5.2.3 Dealing with Mobility
The mobility concept is basically the same one used in cellular networks where the system is organized in groups or clusters of cells to form location areas. The system periodically will order the mobiles to update their information, thus producing data that help to determine the location of such nodes within a certain accuracy range since a location area and a cell and sometimes a sector are known for each user.
If one wants to provide a user's absolute or relative coordinates, any of the techniques discussed in Chapters 2, 3, and 4 are useful. Some concepts can be based on deployment area organization with the use of attractors to indicate locales where user density increases at certain periods of time during the day (e.g., stadiums, malls, and college campuses).
We are interested in predicting the position and mobility of cellular customers, and in determining other parameters like blocking probability in a cellular system. We use the concept of social grouping behavior as an open-and closed-migration process with transition rates given by Kelly :
where φj(nj) = djnj, and ψk(nk) = ak + cknk; ak is the attractiveness to an outside; user of belonging to group k; ck is the attractiveness to an outsider of being an individual in group k; dj is the propensity of an individual to depart from group j of an individual in group j; λjk is a measure of the mobility of a user from groups j and k; and nk is the number of active users in attractor k.
We consider a city to be a finite associated group of zones of activity called attractors, where the number of customers varies according to an attractor's characteristics and its relationship with other adjacent attractors. An attractor is a site that attracts customer movement and at which they remain for a given time (e.g., work areas, residential areas, entertainment areas, shopping centers, theaters).
We define the attractor according to cellular customers; in order to determine the attractors present in a certain zone or cell, we have to analyze the customers, hour of the day and geographical area, and characteristics and interrelation with other attractors. The characteristics of each attractor used in Equation (5.5) now become dependent on time; that is, ak(t), ck(t), dk(t), λjk(t), and nk(t).
We consider a set of J attractors, but we shall allow customers to enter and leave the system as well as to move between attractors; thus Tj. represents a customer leaving the system from a attractor j, T.k represents a customer entering the system to attractor k, and Tjk represents a customer moving from the attractor j to k. We also introduce another factor into the equation that we define as geographical feasibility, which is the parameter that indicates how easily customers can move from one attractor to another as shown in Figure 5.16.
FIGURE 5.16 Feasibility between attractors.
The parameter λjk(t) allows us to measure the mobility of customers from attractor j to k, and is given by
Then we can predict the number of active customers in attractor j at time t, nj(t), by
This simple model helps us organize a network into areas where feasibility parameters and mobility are considered in order to predict user numbers. The number of users can be employed to calculate the amount of traffic expected to be offered to the network in erlangs, which in turn will determine the number of channels needed at a certain grade-of-service level. Base stations must be close to attractors with greater population than others. Further results with this mobility model are in Baca  and Bermudez .