CPSC 826 Internetworking. The Network Layer: Routing & Addressing Outline. The Network Layer: Routing Algorithms. Routing Algorithms Taxonomy

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1 PS Intrntworking Th Ntwork Layr: Routing & ddrssing Outlin Th Ntwork Layr: Routing lgorithms Michl Wigl partmnt of omputr Scinc lmson Univrsity Novmbr, Ntwork layr functions Routr architctur IP Intrnt Protocol» ddrssing Routing algorithms» Last cost path computation algorithms Hirarchical routing» onncting ntworks of ntworks Routing on th Intrnt» Intra-domain routing» Intr-domain routing application transport ntwork link physical application transport ntwork link physical Routing lgorithms Last-cost path computation Goal: To dtrmin a good path through th ntwork from sourc to dstination Graph abstraction for routing algorithms:» s ar routrs» dgs ar physical links» dgs hav a cost mtric ost can b dlay, montary cost, lvl of congstion, tc. Good path typically mans minimum cost path» lso shortst path, (ut oftn ISPs dfin good in trms of businss modls) Routing lgorithms Taxonomy Global or dcntralizd information? Global all routrs hav complt graph (topology, costs)» Link stat algorithms cntralizd routr knows link costs to physically connctd adjacnt nods» Run itrativ algorithm to xchang information with adjacnt nods» istanc vctor algorithms Static or dynamic?» Static routs chang slowly ovr tim» ynamic routs chang mor quickly Priodic updats, or Updats in rspons to link outags or cost changs

2 Global Routing lgorithms link-stat routing algorithm Uss ijkstra s shortst path graph algorithm omplt ntwork topology and link costs known at all nods» ccomplishd link stat flooding» ll nods larn th sam topology and cost data ach nod computs last cost paths from itslf to all othr nods» Producs a routing tabl for that nod» ll nods comput consistnt routing tabls lgorithm complxity:» N nods (routrs) in th ntwork» N x (N+)/ comparisons» (Mor fficint implmntations possibl) ijsktra s lgorithm Initialization: N = {} for all nods v if v adjacnt to thn (v) = c(,v) ls (v) = infinity Loop N is th st of nods to which w hav computd th minimum cost path (x) is th currnt minimum cost path to x c(n,m) is th cost of th link from n to m find nod w not in N such that (w) is a minimum add nod w to N updat (v) for all nods v adjacnt to w and not in N: (v) = min( (v), (w) + c(w,v) ) /* nw cost to nod v is ithr old cost to v or known shortst path cost to w plus cost from w to v */ until all nods in N ijkstra s algorithm: xampl Stp start N (),p(),,, (),p() (),p(),,,,, (),p() infinity, (),p() infinity infinity,,, N is th st of nods to which w hav computd th minimum cost path (x) is th currnt minimum cost path to x p(x) is th prdcssor of x on th currnt minimum cost path to x Link stat routing tabl dstination Link Stat Routing Tabl for first nod in last cost path dstination Link Stat Routing Tabl for first nod in last cost path

3 Link Stat looding lgorithm Th data stord for an dg in th graph (th link btwn nods and ) consists of:» ost from to (-) and from to (-)» uniqu timstamp for th last updat to ach cost nod that discovrs a chang in cost for on of its attachd links forwards th updat to all adjacnt nods nod rciving an updat forwards it basd on a comparison of th updat timstamp and th timstamp on its local data for th link:» Updat is latr (or nw): orward to all adjacnt nods (xcpt sndr) and updat local data» Updat is arlir: Snd local data back to sndr» Updat is qual: o nothing Link Stat looding lgorithm xampl.. = =. =. = = = Link Stat looding lgorithm xampl (ontinud). =. = = = =. =. = = = = Oscillating routs Rout oscillations ar possibl in link stat algorithms Lt th link cost qual th amount of carrid traffic» ssum th link cost is updatd as traffic changs Initially + Path to rcomput + + Path to rcomput + + Path to rcomput + + Path to

4 Routing lgorithms Taxonomy Global or dcntralizd information? Global all routrs hav maintain th complt graph of th ntwork (topology, costs)» Link stat algorithms cntralizd routr knows link costs to physically connctd adjacnt nods» Run itrativ algorithm to xchang information with adjacnt nods» istanc vctor algorithms cntralizd Routing lgorithms istanc Vctor Routing Itrativ:» s xchang cost information until ach nod has th currnt rout costs» Th algorithm is slf-trminating thr s no xplicit stopping point synchronous:» s nd not xchang information and itrat in lock stp» Intrmdiat rsults may b inconsistnt across nods istributd:» ach nod communicats only with dirctly-attachd adjacnt nods» (ut thr is no flooding of cost information) istanc Vctor Routing istanc tabl data structur ach nod has its own tabl with a...» Row for ach possibl dstination» olumn for ach dirctly-attachd adjacnt nod (nighbor) ach tabl ntry givs cost to rach dstination that adjacnt nod» istanc = ost stination () (,) = distanc from to as first hop = c(,) + min w { (,w)} w = {nighbors of } ost to stination istanc Vctor Routing istanc tabl xampl (,) = c(,) + min w { (,w)} = + = (,) = c(,) + min w { (,w)} = + = loop?! (,) = c(,) + min w { (,w)} = + = Loop! stination () ost to stination

5 istanc Vctor Routing istanc tabl xampl istanc Vctor Routing lgorithm Th distanc tabl givs th routing tabl» Just tak th minimum cost pr dstination stination istanc Tabl () Routing Tabl () stination,,,, djacnt to Us, ost Itrativ, asynchronous: ach local itration causd by:» Local link cost chang, or» Mssag from adjacnt nod that its last cost path to som dstination has changd istributd:» ach nod notifis adjacnt nods only whn its last cost path to som dstination changs» djacnt nods thn notify thir adjacnt nods if this updat changs a last cost path ach nod: wait for chang in local link cost or mssag from adjacnt nod rcomput distanc tabl if last cost path to any dstination has changd, notify adjacnt nods istanc Vctor Routing lgorithm Initialization phas: t all nods : for all adjacnt nods V { ( *,V) = /* th cost to rach all dstinations through any nighbor is infinit */ /* th * oprator mans "for all rows" */ (V,V) = c(,v) /* rcord th cost to rach ach adjacnt nod } (cost from to ach V) */ for all dstinations & adjacnt nods v { snd min w (,w) to V /* snd currnt minimum costs for all dstinations to all nighbors */ } /* w takn ovr all 's nighbors */ istanc Vctor Routing lgorithm main loop (at nod ) loop wait until (rciv link cost chang to adjacnt nod v or rciv nw_val == min w V (,w)) from v) if (c(,v) changs by d) { /* d could b + or - */ /* chang cost to all dstinations v by d */ for all dstinations y /* includs v */ (y,v) = (y,v) + d } ls { if (rcivd nw_val for y from v) /* shortst path from v to som y has changd */ /* chang th distanc to y through v*/ (y,v) = c(,v) + nwval } for all dstinations y { find min_cost(y) = min w (y,w) /* w is all 's nighbors */ if (nw min_cost (y)) { /* nw minimum cost to y found */ for all adjacnt nods v snd nw_val = min_cost(y) to v } } forvr

6 istanc Vctor lgorithm xampl istanc Vctor lgorithm xampl st. st. st. ost ost ost st. ost (,) = c(,) + min w { (,w)} = + = (,) = c(,) + min w { (,w)} = + = ost Tim Tim st. st. st. ost ost ost st. st. st. ost ost st. st. st. ost ost ost istanc Vctor lgorithm Link cost changs Whn a nod dtcts a local link cost chang:» Th nods updats its distanc tabl» If th last cost path changs, th nod notifis its nighbors istanc Vctor lgorithm Link cost changs Good nws travls fast, but ad nws travls slow!» Th count to infinity problm Routing Loop! os it Trminat? Good nws travls fast c(,) changs t t t lgorithm t trminats c(,) changs t t t t lgorithm continus on t

7 Th ount to Infinity Problm Th poisond rvrs tchniqu If routs through to gt to :» Thn tlls that s distanc to is infinit Initialization Th ount to Infinity Problm Th poisond rvrs tchniqu If routs through to gt to :» Thn tlls that s distanc to is infinit (Will this compltly solv th problm?) t - t - t - c(,) changs t t t t lgorithm trminats t Last ost Path omputations omparison of th link-stat & distanc vctor algorithms Mssag complxity:» LS: With N nods, links, O(Nx) mssags snt for flooding» V: xchang btwn nighbors only (may triggr furthr xchangs) Spd of onvrgnc:» LS: O(N ) algorithm and O(Nx) mssags May hav oscillations» V: onvrgnc tim varis Routing loops possibl ount-to-infinity problm Robustnss: what happns if thr ar failurs?» LS: can advrtis incorrct link cost ach nod computs only its own tabl» V: can advrtis incorrct path cost ach nod s tabl usd by othrs rrors propagat through ntwork