A Reaction-Diffusion Model for Epidemic Routing in Sparsely Connected MANETs

Abstract

Abstract-We propose and investigate a deterministic traveling wave model for the progress of epidemic routing in disconnected mobile ad hoc networks. In epidemic routing, broadcast or unicast is achieved by exploiting mobility: message-carrying nodes "infect" non message-carrying nodes when they come within communication range of them. Early probabilistic analyses of epidemic routing follow a "well-mixed" model which ignores the spatial distribution of the infected nodes, and hence do not provide good performance estimates unless the node density is very low. More recent work has pointed out that the infection exhibits wave-like characteristics, but does not provide a detailed model of the wave propagation. In this paper, we model message propagation using a reaction-diffusion partial differential equation that has a traveling wave solution, and show that the performance predictions made by the model closely match simulations in regimes where the well-mixed model breaks down. In particular, we show that well-mixed models are generally overly optimistic in regard to the scaling of the message delivery delay with problem parameters such as communication range, node density, and total area. In contrast to prior work, our model provides insight into the spatial distribution of the "infection," and reveals that the performance is sensitive to the geometry of the deployment region, not just its area. I. INTRODUCTIONWe consider the problem of message dissemination in disconnected mobile ad hoc networks (MANETs). Such delaytolerant networks arise naturally in many contexts, including battlefield communication networks, animal tag based sensor networks [1], [2], and emergency response networks. In this setting, a given source node may be unable to reach its intended destination using multiple hops of communication for the current network topology. Instead, knowledge of the message spreads like an infection through the nodes as they employ short-range broadcast opportunistically; hence the commonly used term epidemic routing. Eventual delivery of the message is guaranteed for typical mobility models, so the main focus is on understanding how performance metrics such as end-to-end delay and memory requirements scale as a function of parameters such as the number of nodes, the communication range, the mobility model, and the geometry of the region over which the network is deployed. To this end, we derive a partial differential equation (PDE) model for the dissemination of information via epidemic routing.Early analyses of epidemic routing employ a mathematical simplification that applies for exceedingly sparse deployments

Spatial Representations and Analysis Techniques

“…Connectivity models provide an abstraction of mobility models in that they provide information about intercontact time [52]. Stochastic geometry has been applied to wireless networks [2] and epidemiological approaches using PDEs have been used for routing in networks [57].…”

Cooperative navigation in robotic swarms

“…This means that message spreading depends on a combination of robot mobility and message communication. Several studies investigated message spreading in sparsely connected MANETs [28], [29], [30], [31], [32]. In case robot density is not extremely sparse, so that robots can communicate with others relatively frequently, new messages spread from T in an expanding wave-like propagation [31], [32].…”

Adaptive Online Estimation of Temporal Connectivity in Dynamic Wireless Networks

“…There is a fair amount of related work that studies the delay for information dissemination in wireless networks [5], [6], [9], [13], [14], [23]. We observe that these works are either restricted to analysis, or they focus on specific scenarios of node topology.…”

“…This sets the context for enabling self-* applications, in which nodes can tune parameters such as the message sending rate in data networks, or the extent of interaction between participants at a conference. Existing works [6], [13], [14] analyze the dissemination delay in mobile wireless networks from a purely spatial perspective. That is, the network is always connected at any point in time.…”