1. Minimum Energy Reliable Paths Using Unreliable Wireless Links Qunfeng Dong, Suman Banerjee, Micah Adler, and Archan Misra Mobihoc 2005

2. Outline Introduction Introduction Related work Related work Formulation Formulation Single-path min-energy routes Single-path min-energy routes Multi-path min-energy routes Multi-path min-energy routes Evaluation Evaluation Conclusion Conclusion

3. Introduction Traditional power aware routing schemes do not take link loss rates into account Traditional power aware routing schemes do not take link loss rates into account Energy efficient paths Energy efficient paths Assume that every link is totally reliable Assume that every link is totally reliable Too optimistic Too optimistic Right metric Right metric All transmissions including retransmissions All transmissions including retransmissions

4. Introduction Design of wireless communication protocols are guided by two requirements Design of wireless communication protocols are guided by two requirements Energy efficiency Energy efficiency Resilience to packet losses Resilience to packet losses Achieve end-to-end reliability on multi-hop paths Achieve end-to-end reliability on multi-hop paths Hop-by-hop retransmission Hop-by-hop retransmission End-to-end retransmission End-to-end retransmission Mixed method Mixed method

5. Introduction Solve the problem of computing minimum energy paths for reliable communication in Solve the problem of computing minimum energy paths for reliable communication in End-to-end retransmission model End-to-end retransmission model Mixed retransmission model Mixed retransmission model Examine the problem of reliability through utilization of multiple routes Examine the problem of reliability through utilization of multiple routes Throughput Throughput Reliability Reliability

6. Related work Finding minimum cost path Finding minimum cost path Link cost is set to the transmission power Link cost is set to the transmission power Residual battery is used as a routing metric Residual battery is used as a routing metric None of these papers considered the lossy property of wireless links. None of these papers considered the lossy property of wireless links.

7. Related work Minimum energy paths for reliable communication in multi-hop wireless networks Minimum energy paths for reliable communication in multi-hop wireless networks ACM MobiHoc 2002 ACM MobiHoc 2002 BMA BMA Transmission power Error rate of a hop by hop retransmission link

8. Related work Not true in the end-to-end retransmission model Not true in the end-to-end retransmission model L>=2 makes lossy links appear to be even more expensive L>=2 makes lossy links appear to be even more expensive Reasonable but not optimal Reasonable but not optimal More general and realistic mixed retransmission model in not explored More general and realistic mixed retransmission model in not explored I >=2 is some constant

9. Formulation Two metrics are used to calculate the lick cost Two metrics are used to calculate the lick cost Weight of link (i,j): W(i,j) Weight of link (i,j): W(i,j) Expected number of transmissions of a successful delivery over a link (i,j): N(i,j) Expected number of transmissions of a successful delivery over a link (i,j): N(i,j)

10. Formulation Weight of link (i,j): W(i,j) Weight of link (i,j): W(i,j)

11. Formulation Expected number of transmissions of a successful delivery over a link (i,j): N(i,j) Expected number of transmissions of a successful delivery over a link (i,j): N(i,j) Er(i, j) is the probability that a transmission over link (i; j) Er(i, j) = 0: link (i, j) is considered reliable

12. Formulation C min (u, v): expected energy consumption of a successful delivery along a minimum energy path from u to v.

13. Single-path min-energy routes Basic Algorithm for Minimum Energy Routing (BAMER) Basic Algorithm for Minimum Energy Routing (BAMER) General Algorithm for Minimum Energy Routing (GAMER) General Algorithm for Minimum Energy Routing (GAMER) BAMER for the mixed retransmission model BAMER for the mixed retransmission model Distributed Algorithm for Minimum Energy Routing (DAMER) Distributed Algorithm for Minimum Energy Routing (DAMER)

14. BAMER Generalized extension of Dijkstra’s shortest path algorithm Generalized extension of Dijkstra’s shortest path algorithm End-to-end transmission model End-to-end transmission model

15. BAMER-example C(s)=0

16. GAMER Further generalization of BAMER Further generalization of BAMER Each individual link may or may not provide per hop reliability Each individual link may or may not provide per hop reliability

17. GAMER-example C(s)=0 Hop by hop retransmission 10+4*12=58

18. BAMER for the mixed retransmission model An appropriate preprocessing stage enable BAMER to solve the same problem in mixed retransmission model An appropriate preprocessing stage enable BAMER to solve the same problem in mixed retransmission model GAMER BAMER

19. BAMER for the mixed retransmission model-example (48,1)

20. DAMER Both BAMER and GAMER are centralized algorithms Both BAMER and GAMER are centralized algorithms Has to be implemented as a distributed protocol in a lightweight fashion Has to be implemented as a distributed protocol in a lightweight fashion (1,0) (12,0) (1,0) (0, 4) 15 12 4

21. DAMER Computes an energy efficient path from each node to every other node. u w v M v.C(w) N(u.v)W(u.v)N(u.v)W(u.v) M v.R(w) C(w)C(w)

22. DAMER-example 0+1*2*8=16 0+1*2*5=16 16+2*2*6=40 40+4*2*5=16 10+2*2*8=42

23. Multi-path min-energy routes Multi-path routing is considered beneficial for improved throughput and reliability Multi-path routing is considered beneficial for improved throughput and reliability Cost more energy consumption Cost more energy consumption In the presence of such noisy routing information In the presence of such noisy routing information Multi-path routing may outperform Dijkstra’s shortest path routing Multi-path routing may outperform Dijkstra’s shortest path routing

24. Multi-path min-energy routes Reveal that Reveal that If perfect routing information is given and link loss rates are taken into account, multi-path routing can still potentially reduce the expected energy consumption of one-to-one communication. If perfect routing information is given and link loss rates are taken into account, multi-path routing can still potentially reduce the expected energy consumption of one-to-one communication.

25. Multi-path min-energy routes (1,2) (0,0) 2 8/7

26. “Should the intermediate node forward every copy of the packet? “ “Should the intermediate node forward every copy of the packet? “ No No Formally analyze the complexity of finding minimum energy multi-path routes and prove that it is NP-hard Formally analyze the complexity of finding minimum energy multi-path routes and prove that it is NP-hard By reducing form the 3-dimensional matching problem By reducing form the 3-dimensional matching problem Multi-path min-energy routes

28. W = {w1,w2} X = {x1, x2} Y = {y1, y2}: M = {m1,m2,m3,m4} m1 = (w1, x2, y2) m2 = (w1, x1, y1) m3 = (w2, x2, y2) m4 = (w1, x1, y2) Weight 0, error rate p=e -1/3q Weight 1, error rate 0 Weight c=(e-1)q, error rate=0

29. Multi-path min-energy routes M contains a 3-DM of size q if and only if the minimum expected energy consumption to deliver a packet from s to t is

30. Multi-path min-energy routes “Only if” direction “Only if” direction S->m: q S->m: q M->w,x.y; 3q M->w,x.y; 3q Energy consumption Energy consumption c+q c+q Probability Probability 1-p 3q 1-p 3q Weight 0, error rate p=e -1/3q Weight 1, error rate 0 Weight c=(e-1)q, error rate=0

31. Multi-path min-energy routes “if” direction “if” direction The number of triplet nodes that participate to forward packets in this routing scheme n 0, 1<= n 0 <= n The number of element nodes that participate to forward packets in this routing scheme, q0. 1<= q 0 <= min(3q, 3n 0 ). Prove by contradiction Assume that M does not contain a matching of size q

32. Multi-path min-energy routes n 0 > q n 0 = q, q 0 < 3q n 0 < q then q 0 < min(3q, 3n 0 ) = 3n 0

33. Evaluation 100 nodes 100 nodes 10*10 square fields 10*10 square fields Link error rate 0<=MaxLER<=1 Link error rate 0<=MaxLER<=1 Link error rate of link(u,v) and link(v,u) is different Link error rate of link(u,v) and link(v,u) is different Normalized energy efficiency (NEE) Normalized energy efficiency (NEE) The ratio of its average energy consumption to that of BAMER and GAMER The ratio of its average energy consumption to that of BAMER and GAMER

34. Evaluation a = 2, 3, 4

35. Evaluation UPGrate: percentage of links supporting hop-by-hop retransmission UPGrate NEE MaxLER = 0.1, 0.4, 0.7

36. Evaluation 30, 150, 250 nodes, UPGrate NEE

37. Conclusion Study the problem of minimum energy routing for reliable one-to-one communication in the presence of lossy links Study the problem of minimum energy routing for reliable one-to-one communication in the presence of lossy links Each link support link layer hop-by-hop retransmission and guarantee reliable delivery Each link support link layer hop-by-hop retransmission and guarantee reliable delivery BAMER BAMER GAMER GAMER DAMER DAMER

38. Conclusion Our another interesting finding In some cases multi-path routing may reduce the expected energy consumption in the presence of lossy links. Formally analyze the problem of finding the minimum energy multi-path routing scheme and prove that it is actually NP- hard.

39. Thanks!