3, 3,200 200-node ode Ne Network ork w with ith Obs Obstacles es Actual PSVC NoGeo Coordinate assignment + Spring relaxation ⇒ increase convexity
Gre Greedy f forw orwarding ng s suc uccess rate rate vs. I Ite terat ations (for 3, or 3,200 200-node node 2D 2D ne netw twor orks) PSVC relaxation unstable NoGeo
Ove Overh rhead d pe per n r node ode vs vs. Ne Network ork size ize NoGeo Cost from propagation of reference PSVC node hop counts
Limitations/Future Work • PSVC fits in 48 KB TelosB executable memory • NoGeo, PSVC/GDSTR cannot fit • Improve memory footprint • Evaluation for incremental growth and node failures
More details in paper • PSO Algorithm • Details of PSVC • PSVC easily extensible to 3D • Comparison of storage costs • Two-hop greedy forwarding can improve performance significantly • Evaluations on 1 20-node Indriya TelosB testbed
TinyOS Source Code Available here: https://sites.google.com/site/geographicrouting
Conclusion • Routing stretch – Lower than NoGeo – Comparable to actual physical coordinates – Superior for networks with obstacles • Converges fast (~1 0 iterations) • Works for 3D networks (!) • Practical : implemented in TinyOS and evaluated in TelosB testbed Q UESTI UESTIONS? S?
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Background • Geographic routing is a promising approach for wireless networks – Achieve close to optimal routing stretch – Scale well – Routing states is dependent on local network density and not on network size • Nodes need location information while no location information is useful at hand – Employ virtual coordinates
Case for Virtual Coordinates • Not feasible to manually configure coordinates for each node • GPS does not work always • Virtual coordinates are sometimes better, e.g. sensornet on ship • Actual physical locations are not required (Rao et al., 2003) • Previous work: good for dense networks and focused on 2D networks • Know: greedy forwarding is efficient • Challenge: can we assign coordinates so that greedy forwarding always works even for 3D networks?
Related Work • Routing algorithms based non- Euclidean coordinate systems – VPCR (Newsome et al., 2003) – BVR(Fonseca et al., 2005) – S4(Mao et al., 2007) • Do not scale as well as geographic routing for large (3,200 node) networks (SenSys 201 0)
GSpring (Leong et al., 2007) reference node
GSpring (Leong et al., 2007) p 1 maximum hops
GSpring (Leong et al., 2007) p 1 maximum hops p 2
GSpring (Leong et al., 2007) p 1 h p 2 1 h 2 p 3
GSpring (Leong et al., 2007) p 4 p 1 h 1 h 2 h 3 p 2 p 3
GSpring (Leong et al., 2007) p 6 p 4 p 8 p 1 Each will know of the hop counts between every pair of perimeter nodes p 2 p 7 p 5 p 3
Projection onto Circle p 4 p 6 p 8 p 1 Circumference = spring rest length x total hop count p 2 p 7 p 5 p 3
Projection onto Circle p 4 p 6 p 8 p 1 Arc proportional to hop count p 2 p 7 p 5 p 3
Particle Swarm Virtual Coordinates (PSVC) • Based on hop count • Reference nodes are elected to compute initial coordinates for all nodes • Using PSO algorithm to minimize the error when computing initial coordinates • Running a iterative relaxation procedure to make the virtual topology more convex • PSVC can be trivially extended to 3D coordinates
Determining Initial Coordinates • Select reference nodes • Initialization of reference nodes • Coordinates for Non-reference nodes
Determining Initial Coordinates • Select reference nodes • Initialization of reference nodes • Coordinates for Non-reference nodes
Initialization of reference nodes p 1 (0, 0,0) 0) p 2 (100 100 h 12 12 ,0 ,0) ) // h ij is the hop count from p i to p j p 3 ( x 3 , y 3 ) // x 3 and y 3 are computed with triangle equalities using 1 00 h 31 and 1 00 h 32 , while error function is as − 1 k ∑ = − − 2 (| | 100 ) E x x h k i ik = 1 i
Determining Initial Coordinates • Select reference nodes • Initialization of reference nodes • Coordinates for Non-reference nodes
Coordinates for Non-reference nodes • Hop counts to all the reference nodes • The coordinates of all the reference nodes • Use PSO to minimize the error of objective function that maps the assigned virtual coordinates for each node to their hop counts to the reference nodes
PSO equation and parameters = + − + − ( ) ( ) v w v c r l x c r G x 1 1 2 2 i i i i i i = + x x v i i i k = − − ( ) w w w w max max min k max Parameters: = = = = = = 10 , 1 . 2 , 0 . 1 , 100 , 1 . 8 , POPSIZE w w k c c max min max 1 2 ∈ , 2 [ 0 , 1 ] r r 1 Notes: To prevent floating point overflow, all inputs are normalized by dividing them by 1 00 h 12
Algorithm1 : Compute initial coordinates for non-reference nods with PSO Given: = , 1 , , p i i p Initialize ∈ − ∈ − = = [ 1 , 1 ], [ 1 , 1 ], 0 , 1 , , x v l i POPSIZE i i i = ∞ = = = ∞ , 1 , , , 0 , Lerror i POPSIZE G Gerror i i for k =0 to k max do k = − − ( ) w w w w max max min k max for i =0 to POPSIZE do ← + − + − ( ) ( ) v w v c r l x c r G x // where p is the number of the current 1 1 2 2 i i i i i i ← + x x v node to the reference node j , is the i i i ∑ = = p − − 2 p (| | ) error x p h h position for reference node j . j i j j ij j 1 error < if then Lerror i ← l x i i = Lerror error i end if error < if then Gerror ← G x i = Gerror error end if end for end for
Relaxation after initialization • Spring force: = κ × − − × − ( | |) ( ) F l x x u x x ij ij i j i j (Hooke ’ s Law) • Net force: ∑ = F F i ij ≠ j i • Update rule: α min(| |, ) F i t = + x x F i i i | | F i
Node joins after Convergence • Listens to the stayalive beacons of its neighbors to obtain their coordinates • If all its neighbors have stabilized, it computes its coordinates as a weighted sum of the coordinates of its neighbors’ coordinates 1 ∑ = x r x ∑ i ij j r j ij j 1 ∑ = y r y ∑ i ij j r j ij j
Performance • Evaluation – Testbed – TinyOS Simulator • Measured metrics: – Greedy forwarding success rate – Hop Stretch – Storage cost – Overhead • Simulation topologies – range of network densities (average node degree) – larger networks up to 3,200 nodes • low/high density • obstacles
Performance • Routing algorithm: GDSTR • Compare with –actual coordinates –NoGeo (Rao et al., 2003)
Ave Averag age hop s hop stre tretch f h for GDS or GDSTR agai against ne netw twor ork de k dens nsity
Two wo-hop hop gre greedy for orwar arding suc uccess rate rate against ne agai netw twor ork k size ize in 2D ne in 2D netw twor orks
Ave Averag age hop s hop stre tretch h agai against ne netw twor ork k size ize in 2D ne in 2D netw twor orks
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