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ASWP – Ad-hoc Routing with Interference Consideration

ASWP – Ad-hoc Routing with Interference Consideration. Zhanfeng Jia, Rajarshi Gupta, Jean Walrand , Pravin Varaiya Department of EECS University of California, Berkeley ISCC, June 28, 2005. Scenarios. Deploy troops into field Goals QoS Traffic classes, flow requirements Scalable

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ASWP – Ad-hoc Routing with Interference Consideration

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  1. ASWP– Ad-hoc Routing with Interference Consideration Zhanfeng Jia, Rajarshi Gupta, Jean Walrand, Pravin Varaiya Department of EECS University of California, Berkeley ISCC, June 28, 2005

  2. Scenarios • Deploy troops into field • Goals • QoS • Traffic classes, flow requirements • Scalable • Difficulty • Interference

  3. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions

  4. Outline • QoS Routing in Ad-Hoc Network • Interference  • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions

  5. Interference • Wired networks • Independent links • Ad-hoc networks • Neighbor links interfere • Interference range > Transmission range • For simulations • Tx range = 500 m • Ix range = 1 km

  6. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph  • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions

  7. Link Conflict Node Interference Model Link

  8. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints  • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions

  9. 50% 40% 50% Non-Local Constraints • Examples: • Local constraints would indicate 50% • Ratio between global and local is bounded by the (chromatic) degree of imperfection • Square: 100%, Pentagon: 80%, Hexagon: 100%

  10. Links with current load (Mbps) Channel = 100Mbps 10Mbps Request for new flow Non-Local Constraints • Is new request feasible?

  11. Non-Local Constraints • With new flow: • Local constraints satisfied: Sum of locally conflicting links < 100 • However, new flow is not possible

  12. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality  • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions

  13. Failure of Principle of Optimality • Principle states: If optimal path from S to D goes through A, then it follows optimal path from A to D. (Bellman)

  14. Failure of Principle of Optimality • Widest Path (31): path A (Capacity = 1) • Widest Path (51): path EDCB (Capacity = 1/2) Path EDA has capacity only 1/3

  15. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness  • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions

  16. NP-Completeness • Fact: Finding the widest path in conflict graph is NP-Complete Essentially, one has to try all the paths; there is no know polynomial algorithm.

  17. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation  • K-Best Paths • Simulations • Conclusions

  18. Approach: Approximation • Clique Approximation: We assume that scaled local constraints are sufficient. • Fact: Known to be correct for • Unit disk graphs (scaling = 0.46) • Graph with conflict radius in [x, 1] (e.g., scaling = 0.40 if x = 0.8) • Unfortunately, many graphs are not of this type. • E.g., unit disk graph with arbitrary obstructions: Scaling can be arbitrarily close to 0.

  19. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths  • Simulations • Conclusions

  20. K-Best Paths • Recall Problem: Find widest path between s and d. Width = available bandwidth measured by scaled clique constraints. • Since this problem is NP-Complete, we adopt the following heuristic:Each node maintains the list of the k-best paths; extensions by neighbors.Best: widest; ties resolved in favor of shorter.

  21. K-Best Paths • Bellman approach • Key step • Compute path width for one-hop extension • Bottleneck clique • Unchanged • A maximal clique that the extending link belongs to • Can be done locally

  22. Path Capacity K-Best Paths – Example (1 5) 1: [- , 1] 2: [B, 1] 3: [A, 1], [BC, ½] 4: [AD, ½], [BCD, ½] 5: [ADE, 1/3], [BCDE, ½]

  23. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations  • Conclusions

  24. Simulations – path width • 50-node network • Distant s/d pair • 7 hops away • X axis: load = average clique utilization • Y axis: path width

  25. Simulations – path width • 50-node network • Load = 0.32 • All pairs performance • X axis: distance between s/d pair • Y axis (upper): ratio of improved s/d pair • Y axis (lower): average improvement

  26. Simulations – admission ratio • 50-node network • Dynamic simulation • 5 s/d pairs • Randomly chosen • Given distance • Traffic model • Flow requests: 4Kb/s, 10,000 flow requests • Incoming rate: 0.32 flows per second • Duration: uniform distribution between 400 and 2800 seconds • Load = 0.32(400+2800)/24 = 2048 Kb/s = 2 Mb/s • Results: admission ratio (%) • Note: Larger k is not necessarily better

  27. More on ASWP • Optimal path = shortest widest path • Complexity • Polynomial, but … • Running time (sec): • Optimal SWP necessary? • Wide path = long path • Long term behavior: bad 50 nodes; MATLAB 6.0; 700MHz Pentium

  28. Outline • QoS Routing in Ad-Hoc Network • Interference • Interference Model: Conflict Graph • Non-Local Constraints • Failure of Principle of Optimality • NP-Completeness • Approach: Ad-Hoc Shortest Widest Path • Clique Approximation • K-Best Paths • Simulations • Conclusions 

  29. Conclusions • Overall goals • Bandwidth guaranteed path • Long-term admission ratio • Interference model • Conflict constraints • ASWP solution • Find shortest widest path • Distributed algorithm • Bellman-Ford architecture + k-best-paths approach • A small k value is a good trade-off

  30. Thank You! www.eecs.berkeley.edu/~wlr Google: jean walrand

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