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Clearly, the two goals above are conflicting: the more realistic the model is, the more the details that must be included in it, and the model complexity increases. Thus, a synthetic mobility model should be a good compromise between representativeness and simplicity, that is, it should consider the salient features of a certain movement pattern, while disregarding secondary details.
In this section, we briefly describe the most important mobility models used in the simulation of ad hoc/sensor networks. For a more detailed description of mobility models for ad hoc networks, see (Bettstetter 2001a; Camp et al. 2002).
Random waypoint model. This is by far the most commonly used mobility model for ad hoc networks. One of the reasons for its popularity is the fact that it is implemented in network simulations tools such as Ns2 (Ns2 2002) and GloMoSim (Zeng et al. 1998). The Random Waypoint (RWP) model has been introduced in (Johnson and Maltz 1996) to study the performance of the DSR routing protocol. In this model, each node chooses uniformly at random a destination point (the ‘waypoint’) within the deployment region R, and moves toward it along a straight line. Node velocity is chosen uniformly at random in the interval [vmm, vmax], where vmin and vmax are the minimum and maximum node velocities. When the node arrives at destination, it remains stationary for a predefined pause time, and then starts moving again according to the same pattern.
The RWP model is representative of an individual movement, obstacle-free scenario: each node moves independent of each other (individual movement), and it can potentially move in any subregion of R (obstacle-free). For instance, a similar type of mobility could arise when users move in a large room, or in a open air, flat environment.
Given its popularity, RWP mobility has been deeply studied in the literature. In particular, it has been recently discovered that the long-term node spatial distribution of RWP mobile networks is concentrated in the center of the deployment region (border effect) (Bettstetter and Krause 2001; Bettstetter et al. 2003; Blough et al. 2004), and that the average nodal speed, defined as the average of the node velocities at a given instant of time, decreases over time (Yoon et al. 2003). These observations have brought to the attention of the community the fact that RWP mobile networks must be carefully simulated. In particular, network performance should be evaluated only after a certain ‘warm-up’ period, which must be long enough for the network to reach the node spatial and average velocity ‘steady-state’ distribution.
The RWP model has also been generalized to slightly more realistic, though still simple, models. For instance, in (Bettstetter et al. 2003) the RWP model is extended by allowing nodes to choose pause times from an arbitrary probability distribution. Furthermore, a random fraction of the network nodes remains stationary for the entire simulation time.
Random direction model. Similar to the RWP model, the random direction model resembles individual, obstacle-free movement. This model was created to maintain a uniform node spatial distribution during the simulation time, thus avoiding the border effect typical of RWP mobility.
MODELING AD HOC NETWORKS
In this model (Royer et al. 2001), any node chooses a direction uniformly at random in the interval [0, 2n], and a random velocity in the interval [r>min, umax]. Then, it starts moving in the selected direction with the chosen velocity. When the node reaches the boundary of R, it chooses a new direction and velocity, and so on.
Variants of this model have also been presented. In a first variant (Haas and Pearlman 1998; Pearlman et al. 2000b), a node is ‘bounced back’ when it reaches the boundary of the deployment region. In another (Bettstetter 2001b), the node moves for a random (exponentially distributed) time, and then it changes direction and velocity of movement.
Brownian-like motion. Contrary to the case of RWP and random direction mobility, which resemble intentional movement, the class of Brownian-like mobility models resembles nonintentional motion. For this reason, these models are sometimes called drunkardlike models.
In Brownian-like motion, the position of a node at a given time step depends (in a certain, probabilistic, way) on the node position at the previous step. In particular, no explicit modeling of movement direction and velocity is used in this model.
An example of Brownian-like motion is the model used in (Santi and Blough 2003). Mobility is modeled using three parameters: pstat, pmove and m. The first parameter represents the probability that a node remains stationary for the entire simulation time. Parameter pmove is the probability that a node moves at a given time step. Parameter m models, to some extent, velocity: if a node is moving at step i, its position at step i + 1 is chosen uniformly at random in the square or side 2m centered at the current node position.