Modeling Time-variant User Mobility in Wireless Mobile Networks Wei-jen Hsu ∗ , Thrasyvoulos Spyropoulos † , Konstantinos Psounis ‡ and Ahmed Helmy ∗ ∗ Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, Florida 32611-6120 † INRIA, Sophia-Antipolis, France ‡ Dept. of Electrical Engineering, University of Southern California, Los Angeles, California 90089-2560 Email: wjhsu@ufl.edu, Thrasyvoulos.Spyropoulos@sophia.inria.fr, kpsounis@usc.edu, helmy@cise.ufl.edu Abstract— Realistic mobility models are important to under- stand the performance of routing protocols in wireless ad hoc networks, especially when mobility-assisted routing schemes are employed, which is the case, for example, in delay-tolerant networks (DTNs). In mobility-assisted routing, messages are stored in mobile nodes and carried across the network with nodal mobility. Hence, the delay involved in message delivery is tightly coupled with the properties of nodal mobility. Currently, commonly used mobility models are simplistic random i.i.d. model that do not reflect realistic mobility charac- teristics. In this paper we propose a novel time-variant community mobility model. In this model, we define communities that are visited often by the nodes to capture skewed location visiting preferences, and use time periods with different mobility pa- rameters to create periodical re-appearance of nodes at the same location. We have clearly observed these two properties based on analysis of empirical WLAN traces. In addition to the proposal of a realistic mobility model, we derive analytical expressions to highlight the impact on the hitting time and meeting times if these mobility characteristics are incorporated. These quantities in turn determine the packet delivery delay in mobility-assisted routing settings. Simulation studies show our expressions have error always under 20%, and in 80% of studied cases under 10%. I. I NTRODUCTION In recent years, there has been an exponential growth in the popularity of portable computation and communication devices. Advances in wireless communication technologies and standards have made ubiquitous communication an emerg- ing reality. With the ever expanding deployment of these wireless-capable devices, there is an increasing interest in a new communication paradigm and applications that are made possible through the new opportunities. Ad hoc networks are self-organized, infrastructure-less net- works consist of only wireless devices. In traditional ad hoc networks, it is generally assumed, albeit implicitly, that com- munications between nodes occur through multi-hop, complete paths in space. However, this assumption is in question for several reasons. First, multi-hop spatial routing increases the number of transmissions and channel contention, and hence reduces the capacity of scarce wireless bandwidth [6]. Second, such end-to-end paths may not always exist, given the wide variation of potential adverse settings (e.g., low node den- sity, unpredictable mobility) in which wireless communication may take place. Due to the fore-mentioned reasons, routing schemes falling under the general framework of mobility- assisted routing have been proposed recently, as a measure to improve the wireless network capacity[7] and increase the fea- sibility of communication in more challenged environments[1]. Mobility-assisted routing schemes, as opposed to path-based ad hoc routing protocols, utilize nodal mobility to dissemi- nate messages in the network. In mobility-assisted routing, transmissions from the senders to the receivers are not always completed immediately through a connected, complete multi- hop path. Rather, when a sender moves to close proximity of some other nodes in the network, the packet is forwarded to and stored in these intermediate nodes for potentially long time periods, waiting for the transmission opportunities to other nodes in the network. Instead of being considered as a detrimental factor that makes reliable communication difficult, mobility provides communication opportunities in mobility- assisted routing. Hence, in these settings, mobility and nodal encounter are crucial components to understand the network performance. However, most research studies on mobility-assisted rout- ing assume simplistic mobility models, such as the random walk[3], [4], [5] (in general, i.i.d. models), or a priori knowl- edge of future mobility[2]. These assumptions provide sce- narios amenable to mathematical analysis that provides good insights to system performance. However, these simple mobil- ity models do not address the complexity of nodal mobility in real-life settings. In all these models, all mobile nodes behave statistically identical to each other, and their behaviors do not change with respect to time. As the underlying mobility model is an important factor of the performance of mobility-assisted routing schemes, there is an increasing need for mobility models that capture the realistic mobility characteristics and remain mathematically manageable. Our main contribution in this paper is the proposal of a time-variant community mobility model. The model captures several important mobility characteristics we observed from empirical wireless LAN (WLAN) traces. Specifically, we utilize the WLAN traces from the archives at [22] and [23] to understand the prominent mobility characteristics of current wireless network users in university campuses and corporate buildings. We have identified skewed location visiting prefer- ences and periodical re-appearance at the same location as two prominent trends existing in multiple traces[12]. 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