Tracking message spread in mobile delay tolerant networks

We consider a delay tolerant network under two message forwarding schemes-a non-replicative direct delivery scheme and a replicative epidemic routing scheme. Our objective is to track the degree of spread of a message in the network. Such estimation can be used for on-line control of message dissemination. With a homogeneous mobility model with pairwise i.i.d. exponential inter-meeting times, we rigorously derive the system dynamic and measurement equations for optimal tracking by a Kalman filter. Moreover, we provide a framework for tracking a large class of processes that can be modeled as density-dependent Markov chains. We also apply the same filter with a heterogeneous mobility, where the aggregate inter-meeting times exhibit a power law with exponential tail as in real-world mobility traces, and show that the performance of the filter is comparable to that with homogeneous mobility. Through customized simulations, we demonstrate the trade-offs and provide several insightful observations on how the number of observers impacts the filter performance.