Outline

1. Outline Dynamic Source Routing（DSR） Multipath extension to DSR Disjoint Multipath(protocol 1) Multipath protocol 2 Analytic Modeling Modeling of Protocol 1 Modeling of Protocol 2 Modeling of Braided path Modeling of Advanced Braid

2. Dynamic Source Routing（DSR） 2 <1,2> 7 <1> <1,3,5,7> 5 <1> <1,3,5> S 1 3 <1,3> 8 D <1,4,6> <1> <1,4,6> <1,4,6> <1,4> 6 4 <1,4,6>

3. Disjoint Multipath DSR（1/3） • Many flooded query message arrive at the destination via different routes. • Primary source route is the route taken by the first query reaching the destination. • The destination “remembers” the primary source, in order to figure out disjoint routes. • The destination controls the total number of replies ,thus preventing a reply flood • The source keeps all routes received on reply packets in its route cache. • When the primary route breaks ,the shortest remaining alternate route is used.

4. Disjoint Multipath DSR（2/3） PN P2 S D P1

5. Disjoint Multipath DSR（3/3） • Shortcoming An intermediate link failure on the primary route still sends an error packet back to the source ,which will then use an alternate route This cases a temporary loss of route for the data packets that are already in transit upstream from the failed link Let us call this technique as protocol 1

6. Multipath protocol 2 (1/3) • The destination replies to each intermediate node in the primary route with an alternate disjoint route to the destination. • The reply is targeted to the intermediate node instead of the source

7. Multipath protocol 2 (2/3) P2 P4 n1 n3 nk+1 L1 L2 L3 L4 Lk S D n2 n4 P3 P1

8. Multipath protocol 2 (3/3) • When the link Liis broken ,the node nireplace the unused portion of the route, Lito Lk,in the data packet header by the alternate route Pi. • The node ni is responsible for modifying the source route on all later data packets to use its own alternate route. • This will continue until a link on Pibreaks. • It will cause an error packet transmitted backward up to node ni-1,which will quench the error packet and switch all later data packets to its own alternate route Pi-1 . • This process continues until the source gets an error packet and has no alternate route

9. Analytic Modeling(1/2) • The lifetime of Li is denoted by XLi • We represent the lifetime of a wireless link between a pair of nodes by a random variable • Assume that XLi ,i=1,2,….k, are independent and identically distributed exponential random variables ,each with mean ι • EX:

10. Analytic Modeling(2/2) • Since a route fails when any one of the wireless links in its path breaks , the lifetime of a route P ,consisting of k wireless links, is a random variable XP that can be expressed as XP =min(XL1, XL2,….., XLk) • It is well known that XP is also an exponentially distributed random variable with a mean of

11. Modeling of Protocol 1 (1/4) • Assume a source S has N routes to a destination D . • The primary route is denoted by P1 and the N-1 alternate routes are denoted by P2, P3,…. PN • The length of route Pi is ki • The time after which none of the routes are useful is a random variable T, where T=max(XP1, XP2,….., XPN) • T represents the time between successive route discoveries

12. Modeling of Protocol 1 (2/4) • XP1, XP2,….., XPN are exponential random variables ,where the pdf of XPi is Note that XPi ‘s are independent • the cdf of XPi is

13. Modeling of Protocol 1 (3/4) • The cdf of T ,FT(t) is obtained as

14. Modeling of Protocol 1 (4/4) • The pdf of T ,the time between successive route discoveries ,is given by • Where λi =ki /ι=1/lifetime of the i-th route

15. Modeling of Protocol 2 (1/5) • The time until the next route discovery T is the time until the event E is true ,where E is described by the following logical expression: • Then T can be expressed as

16. Multipath protocol 2 (2/3) P2 P4 n1 n3 nk+1 L1 L2 L3 L4 Lk S D n2 n4 P3 P1

17. Modeling of Protocol 2 (2/5) • Let us denote the random variable by Zi , • the pdf of Zi ,fZi(t) is given by • Where

18. Modeling of Protocol 2 (3/5) • the cdf of Zi , FZi(t) is given by • where

19. Modeling of Protocol 2 (4/5) • The pdf of T =min(Z1 ,Z2 ,…, Zk ) • min(Z1 ,Z2 ,…, Zk )= max((1-Z1 ),(1-Z2 ),…,(1- Zk )) • the cdf of T , FT(t) is given by

20. Modeling of Protocol 2 (5/5) • the pdf of T , fT(t) is given by

21. The expected value of T ,E[T] is given by • No. of disjoint paths=N • Mean lifetime of a single link, ι=5

25. Node fail • Link fail • Node fail

26. Multipath protocol 2 P2 P4 n1 n3 nk+1 L1 L2 L3 L4 Lk S D n2 n4 P3 P1

28. Modeling of Braided path Pk-2 P1 K-1 K+1 1 2 3 4 K-2 K P2 Pk-1

30. Modeling of Advanced Braid(1/2) • Assume length of a= length of Pi a P3 P1 Pk-2 1 2 3 4 5 6 K-3 K-2 K-1 K K+1 P4 P2 Pk-3 a Pk-1 a

31. Modeling of Advanced Braid(2/2)

33. Comparison of CASE A

34. Comparison of CASE B

35. Comparison of CASE C