Mobility causes network structures to change. In PSNs where underlying network structure is changing rapidly, we are interested in studying how information dissemination can be enhanced in a sparse disconnected network where nodes lack the global knowledge about the network. We use beamforming to study the enhancement in the information dissemination process. In order to identify potential beamformers and nodes to which beams should be directed we use the concept of stability. We first predict the stability of a node in the dynamic network using truncated levy walk nature of jump lengths of human mobility and then use this measure to identify beamforming nodes and the nodes to which the beams are directed. We also develop our algorithm such that it does not require any global knowledge about the network and works in a distributed manner. We also show the effect of various parameters such as number of sources, number of packets, mobility parameters, antenna parameters, type of stability used and density of the network on information dissemination in the network. We validate our findings with three validation model, no beamforming, beamforming using different stability measure and when no stability measure is associated but same number of node beamform and the selection of the beamforming nodes is random. Our simulation results show that information dissemination can be enhanced using our algorithm over other models.
Many mobility models have been proposed that capture the characteristics of human mobility. A comprehensive survey of mobility properties associated with humans can be found in @cite_11 @cite_6 , while a clear difference between different human mobility models can also be found in @cite_11 . Most of the traditional models on human mobility use spatial properties of human mobility in the model. However, it was brought up that human mobility also has temporal characteristics and follows truncated power law distribution. Truncated Power Law is characterized by a probability distribution that has the properties of a power law with an exponential cutoff, eq. where proportionality constant is equal to @math , @math is the power law decay exponent constant while @math is the cutoff value. Truncated power law distribution means that the distribution starts as a power law and ends as an exponential curve. The exponential cutoff is because @math r_ g @math @math @math @math @math r_ g $. We next provide a brief overview of antenna models and beamforming in section .
@cite_6 @cite_11
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We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of intercontact 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 intercontact time has a power law tail, and that common mobility models are not adequate. However, we observe that the timescale 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 intercontact time as 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. 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 powerlaw 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 way point can exhibit the same dichotomy in the distribution of inter-contact time ascin 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 basedon power-law tails might be overly pessimistic. The routing performance of delay tolerant networks (DTN) is highly correlated with the distribution of inter-contact times (ICT), the time period between two successive contacts of the same two mobile nodes. As humans are often carriers of mobile communication devices, studying the patterns of human mobility is an essential tool to understand the performance of DTN protocols. From measurement studies of human contact behaviors, we find that their distributions closely resemble a form of power-law distributions called truncated Pareto. Human walk traces has a dichotomy distribution pattern of ICT; it has a power-law tendency up to some time, and decays exponentially after that time. Truncated Pareto distributions offer a simple yet cohesive mathematical model to express this dichotomy in the measured data. Using the residual and relaxation time theory [17] [4], we apply truncated Pareto distributions to quantify the performance of opportunistic routing in DTN. We further show that Truncated Levy walk (TLW) mobility model [22] commonly used in biology to describe the foraging patterns of animals [25], provide the same truncated power-law ICT distributions as observed from the empirical data, especially when mobility is confined within a finite area. This result confirms our recent finding that human walks contain similar statistical characteristics as Levy walks [22]. Individual human trajectories are characterized by fat-tailed distributions of jump sizes and waiting times, suggesting the relevance of continuous-time random-walk (CTRW) models for human mobility. However, human traces are barely random. Given the importance of human mobility, from epidemic modelling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile-phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model accounts for the empirically observed scaling laws, but also allows us to analytically predict most of the pertinent scaling exponents.