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Network Optimization

Network Optimization. Lecture 15,16 - 2. Taxonomy of TC. Direction-based TC. Rely on the ability of the nodes to estimate the relative direction of their neighbors Less accurate information than knowing exact node locations

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Network Optimization

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  1. Network Optimization Lecture 15,16 - 2

  2. Taxonomy of TC

  3. Direction-based TC • Rely on the ability of the nodes to estimate the relative direction of their neighbors • Less accurate information than knowing exact node locations • Produce almost as good topologies as in the cast of location-based TC • Angle-of-Arrival (AoA) Problem • e.g. solved by equipping nodes with more than one directional antenna

  4. Cone-based Topology Control (CBTC) • Idea: set the transmit power level of node u to the minimum value pu,ρsuch that u can reach at least one node in every cone of width ρ centered at u ρ = π/2 node u must use a transmit power level at least sufficient to reach node v

  5. Cone-based Topology Control (CBTC) • Difference between CBTC and YGk k = 6 and ρ = π/3 angular gap between any two neighbors of u is at most ρ stronger requirement than in case of YG6

  6. Distributed implementation of CBTC • Basic operation • Shrink back operation • Dealing with asymmetric links

  7. p0 Distributed implementation of CBTC • Basic operation  = 2/3 w u y v z Initially, node u sends the beacon at power p0 and collects the Ack messages sent by the nodes that received the beacon.

  8. p1 Ack Distributed implementation of CBTC • Basic operation  = 2/3 w u y v z Node u verifies whether the condition on the angular gap between neighbors is met

  9. Ack Ack p2 Distributed implementation of CBTC • Basic operation  = 2/3 w u y v z If not satisfied, node u increases the transmit power level to the next level p2 and checks the condition again

  10. Distributed implementation of CBTC • Basic operation  = 2/3 w u y v z If not satisfied, node u increases the transmit power level to the next level p2 and checks the condition again

  11. Ack p3 Distributed implementation of CBTC • Basic operation  = 2/3 w u y v z

  12. Pmax = p4 p3 Distributed implementation of CBTC • Shrink back operation (for boundary nodes)  = 2/3 w p2 p1 p0 u y v Set pu = p2

  13. Distributed implementation of CBTC • Dealing with asymmetric links  = 2/3 z d u v u w Two approaches: (i) edge argumentation (ii) edge removal

  14. Distributed implementation of CBTC • (i) Edge augmentation (AUGMCBTC) z d u v u w

  15. Distributed implementation of CBTC • (ii) Edge removal (REMCBTC) z d u v u w

  16. Protocol analysis • Theorem 11.1.1 (Li et al. 2001) • Let G be the maxpower communication graph, and assume G is connected. • Let Gρ+CBTC be the topology generated by AUGMCBTC. • Gρ+CBTC is (worst-case) connected i.f.f.  ≤ 5/6.

  17. Protocol analysis • Theorem 11.1.1 (Li et al. 2001) • Let G be the maxpower communication graph, and assume G is connected. • Let Gρ−CBTC be the topology generated by REMCBTC. • Gρ −CBTC is (worst-case) connected i.f.f.  ≤ 2/3.

  18. Protocol Analysis • Trade-off between using AUMGCBTC with = 5/6and using REMCBTC with  = 2/3. which one of the two symmetric versions of CBTC performs better is not clear RemCBTC performs slightly better than AugmCBTC in case of random node deployment

  19. Protocol Analysis

  20. CBTC Variants • Theorem 11.1.4 (Bahramgiri et al. 2002) • Let G be the maxpower communication graph, and assume G is k-connected, for some constant k > 0. • Let Gρ−CBTC be the topology generated by REMCBTC. • Gρ−CBTC is (worst-case) k-connected if ≤ 2/3k ,

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