58 days. The data in Infocom 05, Cambridge 06 and MIT Reality Traces were collected every 120 second, 600 second and 300 second respectively, representing different precision of dataset. As we can see, there are 97 devices in MIT Reality Traces, more than two times as much as Infocom 05 and almost three times as much as Cambridge 06. Thus, MIT Reality Traces can be considered as a large-scale scenario with a long duration and a high node density, comparing to the other two scenarios. The varied duration of real traces can be helpful to test the applicable time scope of our mobility model while varied-number of nodes can directly reflect the scale of scenarios. Consequently, the three real trace datasets can effectively validate comparatively whether SMAM could be applied in both small-scale, like Infocom 05 and Cambridge 06, and large-scale scenarios such as MIT Reality Traces.

We set the parameters of synthetic mobility models similar to those extracted respectively from the three real traces and then generate with SMAM, RWP, SLAW and Levy Walks each of the real scenarios, to see how the expected social-aware behaviors of the nodes can be gained. To show accurately the difference between synthetic models and reality traces, we use root-mean-square error (RMSE) to identify the difference degree in Fig. 4-Fig. 6 and Fig. 8-Fig. 10, where Fig. 4-Fig. 6 shows the complementary cumulative distributions of inter-contact time, contact duration and the number of contacts in both real traces and mobility models, and Fig. 8-Fig. 10 shows the performance evaluation results of BUBBLE on real traces and mobility models in terms of delivery ratio, latency average and overhead ratio. The RMSE in Fig. 4-Fig. 6 is presented in Fig. 7 and the RMSE in Fig. 8-Fig. 10 is presented in Fig. 11. The RMSE can be calculated as Eq. (10) [21], where ei(i = 1,2,…,n) presents the errors between the curves of synthetic models and reality traces and equals to the absolute difference.

In Fig. 4, the curves of SMAM are the closest to that of Infocom 05. That’s because SMAM takes full consideration of mobility motivations of students in Infocom 05 scenario, and captures the basic laws of human mobility that is to meet social needs. Therefore, SMAM can depict accurately the statistical features of Infocom 05. As show in Fig. 7(a), RWP has the largest average root-mean-square error. The main reason is that wait time in RWP follows a uniform distribution or Gaussian distribution in [0, Tmax] and doesn’t consider the nodal correlation such as social ties between nodes. Besides, SLAW doesn’t capture the accurate features shown in Infocom 05. Because users don’t have a definite bounded mobility area and closer destinations are not first to go in Infocom 05 which is in contrast to SLAW. Moreover, Levy Walks performs better than RWP and SLAW but still worse than SMAM.

Fig. 4.Infocom 05 vs Synthetic traces: (a) CCDF of the inter-contact time; (b) CCDF of the contact duration; (c) CCDF of the number of contacts.

In Fig. 5, SMAM shows the lowest average root-mean-square errors, in which the RMSEs of inter-contact time distribution, contact duration distribution and contacts number distribution are comparatively smaller than the others. RWP still has the largest average RMSE as we can predict. From Fig. 7(b), it is obvious that Levy Walks doesn’t predict accurately in contacts number as it does in Infocom 05, which results from the frequent generation of short-length walks. However, the truth is that people do not encounter each other as frequently as Levy Walks does. From Fig. 5(c), we can see pair nodes have more encounters in SLAW than in Cambridge 06, which proves that it is not comprehensive to model the human mobility behavior by some statistical features which are shown in the human movement, just as SLAW does.

Fig. 5.Cambridge 06 vs Synthetic traces: (a) CCDF of the inter-contact time; (b) CCDF of the contact duration; (c) CCDF of the number of contacts.

In Fig. 6, SMAM is becoming more and more accurate in the prediction of inter-contact time, contact duration and contacts number with the increasing number of devices and the longer duration of simulation. In Fig. 7(a)-(c), we can see that SMAM has the lowest RMSE in the three scenarios, implying it performs better in simulating MIT Reality Traces, which is a large-scale scenario with a higher node density and a longer duration than Infocom 05 and Cambridge 06. At the same time, all the root-mean-square errors of SMAM in three scenarios are less than 0.1, proving that SMAM is accurate enough to be used to simulating human mobility in varied-scale scenarios. We can see from Fig. 7 that RWP, Levy Walks and SLAW show more significant differences from the curves of MIT Reality Traces than Infocom 05 and Cambridge 06, as the nodes increase and the simulation time extends. However, SMAM has similar root-mean-square errors in the three varied-scale scenarios, which demonstrates that SMAM is more accurate to simulate the statistical characteristics (inter-contact time, contact duration, contacts number) of varied-scale scenarios while RWP, Levy Walks and SLAW are not suitable to simulate human mobility especially in large-scale scenarios such as MIT Reality Traces.

Fig. 6.MIT Reality Traces vs Synthetic traces: (a) CCDF of the inter-contact time; (b) CCDF of the contact duration; (c) CCDF of the number of contacts.

Fig. 7.RMSE in Fig. 4-Fig. 6: (a) RMSE in Infocom 05 corresponding to Fig. 4; (b) RMSE in Cambridge 06 corresponding to Fig. 5; (c) RMSE in MIT Reality Traces corresponding to Fig. 6.

5.2 Performance evaluation of BUBBLE

Mobile opportunistic networks has presented many challenges to the research community, especially in designing suitable, efficient and well performing social routing protocols. The practical analysis and validation of such protocols often depends on synthetic data generated by human mobility models. Therefore, to further validate the accuracy of the social motivation aware mobility model, we run MON simulations on ONE simulator using the representative social based routing protocol BUBBLE [22] on real traces (Infocom 05, Cambridge 06 and MIT Reality Traces) and mobility models (SMAM, Levy Walks, SLAW and RWP) with varied message size. In the experiments, the message delivery ratio, latency average and overhead ratio are collected, which are shown in Fig. 8-Fig. 10. At the same time, to show the detailed difference, we use root-mean-square error (RMSE) to identify the difference degree in Fig. 8-Fig. 10, which can be calculated by Eq. (10).

Fig. 8.Performance Evaluation of BUBBLE on Infocom 05 traces, SMAM, Levy Walks, RWP and SLAW varies by messages with different sizes.

Fig. 9.Performance Evaluation of BUBBLE on Cambridge 06 traces, SMAM, Levy Walks, RWP and SLAW varies by messages with different sizes.

Fig. 10.Performance Evaluation of BUBBLE on MIT Reality traces, SMAM, Levy Walks, RWP and SLAW varies by messages with different sizes.

1) Delivery probability: It is a ratio between the messages number arrives at destination and the number of messages sent. The delivery probability is defined as in Eq. (11).

where D is the number of messages delivered at destination and C is the number of messages created at a source node. High delivery probability means that more messages are delivered to the destination.

2) Latency average: The latency average is an average time taken for a message to reach destination, as defined in Eq. (12).

where n is a number of messages arrived at destination, Ri is the time when a message i reaches the destination, and Ci is the time when a message i is created.

3) Overhead ratio: It is a ratio between the difference, which is between the relayed times of messages and the number of delivered messages, and the number of delivered messages, defined in Eq. (13).

where R is the relayed times of messages and D is the number of delivered messages.

In Fig. 8-Fig. 10, SMAM is proved to be the most accurate in evaluating the performance of typical social routing protocol BUBBLE, which can also be concluded from the detailed RMSE in Fig. 11. Fig. 11 shows the detailed root-mean-square errors between synthetic traces and real traces in Fig. 8-Fig. 10. From Fig. 11(a), we can see that SMAM shows a little better in evaluating the delivery probability of BUBBLE than the other three mobility models under the three scenarios. Besides, SMAM outperforms the other models obviously in latency average evaluation, which can be seen in detail from Fig. 11(b). In Fig. 11(c), SMAM doesn’t show an apparent advantage in overhead ratio evaluation under Infocom 05 and Cambridge 06 except MIT Reality Traces. However, even though SMAM just shows a little better in terms of delivery probability evaluation and overhead ratio evaluation under some scenarios, it still has a good performance in the evaluation of social routing protocols through comprehensive consideration, especially in latency average. Hence we conclude that SMAM is more accurate in the performance evaluation of social routing protocols.

Fig. 11.RMSE in Fig. 8-Fig. 10: (a) RMSE of Delivery Probability; (b) RMSE of Latency Average; (c) RMSE of Overhead Ratio.

6. Conclusions

In this paper, we illustrate the basic laws of human mobility from the psychological point of view, and propose a social motivation-aware mobility model (SMAM) for mobile opportunistic networks. Firstly, to form a widely-used mechanism, we introduce a new concept of geographic functional cells. Each cell is assigned with a geographical function and dynamic popularity for individuals. Then we assume there are a limited number of social needs. To meet these social needs, individuals make choices depending on the expectancy value theory, which considers individuals’ next destinations from two aspects: whether it can meet the current social need; a trade-off between proximity and the popularity of geographic cells. From the above perspective, SMAM presents both the intrinsic and extrinsic factors of human mobility. On the other hand, considering the affiliation motivation of human mobility, the lowest level of interpersonal attraction, SMAM can raise the clustered phenomenon by individuals’ interaction through social ties.

On the other side, we validate our model by comparing the CCDF of inter-contact time, contact duration and number of contacts between pair nodes with both real traces and some classical synthetic mobility models such as SLAW, RWP and Levy Walks, and the results of SMAM shows a better match with the real traces. That presents the accuracy of our mobility model in depicting the main statistical properties of human mobility traces. To further validate our model, we evaluate the BUBBLEs performance on real traces and mobility models (SLAW, RWP, Levy Walks and SMAM) in terms of delivery probability, latency average and overhead ratio. The experimental results also demonstrate that SMAM can accurately evaluate the performance of social based routing protocols. To be concluded, our mobility model shows a better performance in terms of accuracy, easy to use and universal applicability.