Network Layer: Routing Classifications; Shortest Path Routing

Transcription

1 igitl ommuniction in the Modern World : Routing lssifictions; Shortest Pth Routing s min prolem: To get efficiently from one point to the other in dynmic environment com@cs.huji.c.il Some of the slides hve een orroed from: omputer Netorking: Top on pproch Feturing the Internet, nd edition. Jim Kurose, Keith Ross ddison-wesley, July 00. omputer ommuniction 00- omputer ommuniction 00- Routing protocol Gol: determine good pth (sequence of routers) thru netork from source to dest. Grph strction for routing lgorithms: grph nodes re routers grph edges re physicl links link cost: dely, $ cost, or congestion level Routing good pth: F typiclly mens minimum cost pth other def s possile (min. num of links) tgrm Routing lgorithm lssifiction Glol (Link Stte) Routing Shortest Pth routing ijkstr routing ecentrlized istnce Vector routing Hierrchicl Routing rodcst routing Multicst routing omputer ommuniction 00- Link-Stte Routing lgorithm ijkstr s lgorithm ijkstr s lgorithm net topology, link costs knon to ll nodes ccomplished vi link stte rodcst ll nodes hve sme info computes lest cost pths from one node ( source ) to ll other nodes gives routing tle for tht node itertive: fter k itertions, kno lest cost pth to k dest. s Nottion: c(i,j): link cost from node i to j. ost infinite if not direct neighors (v): current vlue of cost of pth from source to dest. V p(v): predecessor node long pth from source to V, tht is next v N: set of nodes hose lest cost pth definitively knon Initiliztion: N {} for ll nodes v if v djcent to then (v) c(,v) 6 else (v) infinity 8 Loop 9 find not in N such tht () is minimum 0 dd to N updte (v) for ll v djcent to nd not in N: (v) min( (v), () + c(,v) ) /* ne cost to v is either old cost to v or knon shortest pth cost to plus cost from to v */ until ll nodes in N omputer ommuniction 00- F

2 ijkstr s lgorithm in ijkstr s lgorithm in -8 top ijkstr's lgorithm to compute the shortest pth through grph. -8 ottom ijkstr's lgorithm to compute the shortest pth through grph. omputer ommuniction 00- omputer ommuniction 00- Step 0 ijkstr s lgorithm: exmple strt N F (),p(),,, (),p(),,,, (),p(), F omputer ommuniction 00- (),p() infinity, (F),p(F) infinity infinity,,, ijkstr s lgorithm, discussion lgorithm complexity: n nodes ech itertion: need to check ll nodes,, not in N n n( n + ) n i O( n ) i more efficient implementtions possile: O(nlogn) Oscilltions possile: e.g., if link cost mount of crried trffic +e e e initilly +e 0 +e 0 0 recompute routing 0 +e 0 0 +e recompute +e 0 +e 0 e recompute Spontneous synchroniztion To void oscilltions mke the routers recompute&send the link costs t different times? Turns out tht if the recomputtion periodicity is more or less the sme on ll routers then they eventully synchronize their execution times! The phenomenon of spontneous synchroniztion occurs in physics, iology, chemistry, sociology, medicine, etc.

3 Shortest Pth Routing Summry ch router does the folloing: iscover its neighors, lern their netork ddress nd UP stte (HLLO messge) Mesure the dely or cost to ech of its neighors (HO messge or cost function) onstruct pcket telling ht it knos (LS messge) Send this pcket to ll other routers (every ROUT RFRSH INTRVL) ompute the shortest pth to every other router (ijkstr) omputer ommuniction 00- Shortest Pth Routing Summry Moreover: On every Link Stte chnge flood LS to ll other routers void oscilltions through different periods Keep LS messge counter to keep flooding in check Keep LS messge ge to keep counter in check ounter nd ge lso used for fult tolernce istnce Vector Routing lgorithm ch node communictes only ith directlyttched neighors Mesures the cost to the directly-ttched neighors only stimtes the cost to the rest of the nodes ch node hs vector ith the estimted cost to every other node Info chnge done ith the neighors every time period Vector updted ccording to neighors routing tle omputer ommuniction 00- istnce Vector Routing lgorithm istnce Tle: exmple itertive: continues until no nodes exchnge info. self-terminting: no signl to stop synchronous: nodes need not exchnge info/iterte in lock step! distriuted: ech node communictes only ith directly-ttched neighors istnce Tle dt structure ech node hs its on ro for ech possile destintion column for ech directlyttched neighor to node exmple: in node, for dest. vi neighor : (,) distnce from to, vi s next hop c(,) + min { (,)} (,) (,) (,) 8 c(,) + min { (,)} + c(,) + min { (,)} + loop! c(,) + min { (,)} 8+6 loop! destintion () cost to destintion vi 6 8 9

4 istnce tle gives routing tle istnce Vector Routing: overvie destintion () cost to destintion vi istnce tle destintion Outgoing link to use, cost,,,, Routing tle Itertive, synchronous: ech locl itertion cused y: locl link cost chnge messge from neighor: its lest cost pth chnge from neighor istriuted: ech node notifies neighors only hen its lest cost pth to ny destintion chnges neighors then notify their neighors if necessry ch node: it for (chnge in locl link cost of msg from neighor) recompute distnce tle if lest cost pth to ny dest hs chnged, notify neighors istnce Vector lgorithm: t ll nodes, : Initiliztion: for ll djcent nodes v: (*,v) infinity /* the * opertor mens "for ll ros" */ (v,v) c(,v) for ll destintions, y 6 send min (y,) to ech neighor /* over ll 's neighors */ istnce Vector lgorithm (cont.): 8 loop 9 it (until I see link cost chnge to neighor V 0 or until I receive updte from neighor V) if (c(,v) chnges y d) /* chnge cost to ll dest's vi neighor v y d */ /* note: d could e positive or negtive */ for ll destintions y: (y,v) (y,v) + d 6 else if (updte received from V rt destintion ) 8 /* shortest pth from V to some hs chnged */ 9 /* V hs sent ne vlue for its min V(,) */ 0 /* cll this received ne vlue is "nevl" */ for the single destintion y: (,V) c(,v) + nevl if e hve ne min (,)for ny destintion send ne vlue of min (,) to ll neighors 6 forever istnce Vector lgorithm: exmple istnce Vector lgorithm: exmple (,) c(,) + min { (,)} + 8 (,) c(,) + min { (,)} +

5 istnce Vector: link cost chnges istnce Vector: link cost chnges Link cost chnges: node detects locl link cost chnge updtes distnce tle (line ) if cost chnge in lest cost pth, notify neighors (lines,) 0 Link cost chnges: good nes trvels fst d nes trvels slo - count to infinity prolem! 60 0 good nes trvels fst lgorithm termintes lgorithm continues on! istnce Vector: poisoned reverse omprison of LS nd V lgorithms If routes through to get to : tells its ( s) distnce to is infinite (so on t route to vi ) ill this completely solve count to infinity prolem? 60 0 lgorithm termintes Messge complexity LS: ith n nodes, links, O(n) msgs sent ech V: exchnge eteen neighors only convergence time vries Speed of onvergence LS: O(n ) lgorithm requires O(n) msgs my hve oscilltions V: convergence time vries my e routing loops count-to-infinity prolem Roustness: ht hppens if router mlfunctions? LS: node cn dvertise incorrect link cost ech node computes only its on tle V: V node cn dvertise incorrect pth cost ech node s tle used y others error propgte thru netork Hierrchicl Routing Hierrchicl Routing Our routing study thus fr - ideliztion ll routers identicl netork flt not true in prctice scle: ith 00 million destintions: cn t store ll dest s in routing tles! routing tle exchnge ould smp links! dministrtive utonomy internet netork of netorks ech netork dmin my nt to control routing in its on netork ggregte routers into regions, utonomous systems (S) routers in sme S run sme routing protocol intr-s routing protocol routers in different S cn run different intr- S routing protocol gtey routers specil routers in S run intr-s routing protocol ith ll other routers in S lso responsile for routing to destintions outside S run inter-s routing protocol ith other gtey routers

6 Intr-S nd Inter-S routing Intr-S nd Inter-S routing. d. inter-s, intr-s routing in gtey.c.c c. c Gteys: perform inter-s routing mongst themselves perform intr-s routers ith other routers in their S netork lyer link lyer physicl lyer Host h Inter-S. routing eteen. nd.c d c Intr-S routing ithin S. Host c h Intr-S routing ithin S We ll exmine specific inter-s nd intr-s Internet routing protocols (RIP, GP, OSPF)