1. Coverage of Sensor Networks: fundamental limits Benyuan Liu joint work with Don Towsley

2. Coverage measures detectability P d (x): probability sensors detect moving objects area coverage f a : fraction of area covered by sensors node coverage f n : fraction of sensors covered by other sensors fundamental measures of quality of service (surveillance) of sensor networks approach using stochastic geometry S D x

3. Area and node coverage for large random sensor networks area coverage to achieve desired coverage node coverage small until high density e.g. f n < 1% when f a = 47%

4. no knowledge of sensor locations detection zone : d < r d P d (x) = 1-e -2 rx shortest path least likely to be detected x S D 2-d infinite random sensor networks: detectability

5. consider x case: probability of detecting crossing objects results of percolation theory < c all clusters finite move around clusters P d ( ) = 0 full knowledge of sensor locations 2-d infinite random sensor networks: detectability

6. c : infinite cluster will always detect crossing objects P d ( ) = 1 phase transition at c c P d ( ) 1 to effectively block the field, need density > c h 2-d infinite random sensor networks: detectability

7. General sensing models general sensing model: p sensor field intensity a location is covered if sensing signal of sensor s at point p S1 S2 S3 obtained area coverage, node coverage, and detectability measures