1. University of Stuttgart Institute of Parallel and Distributed Systems (IPVS) Breitwiesenstraße 20 - 22 D-70565 Stuttgart An Epidemic Model for Information Diffusion in MANETs Abdelmajid Khelil, Christian Becker, Jing Tian, Kurt Rothermel Canu@informatik.uni-stuttgart.de

2. University of Stuttgart IPVS Research Group “Distributed Systems“ 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. University of Stuttgart IPVS Research Group “Distributed Systems“ 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 Simulator density d Model 0< p <= 1 density d 0< p <= 1

4. University of Stuttgart IPVS Research Group “Distributed Systems“ 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) System Model + + + + + + ++ +

5. University of Stuttgart IPVS Research Group “Distributed Systems“ 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  Epidemic Model Time in s I(t, N=100, a=0.04/s)

6. University of Stuttgart IPVS Research Group “Distributed Systems“ 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:  time in s I(t)/N d = 100 1/km2

7. University of Stuttgart IPVS Research Group “Distributed Systems“ Application of Model: Adaptation of HG(p) Assumption: MANET density d 0 is known by nodes Application requirement: “Diffuse as fast as possible“ Approach: Find p so that a(p, d 0 ) is maximal Node uses the parameter p for HG(p). d0

8. University of Stuttgart IPVS Research Group “Distributed Systems“ 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. University of Stuttgart IPVS Research Group “Distributed Systems“ 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. University of Stuttgart Institute of Parallel and Distributed Systems (IPVS) Breitwiesenstraße 20 - 22 D-70565 Stuttgart Q&A E-mail: {khelil, becker, tian, rothermel}@informatik.uni-stuttgart.de