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
2109528718 2105273407 1572481965
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. A stochastic model is introduced that accurately models the message delay in mobile ad hoc networks where nodes relay messages and the networks are sparsely populated. The model has only two input parameters: the number of nodes and the parameter of an exponential distribution which describes the time until two random mobiles come within communication range of one another. Closed-form expressions are obtained for the Laplace-Stieltjes transform of the message delay, defined as the time needed to transfer a message between a source and a destination. From this we derive both a closed-form expression and an asymptotic approximation (as a function of the number of nodes) of the expected message delay. As an additional result, the probability distribution function is obtained for the number of copies of the message at the time the message is delivered. These calculations are carried out for two protocols: the two-hop multicopy and the unrestricted multicopy protocols. It is shown that despite its simplicity, the model accurately predicts the message delay for both relay strategies for a number of mobility models (the random waypoint, random direction and the random walker mobility models). Mobile ad hoc routing protocols allow nodes with wireless adaptors to communicate with one another without any pre-existing network infrastructure. Existing ad hoc routing protocols, while robust to rapidly changing network topology, assume the presence of a connected path from source to destination. Given power limitations, the advent of short-range wireless networks, and the wide physical conditions over which ad hoc networks must be deployed, in some scenarios it is likely that this assumption is invalid. In this work, we develop techniques to deliver messages in the case where there is never a connected path from source to destination or when a network partition exists at the time a message is originated. To this end, we introduce Epidemic Routing, where random pair-wise exchanges of messages among mobile hosts ensure eventual message delivery. The goals of Epidemic Routing are to: i) maximize message delivery rate, ii) minimize message latency, and iii) minimize the total resources consumed in message delivery. Through an implementation in the Monarch simulator, we show that Epidemic Routing achieves eventual delivery of 100 of messages with reasonable aggregate resource consumption in a number of interesting scenarios.