Different from the conventional social network where users use the desktop computers, users take mobile devices to access MSNs [56-58]. As users may change their locations during moving, the network topology and communication status become dynamic. Mobility of users plays a crucial role in the performance of social network applications such as content sharing, spreading and search. To design the efficient protocols and algorithms in MSNs, the mobility features should be studied.

Lin et al. [59] propose a random waypoint model for MSNs, in which each user selects a random destination and moves to the destination by a random speed. By considering the distance and speed, [59] can obtain an accurate derivation of distribution functions for the steady state. Kim et al. [60] develop a mobility model of users movements among Wi-Fi access points (APs). The authors collect the number of visitors on each AP and aggregate multiple days log into a single day to study the hourly arrival and departure rates on each AP. Lee et al. [61] use the semi-Markov process to develop a mathematical model to characterize both the steady-state and transient behaviors of users among APs. The steady-state behavior is to estimate the time that the user connects with an AP and the transient behavior is to predict the user’s future locations.

Bettstetter et al. [62] study the node distribution by using the random waypoint mobility model and propose a general mobility model in which the pause time is arbitrarily chosen in the node’s waypoint. The structure of distribution is shown by using three independent components which are the pause, static, and mobility component. Resta et al. [63] study the relation between nodes’ mobility and the QoS. The authors propose a wireless QoS-aware mobility model which contains a user mobility model, a user traffic model, a wireless technology model and a QoS model. Balazinska [64] examine a trace with 1366 users and 117 APs over 4weeks and focus on the study of population characteristics, load distribution among APs and node mobility.

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