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An Epidemic Model for Information Diffusion in MANETs

Abdelmajid Khelil , Christian Becker, Jing Tian, Kurt Rothermel. An Epidemic Model for Information Diffusion in MANETs. Canu @informatik.uni-stuttgart.de. Diffusion in MANETs. Scenario: Information collected by sensors shall be distributed to all other MANET nodes.

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An Epidemic Model for Information Diffusion in MANETs

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  1. Abdelmajid Khelil, Christian Becker, Jing Tian, Kurt Rothermel An Epidemic Model for Information Diffusion in MANETs Canu@informatik.uni-stuttgart.de

  2. Diffusion in MANETs • Scenario: Information collected by sensors shall be distributed to all other MANET nodes. • Diffusion: Strategies based on flooding • Plain flooding (PF): on_receive(new_msg), broadcast(new_msg); • Gossiping G(p): on_receive(new_msg), if (random()<p) broadcast(new_msg); • Hyper flooding: PF & {on_discover_new_neighbours, rebroadcast(cached_msg)}; • Our algorithm: “Hyper Gossiping“: HG(p) • Probabilistic repetitive sending on_receive(new_msg), if (random()<p) broadcast(new_msg); on_discover_new_neighbours, if (random()<p) rebroadcast(cached_ msg);

  3. Goals and Approach • Evaluate HG(p) (e.g. Spreading speed) depending on MANET properties (e.g. node density) • Develop a performance model • Use performance model to adapt the protocol at run-time • Simulation • Time-intensive • Results are provided as data sets • Coarse grain evaluation, e.g performance= table(d,p) • Analytical model • Results are provided as analytical expressions • Fine grain evaluation, e.g. performance=function(d,p) • Complex • Our modeling approach: Adjustment of existing epidemic models to simulation results density d Simulator 0< p <= 1 density d Model 0< p <= 1

  4. + + System Model • N mobile nodes populating a fixed area A (density: d=N/A) • Random waypoint mobility model • Information model: 1 information source per object • Diffusion algorithm: HG(p) + + + + + + +

  5. Epidemic Model • Node can be either • Without the information (Susceptible) or • Possessing the information (Infective) • Once infected node remains infective • S(t): Number of susceptibles, I(t): Number of infectives at time t • SI-Model • a: Infection Rate • S(t) + I(t) = N • Initial condition: I(0)=1 I(t, N=100, a=0.04/s) Time in s

  6. Processing of Model Parameter • Approach: Calibration of model using simulation data. • Simulation environment: • Area (1kmX1km), d (variable) • Speed: 3-70 km/h, pause: 0-100s • MAC: a simple implementation of IEEE802.11b • Comm. range: 75 m, rate: 2,048 Kbit/s, discovery time: 2-3s • Diffusion algorithm: HG(1) • Results: Infection rate in dependency on density • Analytical expression through interpolation: I(t)/N d = 100 1/km2 time in s

  7. Application of Model: Adaptation of HG(p) • Assumption: MANET density d0 is known by nodes • Application requirement: “Diffuse as fast as possible“ • Approach: Find p so that a(p, d0 ) is maximal • Node uses the parameter p for HG(p). d0

  8. Related Work • Stochastic epidemic model for information dissemination in small population (pure birth process) [Schulzrinne]. • Diffusion-Controlled model (static trapping): Infective nodes are static servers [Schulzrinne]. • Compartmental models [Epidemiology literature]. • Epidemic algorithms for maintaining replicated databases [Demers]. • Modeling of the spreading of computer viruses in the Internet [IBM Research].

  9. Conclusion and Future Work • Conclusion • SI-Epidemic-Model is suitable to model diffusion i.e. HG(p) • Model can be used to adapt HG(p) • Future Work • How can nodes perceive MANET properties at run-time, e.g. node density? • Globality versus locality for adaptation • Investigate analytically the impact of further parameters on infection rate • Diffusion algorithm parameters, e.g. p • Mobility model parameters, e.g. speed • Communication parameters, e.g. communication range

  10. E-mail: {khelil, becker, tian, rothermel}@informatik.uni-stuttgart.de Q&A

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