When nodes in a mobile network cluster together or move according to common external factors (e.g., cars that follow the road network), the resulting contact patterns become correlated. In this work we address the question of modelling such correlated mobility movements for the analysis of intermittently connected networks. We propose to use the concept of node colouring time to characterise dynamic node contact patterns. We analyse how this model compares to existing work, and demonstrate how to extract the relevant data from actual trace files. Moreover, we show how this information can be used to derive the latency distribution of DTN routing protocols. Our model achieves a very good fit to simulated results based on real vehicular mobility traces, whereas models which assumes independent contacts do not.
Our work on the other hand, suggests that the exact characteristic of the inter-contact distribution is less relevant when contacts are not independent. Correlated and heterogeneous mobility and the effect on routing have recently been discussed in several papers @cite_6 @cite_16 @cite_4 @cite_26 , but to our knowledge, we are the first to provide a framework that accurately captures the routing latency distribution for real traces with heterogeneous and correlated movements.
@cite_16 @cite_4 @cite_6 @cite_26
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In this paper we focus on how the heterogeneous contact dynamics of mobile nodes impact the performance of forwarding routing algorithms in delay disruption-tolerant networks (DTNs). To this end, we consider two representative heterogeneous network models, each of which captures heterogeneity among node pairs (individual) and heterogeneity in underlying environment (spatial), respectively, and examine the full extent of difference in delay performances they cause on forwarding routing algorithms through formal stochastic comparisons. We first show that these heterogeneous models correctly capture non-Poisson contact dynamics observed in real traces. Then, we consider direct forwarding and multicopy two-hop relay protocol and rigorously establish stochastic convex ordering relationships on their delay performances under these heterogeneous models and the corresponding homogeneous model, all of which have the same average inter-contact time over all node pairs. We show that heterogeneous models predict an entirely opposite ordering relationship in the delay performances depending on which of the two heterogeneities is captured. This suggests that merely capturing non-Poisson contact dynamics - even if the entire distribution of aggregated inter-contact time is precisely matched, is not enough and that one should carefully evaluate the performance of forwarding routing algorithms under a properly chosen heterogeneous network setting. Our results will also be useful in correctly exploiting the underlying heterogeneity structure so as to achieve better performance in DTNs. 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. A pioneering body of work in the area of mobile opportunistic networks has shown that characterising inter-contact times between pairs of nodes is crucial. In particular, when inter-contact times follow a power-law distribution, the expected delay of a large family of forwarding protocols may be infinite. The most common approach adopted in the literature to study inter-contact times consists in looking at the distribution of the inter-contact times aggregated over all nodes pairs, assuming it correctly represents the distributions of individual pairs. In this paper we challenge this assumption. We present an analytical model that describes the dependence between the individual pairs and the aggregate distributions. By using the model we show that in heterogeneous networks - when not all pairs contact patterns are the same - most of the time the aggregate distribution is not representative of the individual pairs distributions, and that looking at the aggregate can lead to completely wrong conclusions on the key properties of the network. For example, we show that aggregate power-law inter-contact times (suggesting infinite expected delays) can frequently emerge in networks where individual pairs inter-contact times are exponentially distributed (meaning that the expected delay is finite). From a complementary standpoint, our results show that heterogeneity of individual pairs contact patterns plays a crucial role in determining the aggregate inter-contact times statistics, and that focusing on the latter only can be misleading. Recent discovery of the mixture (power-law and exponential) behavior of inter-meeting time distribution of mobile nodes presents new challenge to the problem of mobility modeling and its effect on the network performance. Existing studies on this problem via the average inter-meeting time become insufficient when the inter-meeting time distribution starts to deviate from exponential one. This insufficiency necessarily leads to the increasing difficulty in the performance analysis of forwarding algorithms in mobile ad-hoc networks (MANET). In this paper, we analyze the effect of mobility patterns on the inter-meeting time distribution. We first identify the critical timescale in the inter-meeting distribution, at which the transition from power-law to exponential takes place, in terms of the domain size and the statistics of the mobility pattern. We then prove that stronger correlations in mobility patterns lead to heavier (non-exponential) 'head' of the inter-meeting time distribution. We also prove that there exists an invariance property for several contact-based metrics such as inter-meeting, contact, inter-any-contact time under both distance-based (Boolean) and physical interference (SINR) based models, in that the averages of those contact-based metrics do not depend on the degree of correlations in the mobility patterns. Our results collectively suggest a convex ordering relationship among inter-meeting times of various mobility models indexed by their degrees of correlation, which is in good agreement with the ordering of network performance under a set of mobility patterns whose inter-meeting time distributions have power-law 'head' followed by exponential 'tail'.