Abstract-We define "random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm calculus to study the model and give a necessary and sufficient condition for a stationary regime to exist. When this condition is satisfied, we compute the stationary regime and give an algorithm to start a simulation in steady state (perfect simulation). The algorithm does not require the knowledge of geometric constants. For the special case of random waypoint, we provide for the first time a proof and a sufficient and necessary condition of the existence of a stationary regime. Further, we extend its applicability to a broad class of non convex and multi-site examples, and provide a ready-to-use algorithm for perfect simulation. For the special case of random walks with reflection or wrapping, we show that, in the stationary regime, the mobile location is uniformly distributed and is independent of the speed vector, and that there is no speed decay. Our framework provides a rich set of well understood models that can be used to simulate mobile networks with independent node movements. Our perfect sampling is implemented to use with ns-2, and it is freely available to download from http://ica1www.epfl.ch/RandomTrip.

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Abstract-Ultra-Wide Band (UWB) is an emerging wireless physical layer technology that uses a very large bandwidth. We are interested in finding the design objectives of the medium access (MAC, namely, power control and scheduling) and routing protocols of a multi-hop, best-effort, UWB network. Our objective is to maximize flow rates (more precisely, log-utility of flow rates) given node power constraints. The specificity of UWB is expressed by the linear dependence between rate and signal-to-noise ratio at the receiver. It is known that, in wireless networks, different routing strategies can imply differences in MAC protocol design. Hence we search for the jointly optimal routing, scheduling and power control.We find that the optimal solution is characterized by the following. (1) When data is being sent over a link, it is optimal to have an exclusion region around the destination, in which all nodes remain silent during transmission, whereas nodes outside of this region can transmit in parallel, regardless of the interference they produce at the destination. Additionally, the source adapts its transmission rate according to the level of interference at the destination due to sources outside of the exclusion region.(2) The optimal size of this exclusion region depends only on the transmission power of the source of the link, and not on the length of the link nor on positions of nodes in its vicinity. (3) Each node in a given time slot either sends data at the maximum power, or does not send at all. As for the routing, we restrict ourselves to a subset of routes where on each successive hop we decrease the distance toward the destination, and we show that (4) relaying along a minimum energy and loss route is always better than using longer hops or sending directly, which is not obvious since we optimize rate and not power consumption. Finally (5), the design of the optimal MAC protocol is independent of the choice of the routing protocol. For narrow-band networks, (2), (4) and (5) do not hold, which shows that the design of an UWB network should be addressed in a different way than for narrow-band.Our technical approach is based on expressing the design requirements as a mathematical optimization problem. We solve it exactly for simple networks on a line and approximately on random topologies in a plane with up to 50 nodes with various power constraints, traffic matrices, and mobility parameters.

We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of inter-contact times between mobile devices. Using a diverse set of measured mobility traces, we find as an invariant property that there is a characteristic time, order of half a day, beyond which the distribution decays exponentially. Up to this value, the distribution in many cases follows a power law, as shown in recent work. This power law finding was previously used to support the hypothesis that inter-contact time has a power law tail, and that common mobility models are not adequate. However, we observe that the time scale of interest for opportunistic forwarding may be of the same order as the characteristic time, and thus the exponential tail is important. We further show that already simple models such as random walk and random waypoint can exhibit the same dichotomy in the distribution of inter-contact time asc in empirical traces. Finally, we perform an extensive analysis of several properties of human mobility patterns across several dimensions, and we present empirical evidence that the return time of a mobile device to its favorite location site may already explain the observed dichotomy. Our findings suggest that existing results on the performance of forwarding schemes based on power-law tails might be overly pessimistic.