We present an empirical registration model derived from the WLAN registration patterns of the mobile users. There exist models that accurately describe individually the spatial and temporal aspects of user registration, and demonstrate the importance of this modeling. The main distinction of the new model from the previous empirical models is that we are able to formulate the inter-dependence of space and time explicitly by a set of few equations. Our extensive studies of the WLAN traces indicate that a simple but proper notion of popularity radient suffices to capture the correlation across space and time. Indeed, when locations (i.e., AP coverage area) are differentiated with respect to the number of visits they are receiving (i.e., AP popularity), the time spent at each location i before user moves from i to k turns out to be closely related to the difference of popularity between locations i and k This observation led to the design of a joint time-space registration model (referred to as ModelT++) that builds upon the Model T, which itself models only the space aspect of the registration, but is derived from the same campus WiFi network. As part of the process of generating a joint space-time model, we further extend spatial aspects of the Model T. We evaluate our model using various metrics against a random walk model as well as the Model T by superimposing location independent time series on these space-only registration models. Our results suggest that with a slight increase in the model complexity, our joint time-space registration model is able to better capture the real network registration than the independent time models. Model T++ can be easily integrated into both WLAN and multi-hop wireless mesh network simulations that require realistic registration models.

We derive an empirical model for spatial registration patterns of mobile users as they move within a campus wireless local area network (WLAN) environment and register at different access points. Such a model can be very useful in a variety of simulation studies of the performance of mobile wireless systems, such as that of resource management and mobility management protocols. We base the model on extensive experimental data from a campus WiFi LAN installation, representing traces from about 6000 users over a period of about 2 years. We divide the empirical data available to us into training and test data sets, develop the model based on the training set, and evaluate it against the test set.The model shows that user registration patterns exhibit a distinct hierarchy, and that WLAN access points (APs) can be clustered based on registration patterns. Cluster size distributions are highly skewed, as are intra-cluster transition probabilities and trace lengths, which can all be modeled well by the heavy-tailed Weibull distribution. The fraction of popular APs in a cluster, as a function of cluster size, can be modeled by exponential distributions. There is general similarity across hierarchies, in that inter-cluster registration patterns tend to have the same characteristics and distributions as intra-cluster patterns.We generate synthetic traces for intra-cluster transitions, inter-cluster transitions, and complete traces, and compare them against the corresponding traces from the test set. We define a set of metrics that evaluate how well the model captures the empirical features it is trying to represent. We find that the synthetic traces agree very well with the test set in terms of the metrics. We also compare the model to a simple modified random waypoint model as a baseline, and show the latter is not at all representative of the real data.The user of the model has the opportunity to use it as is, or can modify model parameters, such as the degree of randomness in registration patterns. We close with a brief discussion of further work to refine and extend the model.