Internet Technology 3/21/2016

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1 Intrnt Tchnolog //6 Roting algorithm goal st hop rotr = sorc rotr last hop rotr = dstination rotr rotr Intrnt Tchnolog 8. Roting sitch rotr LAN Pal Kranoski Rtgrs Unirsit Spring 6 LAN Roting algorithm: gin rotrs connctd ith links, hat is a good (bst?) path a sorc to a dstination rotr good = last cost cost = tim or mon March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski Roting graphs, nighbors, and cost Path cost,, & shortst path Graph G = (N, E) Cost N = st of nods (rotrs) E = st of dgs (links) Each dg = pair of connctd nods in N Nod is a nighbor of nod if (, ) E Each dg has a al rprsnting th cost of th link c(, ) = cost of dg btn nods & if (, ) E, thn c(, ) = W ill assm c(, ) = c(, ) A path in a graph G = (N, E) is a sqnc of nods (,,, p ) sch that ach of th pairs (, ), (, ),, ( p-, p ) ar dgs in E. Th cost of a path is th sm of dg costs: c(, ), c(, ),, c( p-, p ) Thr cold b mltipl paths btn to nods, ach ith a diffrnt cost. On or mor of ths is a. Eampl: th btn and is (,,, ) c(,,, ) = If all dgs ha th sam cost, thn = shortst path March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 4 Algorithm classifications Additional algorithm classifications Global roting algorithms Compt th sing complt knoldg of th ntork Th algorithm knos th connctiit btn all nods & costs Cntralid algorithm Ths ar link-stat (LS) algorithms Static roting algorithms Rots chang r slol or tim Dnamic roting algorithms Chang roting paths as ntork traffic loads or topolog chang Dcntralid roting algorithms No nod has complt information abot th costs of all links A nod initiall knos onl its dirct links Itrati procss: calclat & chang info ith nighbors Entall calclat th to a dstination Distanc-Vctor (DV) algorithm Load-snsiti algorithms Link costs ar to rflct th crrnt ll of congstion Load-insnsiti algorithms Ignor crrnt or rcnt lls of congstion March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 6 Pal Kranoski

2 Intrnt Tchnolog //6 Link-Stat (LS): Assmption: Entir ntork topolog & link costs ar knon Each nod broadcasts link-stat packts to all othr nods All nods ha an idntical, complt i of th ntork Compt on nod to all othr nods in th ntork Itrati algorithm Aftr k itrations, s ar knon to k nods D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th Initiali: N = crrnt nod N = { } for all nods if is a nighbor of D() = c(, ) ls D() = stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,, March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 8 D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th Loop ntil N = N: Find a nod n not in N sch that D(n) is a minimm Nod has minimm D(n) N = {, } for ach nighbor m of n not in for ach nighbor of nod D(m) = min( D(m), D(n) + c(n, m) ) n cost = old cost or cost throgh if D(m) changd, st p(m) = n Skip: N stp N D(), p() D(), p() D(),p() D(),p() D(),p() Last cost path,,,, 4,, Cost to is not bttr throgh Cost to is bttr throgh Ignor ; it is in N W no ha a path to D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th Loop ntil N = N: find n not in N sch that D(n) is a minimm Nods & ha minimm D(n) Pick an on: choos N = {,, } for ach nighbor m of n not in for ach nighbor of nod D(m) = min( D(m), D(n) + c(n, m) ) n cost = old cost or cost throgh if D(m) changd, st p(m) = n stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,,, 4, Last cost path,,, 4, Cost to is n bttr throgh Skip: and ar in N W no ha a path to March, 6 CS -6 Pal Kranoski 9 March, 6 CS -6 Pal Kranoski D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th Loop ntil N = N: find n not in N sch that D(n) is a minimm Nod has minimm D(n) N = {,,, } for ach nighbor m of n not in for ach nighbor of nod D(m) = min( D(m), D(n) + c(n,m) ) n cost = old cost or cost throgh if D(m) changd, st p(m) = n stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,,, 4,,,, 4,, 4, No impromnt (+) No chang: is not a nighbor D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th Loop ntil N = N: find n not in N sch that D(n) is a minimm Nod has minimm D(n) N = {,,,, } for ach nighbor m of n not in for ach nighbor of nod D(m) = min( D(m), D(n) + c(n,m) ) n cost = old cost or cost throgh if D(m) changd, st p(m) = n stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,,, 4,,,, 4,, 4, 4 4, No impromnt (+) 4 March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski Pal Kranoski

3 Intrnt Tchnolog //6 D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th Loop ntil N = N: find n not in N sch that D(n) is a minimm Nod is th onl on lft! N = {,,,,, } for ach nighbor m of n not in Thr ar no nighbors not in N! W r don stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,,, 4,,,, 4,, 4, 4 4, D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th N = N: All nods ar in N For ach nod, ha th total cost th sorc and th prdcssor along that path. W can look p th prdcssor to find its prdcssor E.g., is stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,,, 4,,,, 4,, () is s 4, prdcssor 4 4, () is s prdcssor () is s prdcssor March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 4 D(): cost of sorc to p(): prios nod (nighbor of ) along th to sbst of nods for hich fond th W can crat a forarding tabl that stors th nt hop on th last-cost rot Forarding tabl for nod Dstination Link stp N D(), p() D(), p() D(),p() D(),p() D(),p(),,,, 4,,,, 4,, 4, 4 4, Comptational cost st itration: sarch n nods to find th minimm cost nod nd itration: sarch n- nods rd itration: sarch n- nods n th itration: sarch nod n Total of n itrations = n + (n - ) + (n - ) + = i= (n i) W nd to sarch n(n+)/ nods Complit = O(n ) March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 6 Oscillations ith congstion-basd roting Oscillations ith congstion-basd roting If link cost = load carrid on th link Aftr rot pdats, LS is rn again Link costs ar not smmtric c(, ) = c(, ) onl if th sam load flos in both dirctions Eampl loads Load of coms into for Load of coms into for Load of coms into for Whn LS is rn dtrmins ( ) cost is compard to ( ) cost, hich is + dtrmins that is a lor-cost path + Initial roting,, and dtct -cost path contrclockis Clockis roting Contrclockis roting March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 8 Pal Kranoski

4 Intrnt Tchnolog //6 Oscillations ith congstion-basd roting Aoiding oscillations Aftr rot pdats, LS is rn t again,, and no dtct -cost path clockis Ensr that not all rotrs rn th LS algorithm at th sam tim Aoid snchronid rotrs b randomiing th tim hn a rotr adrtiss its link stat Contrclockis roting Clockis roting March, 6 CS -6 Pal Kranoski 9 March, 6 CS -6 Pal Kranoski Distanc-Vctor Roting Algorithm Initial assmption Each rotr (nod) knos th rach its dirctl-connctd nighbors Itrati, asnchronos, distribtd algorithm Mltipl itrations Each itration casd b local link cost chang or distanc ctor pdat mssag nighbor Asnchronos Dos not rqir lockstp snchroniation Distribtd Each nod rcis information on or mor dirctl attachd nighbors Notifis nighbors onl hn its distanc-ctor changs Bllman-Ford Eqation What it sas If is not dirctl connctd to, it nds to first hop to som nighbor Th lost cost is (th cost of th first hop to ) + (th lost cost to ) = c(, ) + d () th last cost path to, d (), is th minimm of th lost cost of all of s nighbors d () = min { c(, ) + d () } Th al of that satisfis th qation is th forarding tabl ntr in s rotr for dstination c(, ) ' c(, ) d () d () March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski Distanc-Vctor Roting Algorithm At ach nod stor: c(, ) = cost for th dirct link to for ach nighbor D () = stimat of th cost of th to Distanc Vctor is th st of D () for all nods in N D = [ D (): N ] Last-cost stimats to all othr nods Distanc ctors rcid its nighbors Distanc-Vctor Eampl Nod DV tabl Nod DV tabl Nod DV tabl D = [ D (): N ] St of last-cost stimats ach nighbor to ach nod Each nod priodicall snds its distanc ctor, D to its nighbors Whn a nod rcis a distanc ctor, it sas it and pdats its on distanc ctor sing th Bllman-Ford qation D () = min { c(, ) + D () } for ach nod N If this rslts in a chang to s DV, it snds th n DV to its nighbors Each cost stimat D () conrgs to th actal last-cost D () March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 4 Pal Kranoski 4

5 Intrnt Tchnolog //6 Distanc-Vctor Eampl Distanc-Vctor Eampl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod snds its DV {,, } to nods and Nod snds its DV {,, } to nods and Nod snds its DV {,, } to nods and Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Er pdat to a nod s DV also pdats th forarding tabl c(, ) = c(, ) = From : c(,) is c(, ) = c(, ) = c(, ) + c(,) = c(, ) = = + = Lss than old al, From : c(,) is c(, ) = c(,) + c(,) = = + = Lss than old al, March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 6 Distanc-Vctor Eampl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod DV tabl Nod snds its DV {,, } to nods and Nod s ctor did not chang it stas qit Nod snds its DV {,, } to nods and Link cost changs Th DV algorithm rmains qit onc it conrgs ntil som link cost changs If a nod dtcts link cost chang btn itslf and a nighbor It pdats its distanc ctor If thr is a chang in th cost of an it informs its nighbors of th n distanc ctor Each nighbor compts a n last cost If th al changd its prios al, it snds its DV to its nighbors Rcompt ntil als conrg W conrgd. Eron has th sam i of th ntork. Nobod has pdats to snd. March, 6 CS -6 Pal Kranoski March, 6 CS -6 Pal Kranoski 8 Link loss Mitigation: Poison Rrs C = C = A B C Sppos los th link to C: c(b,c) = B ill snd an pdat to A bt A thinks its C is B ill think thr is a rot to C: B A C ith a cost of (c(b,a) + ) = 4 C = C =4 A B C Updat (A,C)= W cratd a Roting Loop If A rots throgh B to gt to C A ill adrtis to B that its distanc is infinit B ill thn nr attmpt to rot throgh A This dos not ork ith loops inoling or mor nods! Othr approachs Limit si of ntork b stting a hop (cost) limit Snd fll path information in rot adrtismnt Prform plicit qris for loops C = C =4 A B C Updat (B,C)=4 This contins ad infinitm! March, 6 CS -6 Pal Kranoski 9 March, 6 CS -6 Pal Kranoski Pal Kranoski

6 Intrnt Tchnolog //6 Th nd March, 6 CS -6 Pal Kranoski Pal Kranoski 6