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.

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.

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.

No abstract

Population protocols, roughly defined as systems consisting of large numbers of simple identical agents, interacting at random and updating their state following simple rules, are an important research topic at the intersection of distributed computing and biology. One of the fundamental tasks that a population protocol may solve is majority: each node starts in one of two states; the goal is for all nodes to reach a correct consensus on which of the two states was initially the majority. Despite considerable research effort, known protocols for this problem are either exact but slow (taking linear parallel time to converge), or fast but approximate (with non-zero probability of error).In this paper, we show that this trade-off between precision and speed is not inherent. We present a new protocol called Average and Conquer (AVC) that solves majority exactly in expected parallel convergence time O(log n/(s ) + log n log s), where n is the number of nodes, n is the initial node advantage of the majority state, and s = Ω(log n log log n) is the number of states the protocol employs. This shows that the majority problem can be solved exactly in time poly-logarithmic in n, provided that the memory per node is s = Ω(1/ + log n log 1/ ). On the negative side, we establish a lower bound of Ω(1/ ) on the expected parallel convergence time for the case of four memory states per node, and a lower bound of Ω(log n) parallel time for protocols using any number of memory states per node.