Coverage and Connectivity in Sensor Networks Santosh Kumar

Coverage and Connectivity in Sensor Networks -Santosh Kumar

Model • Node distribution – Grid, Poisson, 2 -D Gaussian (centered at grid points), etc. • Node Failure Probability – Nodes fail with some probability p for 0<= p < 1. • Sensing Range - A node can sense events in a disc of radius R. • Transmission Range – A node can communicate with another node if the distance between them is less than r.

Coverage • Full coverage – Every point in the area should be covered by some active node. • K-coverage - Every point in the area should be covered by at least K active nodes.

Problem • What conditions should be satisfied (relation between the number of nodes, sensing radius, and probability of failure of a node) to achieve full-coverage (K-coverage)? • Asymptotic Coverage – Pr (Full coverage) -> 1 as n -> infinity • Necessary and Sufficient conditions

Algorithmic Coverage • Once the physical network is K-covered, you can run distributed algorithms to prune the network to maintain K-coverage while allowing redundant nodes to sleep. • Objective – Minimize Power Consumption. • Sometimes, different degrees of coverage is needed for different applications.

Connectivity • Problem – Every active node should be connected to other active nodes. • K-connectivity – There exist at least K node disjoint paths between every pair of active nodes. • Motivation: load distribution, tolerance to failures. • Asymptotic Connectivity – Pr (network connected) -> 1 as n -> infinity

Relation between Coverage and Connectivity • Coverage does not imply connectivity r = R. • However, coverage implies connectivity if the r >= 2*R (Sensys 2003)

Approaches • Percolation Theory • Random Geometric Graph • Other approaches for Grid-based Model

Link Characteristics • Rayleigh Fading Model for node communication across one-hop • Link quality varies with distance • Link quality for the same distance is variable • Link quality for the same pair of nodes varies with time

Traffic Model • Event to Sink – Detection of an intruder • Locality of Event Detection - Several nodes in the vicinity of an intruder detect the same event. • Everyone sends the information to a sink • The number of packets routed to a node increases as one approaches closer to the base station. • Sometimes a tree is formed to route the event packets.