Routing Algorithm Classification. A Distance Vector Routing Algorithm

Transcription

1 Routing lgorithm lassification Global or decentralied information? Global: ll routers have complete topolog, link cost info Link state algorithms Decentralied: Router knows phsicallconnected neighbors, link costs to neighbors Iterative process of computation, echange of info with neighbors Distance vector algorithms Static or dnamic? Static: Routes change slowl over time Dnamic: Routes change more quickl Periodic update In response to link cost changes Distance Vector Routing lgorithm Decentralied algorithm: Router knows its neighbors and link costs to neighbors Iterative computation, echange of info with neighbors Bellman-Ford Equation (dnamic programming) Define d () := cost of least-cost path to Then d () = min {c(,v) + d v ()} v where min is taken over all neighbors v of

2 Bellman-Ford Eample u v w learl, d v () =, d () =, d w () = Bellman-Ford equation sas: d u () = min { c(u,v) + d v (), c(u,) + d (), c(u,w) + d w () } = min { +, +, + } = Node that ields minimum is net hop in shortest path forwarding table Distance Vector lgorithm Iterative, asnchronous: Each local iteration caused b: Local link cost change DV update message neighbor Distributed: Each node notifies neighbors onl when its Distance Vector changes Neighbors then notif their neighbors if necessar Each node: wait for (change in local link cost of msg neighbor) recompute estimates if Distance Vector to an dest has changed, notif neighbors

3 node table 7 node table node table 7 D () = min{c(,) + D (), c(,) + D ()} = min{+, 7+} = time D () = min{c(,) + D (), c(,) + D ()} = min{+, 7+} = 7 Distance Vector (DV): Link ost hanges Link cost changes: Node detects local link cost change Updates routing info, recalculates distance vector If DV changes, notif neighbors good news travels fast t time t, detects link-cost change, updates its DV, and informs its neighbors. t time t, receives update and updates its table, computes a new least and sends its neighbors its DV t time t, receives s update and updates its distance table. s s least costs do not change does not send updates to. 6

4 node table node table time 7 Distance Vector: Link ost hanges Link cost changes: Good news travels fast Bad news travels slow 6 8

5 6 D () = min{c(,) + D (), c(,) + D ()} = min{6 +, + } = 6 D () = min{c(,) + D (), c(,) + D ()} = min{6 +, + 7} = 8 node table node table time 9 Distance Vector: Link ost hanges Link cost changes: Good news travels fast Bad news travels slow count to infinit problem! E.g., iterations before algorithm stabilies Poissoned reverse: If Z routes through Y to get to X: Z tells Y its (Z s) distance to X is infinite (so Y won t route to X via Z) Will this completel solve count to infinit problem? 6

6 Link-State Routing lgorithm Net topolog, link costs known to all nodes ccomplished via link state broadcast ll nodes have same info omputes least cost paths one node ( source ) to all other nodes Gives routing table for that node Eample: Dijkstra s algorithm Iterative: after k iterations, know least cost path to k dst. s Dijkstra s lgorithm: Eample Step start N D DE DEB DEB DEBF D(B),p(B),,, D(),p(),,D,E,E D(D),p(D), D(E),p(E) infinit,d D(F),p(F) infinit infinit,e,e,e B D E F 6

7 Dijkstra s lgorithm: Eample () Resulting shortest-path tree : B F D E Resulting forwarding table at : destination B D E F link (,B) (,D) (,D) (,D) (,D) Dijkstra s lgorithm: Discussion Oscillations possible: E.g., link cost = amount of carried traffic +e D B e e initiall +e D B +e recompute routing +e D B +e recompute +e D B +e e recompute 7

8 omparison of LS and DV lgorithms Speed of onvergence LS: O(n log n) algorithm requires O(nE) msgs Ma have oscillations DV: onvergence time varies Ma be routing loops ount-to-infinit problem Robustness: What happens if router malfunctions? LS: Node can advertise incorrect link cost Each node computes onl its own table DV: DV node can advertise incorrect path cost Each node s table used b others Error propagate thru network 8