We study delay tolerant networking (DTN) and in particular, its capacity to store, carry and forward messages so that the messages eventually reach their final destinations. We approach this broad question in the framework of percolation theory. To this end, we assume an elementary mobility model, where nodes arrive to an infinite plane according to a Poisson point process, move a certain distance L, and then depart. In this setting, we characterize the mean density of nodes required to support DTN style networking. In particular, under the given assumptions, we show that DTN is feasible when the mean node degree is greater than 4 e(g), where parameter g=L d is the ratio of the distance L to the transmission range d, and e(g) is the critical reduced number density of tilted cylinders in a directed continuum percolation model. By means of Monte Carlo simulations, we give numerical values for e(g). The asymptotic behavior of e(g) when g tends to infinity is also derived from a fluid flow analysis.
We assume epidemic routing which was proposed by Vahdat and Becker in @cite_2 . The operational principle is very simple: whenever two nodes meet they exchange the messages only one of them has. The performance analysis of the epidemic routing often assumes exponentially distributed (i.i.d.) inter-meeting times leading to Markovian models @cite_7 . As the size of the network grows, solving Markov chains becomes infeasible, and , in @cite_21 obtained ODEs as a fluid limit of such Markovian models. In above work, the spatial dimension has been abstracted away.
@cite_21 @cite_7 @cite_2
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Epidemic routing has been proposed as a robust transmission scheme for sparse mobile ad hoc networks. Under the assumption of no contention, epidemic routing has the minimum end-to-end delay amongst all the routing schemes proposed for such networks. The assumption of no contention was justified by arguing that since the network is sparse, there will be very few simultaneous transmissions. Some recent papers have shown through simulations that this argument is not correct and that contention cannot be ignored while analyzing the performance of routing schemes, even in sparse networks.Incorporating contention in the analysis has always been a hard problem and hence its effect has been studied mostly through simulations only. In this paper, we find analytical expressions for the delay performance of epidemic routing with contention. We include all the three main manifestations of contention, namely (i) the finite bandwidth of the link which limits the number of packets two nodes can exchange, (ii) the scheduling of transmissions between nearby nodes which is needed to avoid excessive interference, and (iii) the interference from transmissions outside the scheduling area. The accuracy of the analysis is verified via simulations. In this paper, we develop a rigorous, unified framework based on ordinary differential equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study of Markovian models is quite complex and numerical solution impractical for large networks, the corresponding ODE models yield closed-form expressions for several performance metrics of interest, and a numerical solution complexity that does not increase with the number of nodes. Using this ODE approach, we investigate how resources such as buffer space and the number of copies made for a packet can be traded for faster delivery, illustrating the differences among various forwarding and recovery schemes considered. We perform model validations through simulation studies. Finally we consider the effect of buffer management by complementing the forwarding models with Markovian and fluid buffer models. Epidemic routing has been proposed to reduce the data transmission delay in disruption tolerant wireless networks, in which data can be replicated along multiple opportunistic paths as different nodes move within each other's communication range. With the advent of network coding, it is intuitive that data can not only be replicated, but also coded, when the transmission opportunity arises. However, will opportunistic communication with network coding perform any better than simple replications? In this paper, we present a stochastic analytical framework to study the performance of epidemic routing using network coding in opportunistic networks, as compared to the use of replication. We analytically show that network coding is superior when bandwidth and node buffers are limited, reflecting more realistic scenarios. Our analytical study is able to provide further insights towards future designs of efficient data communication protocols using network coding. As an example, we propose a priority based coding protocol, with which the destination can decode a high priority subset of the data much earlier than it can decode any data without the use of priorities. The correctness of our analytical results has also been confirmed by our extensive simulations. Epidemic outbreaks in human populations are facilitated by the underlying transportation network. We consider strategies for containing a viral spreading process by optimally allocating a limited budget to three types of protection resources: (i) Traffic control resources, (ii), preventative resources and (iii) corrective resources. Traffic control resources are employed to impose restrictions on the traffic flowing across directed edges in the transportation network. Preventative resources are allocated to nodes to reduce the probability of infection at that node (e.g. vaccines), and corrective resources are allocated to nodes to increase the recovery rate at that node (e.g. antidotes). We assume these resources have monetary costs associated with them, from which we formalize an optimal budget allocation problem which maximizes containment of the infection. We present a polynomial time solution to the optimal budget allocation problem using Geometric Programming (GP) for an arbitrary weighted and directed contact network and a large class of resource cost functions. We illustrate our approach by designing optimal traffic control strategies to contain an epidemic outbreak that propagates through a real-world air transportation network.