The Age of Information in Gossip Networks

  • Jori Selen
  • Yoni Nazarathy
  • Lachlan L. H. Andrew
  • Hai L. Vu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7984)


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.


Gossip Networks Discrete Time Markov Chains Approximations Minima of Random Variables 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Asmussen, S.: Applied probability and queues. Springer, Berlin (2003)zbMATHGoogle Scholar
  2. 2.
    Bakhshi, R., Cloth, L., Fokkink, W., Haverkort, B.R.: Mean-Field Framework for Performance Evaluation of Push-Pull Gossip Protocols. Performance Evaluation 68, 157–179 (2011)CrossRefGoogle Scholar
  3. 3.
    Banerjee, N., Corner, M.D., Towsley, D., Levine, B.N.: Relays, Base Stations, and Meshes: Enhancing Mobile Networks with Infrastructure. In: MobiCom 2008, pp. 81–91. ACM, New York (2008)Google Scholar
  4. 4.
    Benjamini, I., Kalai, G., Schramm, O.: First Passage Percolation has Sublinear Distance Variance. The Annals of Probability 31(4), 1970–1978 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bhamidi, S., van der Hofstad, R., Hooghiemstra, G.: Extreme Value Theory, Poisson-Dirichlet Distributions, and First Passage Percolation on Random Networks. Advances in Applied Probability 42(3), 706–738 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized Gossip Algorithms. IEEE/ACM Trans. Networking (TON), 2508–2530 (2006)Google Scholar
  7. 7.
    Chaintreau, A., Le Boudec, J.-Y., Ristanovic, N.: The Age of Gossip: Spatial Mean Field Regime. In: SIGMETRICS 2009, pp. 109–120. ACM, New York (2009)Google Scholar
  8. 8.
    Demers, A., Greene, D., Hauser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H., Swinhart, D., Terry, D.: Epidemic Algorithms for Replicated Database Maintenance. ACM SIGOPS Operating Systems Review 22, 8–32 (1988)CrossRefGoogle Scholar
  9. 9.
    Dimitrakopoulos, G.A., Demestichas, P.: Intelligent Transportation Systems. IEEE Vehicular Technology Magazine 5(1), 77–84 (2010)CrossRefGoogle Scholar
  10. 10.
    Eugster, P., Guerraoui, R., Handurukande, S., Kermarrec, A.-M., Kouznetsov, P.: Lightweight Probabilistic Broadcast. ACM Trans. Computer Systems, 341–374 (2003)Google Scholar
  11. 11.
    Fehnker, A., Gao, P.: Formal Verification and Simulation for Performance Analysis for Probabilistic Broadcast Protocols. In: Kunz, T., Ravi, S.S. (eds.) ADHOC-NOW 2006. LNCS, vol. 4104, pp. 128–141. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Friedrich, T., Sauerwald, T., Stauffer, A.: Diameter and Broadcast Time of Random Geometric Graphs in Arbitrary Dimensions. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 190–199. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Goseling, J., Boucherie, R.J., van Ommeren, J.-K.: Energy-Delay Tradeoff in Wireless Network Coding. Accepted for Publication in Performance Evaluation.Google Scholar
  14. 14.
    Hammersley, J.M., Welsh, D.J.A.: First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory. Bernoulli 1713 Bayes 1763 Laplace 1813, 61–110 (1965)MathSciNetCrossRefGoogle Scholar
  15. 15.
    van der Hofstad, R., Hooghiemstra, G., van Mieghem, P.: First-Passage Percolation on the Random Graph. Probability in the Engineering and Informational Sciences 15(2), 225–237 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Hunter, J.T.: Renewal Theory in Two Dimensions: Asymptotic Results. Advances in Applied Probability 6, 546–562 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Jelasity, M., Montresor, A., Babaoglu, O.: Gossip-based aggregation in large dynamic networks. ACM Trans. Computer Systems 23(3), 219–252 (2005)CrossRefGoogle Scholar
  18. 18.
    Karp, R., Schindelhauer, C., Shenker, S., Vocking, B.: Randomized Rumor Spreading. In: FOCS 41, pp. 565–574. IEEE Computer Society (2000)Google Scholar
  19. 19.
    Kempe, D., Dobra, A., Gehrke, J.: Gossip-Based Computation of Aggregate Information. In: FOCS, pp. 482–491. IEEE Computer Society (2003)Google Scholar
  20. 20.
    Papadimitratos, P., La Fortelle, A., Evenssen, K., Brignolo, R., Cosenza, S.: Vehicular Communication Systems: Enabling Technologies, Applications, and Future Outlook on Intelligent Transportation. IEEE Commun. Mag. 47(11), 84–95 (2009)CrossRefGoogle Scholar
  21. 21.
    Selen, J.: The Age of Information of Situation Awareness Networks. Master project report, Eindhoven University of Technology (2012)Google Scholar
  22. 22.
    Smythe, R.T., Wierman, J.C.: First-Passage Percolation on the Square Lattice. Advances in Applied Probability 9(1), 38–54 (1977)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Tong, Y.L.: The Multivariate Normal Distribution. Springer-Verlag Inc., New York (1990)zbMATHCrossRefGoogle Scholar
  24. 24.
    Vahidi-Asl, M.Q., Wierman, J.C.: First-Passage Percolation on the Voronoi Tessellation and Delaunay Triangulation. Random Graphs 87, 341–359 (1990)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jori Selen
    • 1
  • Yoni Nazarathy
    • 2
    • 3
  • Lachlan L. H. Andrew
    • 3
  • Hai L. Vu
    • 3
  1. 1.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenNetherlands
  2. 2.School of Mathematics and PhysicsThe University of QueenslandBrisbaneAustralia
  3. 3.Faculty of ICTSwinburne University of TechnologyMelbourneAustralia

Personalised recommendations