296 research outputs found

    The age of information in gossip networks

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    We introduce models of gossip based communication networks in which each node is simultaneously a sensor, a relay and a user of information. We model the status of ages of information between nodes as a discrete time Markov chain. In this setting a gossip transmission policy is a decision made at each node regarding what type of information to relay at any given time (if any). When transmission policies are based on random decisions, we are able to analyze the age of information in certain illustrative structured examples either by means of an explicit analysis, an algorithm or asymptotic approximations. Our key contribution is presenting this class of models.Comment: 15 pages, 8 figure

    Asymptotic behavior of Aldous' gossip process

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    Aldous [(2007) Preprint] defined a gossip process in which space is a discrete N×NN\times N torus, and the state of the process at time tt is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate NαN^{-\alpha} to a site chosen at random from the torus. We will be interested in the case in which α<3\alpha<3, where the long range transmission significantly accelerates the time at which everyone knows the information. We prove three results that precisely describe the spread of information in a slightly simplified model on the real torus. The time until everyone knows the information is asymptotically T=(22α/3)Nα/3logNT=(2-2\alpha/3)N^{\alpha/3}\log N. If ρs\rho_s is the fraction of the population who know the information at time ss and ε\varepsilon is small then, for large NN, the time until ρs\rho_s reaches ε\varepsilon is T(ε)T+Nα/3log(3ε/M)T(\varepsilon)\approx T+N^{\alpha/3}\log (3\varepsilon /M), where MM is a random variable determined by the early spread of the information. The value of ρs\rho_s at time s=T(1/3)+tNα/3s=T(1/3)+tN^{\alpha/3} is almost a deterministic function h(t)h(t) which satisfies an odd looking integro-differential equation. The last result confirms a heuristic calculation of Aldous.Comment: Published in at http://dx.doi.org/10.1214/10-AAP750 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Epidemic Spreading with External Agents

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    We study epidemic spreading processes in large networks, when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\`a-vis the underlying network topology. For networks which are `spatially constrained', we show that the spread of infection can be significantly speeded up even by a few such external agents infecting randomly. Moreover, for general networks, we derive upper-bounds on the order of the spreading time achieved by certain simple (random/greedy) external-spreading policies. Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external-spreading policies; these adversarial lower bounds match (up to logarithmic factors) the spreading time achieved by an external agent with a random spreading policy. This demonstrates that random, state-oblivious infection-spreading by an external agent is in fact order-wise optimal for spreading in such spatially constrained networks

    Gossip routing, percolation, and restart in wireless multi-hop networks

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    Route and service discovery in wireless multi-hop networks applies flooding or gossip routing to disseminate and gather information. Since packets may get lost, retransmissions of lost packets are required. In many protocols the retransmission timeout is fixed in the protocol specification. In this technical report we demonstrate that optimization of the timeout is required in order to ensure proper functioning of flooding schemes. Based on an experimental study, we apply percolation theory and derive analytical models for computing the optimal restart timeout. To the best of our knowledge, this is the first comprehensive study of gossip routing, percolation, and restart in this context

    A survey of flooding, gossip routing, and related schemes for wireless multi- hop networks

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    Flooding is an essential and critical service in computer networks that is used by many routing protocols to send packets from a source to all nodes in the network. As the packets are forwarded once by each receiving node, many copies of the same packet traverse the network which leads to high redundancy and unnecessary usage of the sparse capacity of the transmission medium. Gossip routing is a well-known approach to improve the flooding in wireless multi-hop networks. Each node has a forwarding probability p that is either statically per-configured or determined by information that is available at runtime, e.g, the node degree. When a packet is received, the node selects a random number r. If the number r is below p, the packet is forwarded and otherwise, in the most simple gossip routing protocol, dropped. With this approach the redundancy can be reduced while at the same time the reachability is preserved if the value of the parameter p (and others) is chosen with consideration of the network topology. This technical report gives an overview of the relevant publications in the research domain of gossip routing and gives an insight in the improvements that can be achieved. We discuss the simulation setups and results of gossip routing protocols as well as further improved flooding schemes. The three most important metrics in this application domain are elaborated: reachability, redundancy, and management overhead. The published studies used simulation environments for their research and thus the assumptions, models, and parameters of the simulations are discussed and the feasibility of an application for real world wireless networks are highlighted. Wireless mesh networks based on IEEE 802.11 are the focus of this survey but publications about other network types and technologies are also included. As percolation theory, epidemiological models, and delay tolerant networks are often referred as foundation, inspiration, or application of gossip routing in wireless networks, a brief introduction to each research domain is included and the applicability of the particular models for the gossip routing is discussed

    Trust based attachment

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    In social systems subject to indirect reciprocity, a positive reputation is key for increasing one's likelihood of future positive interactions. The flow of gossip can amplify the impact of a person's actions on their reputation depending on how widely it spreads across the social network, which leads to a percolation problem. To quantify this notion, we calculate the expected number of individuals, the "audience", who find out about a particular interaction. For a potential donor, a larger audience constitutes higher reputational stakes, and thus a higher incentive, to perform "good" actions in line with current social norms. For a receiver, a larger audience therefore increases the trust that the partner will be cooperative. This idea can be used for an algorithm that generates social networks, which we call trust based attachment (TBA). TBA produces graphs that share crucial quantitative properties with real-world networks, such as high clustering, small-world behavior, and power law degree distributions. We also show that TBA can be approximated by simple friend-of-friend routines based on triadic closure, which are known to be highly effective at generating realistic social network structures. Therefore, our work provides a new justification for triadic closure in social contexts based on notions of trust, gossip, and social information spread. These factors are thus identified as potential significant influences on how humans form social ties
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