Step N' D(v),p(v) D(w),p(w) D(x),p(x) D(y),p(y) D(z),p(z) 0 u 7,u 3,u 5,u. N (uw) update D(v), D(x), D(y), D(z)
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1 Dijsktra s lgorithm Initialiation: N' = {s} for all nodes n If n adjacent to s then D(n) = c(s,n) 6 else D(n) = 8 Loop 9 Find m not in N' sch that D(m) is a minimm 0 dd m to N' pdate D(m) for all n adjacent to m and not in N' : D(n) = min( D(n), D(m) + c(m,n) ) /* ne n is either old n or knon shortest path m pls cost m to n */ ntil all nodes in N' notation: c(,): link cost node to ; cost= if not direct neighbors D(n): crrent ale of cost of path sorce to n P(n): predecessor node along path sorce to n N': set of nodes hose least cost path definitiel knon Netork Laer -90 Dijkstra s algorithm: eample (Step) Step 0 N' D(),p() D(),p() D(),p() D(),p() D(),p(),,, 6,,, pdate D(m) for all n adjacent to m and not in N' : D(n) = min( D(n), D(m) + c(m,n) ) N () pdate D(), D(), D(), D() D()=min(D(), D()+c(,)) =min(,+)=6 D()=min(D(), D()+c(,)) =min(,+)= D()=min(D(), D()+c(,)) =min(, +8)= D()=min(D(), D()+c(,)) =min(, + )= notation: 8 D(n): crrent ale of cost of path sorce to n N': set of nodes hose least cost path definitiel knon 9 Netork Laer -9 Dijkstra s algorithm: eample (Step ) Step N' D(),p() D(),p() D(),p() D(),p() D(),p() 0,,, 6,,, 6,,, pdate D(m) for all n adjacent to m and not in N' : D(n) = min( D(n), D(m) + c(m,n) ) N () pdate D(), D(), D() D()=min(D(), D()+c(,)) =min(6,+ )=6 D()=min(D(),D()+c(,)) =min(,+)= D()=min(D(), D()+c(,)) =min(,+9)= notation: 8 D(n): crrent ale of cost of path sorce to n N': set of nodes hose least cost path definitiel knon 9 Netork Laer -9 Dijkstra s algorithm: eample (Step ) Step N' D(),p() D(),p() D(),p() D(),p() D(),p() 0,,, 6,,, 6,,, 0,, pdate D(m) for all n adjacent to m and not in N' : D(n) = min( D(n), D(m) + c(m,n) ) N () pdate D(), D() D()=min(D(),D()+c(,)) =min(, 6+)=0 D()=min(D(), D()+c(,)) =min(, 6+ )= notation: 8 D(n): crrent ale of cost of path sorce to n N': set of nodes hose least cost path definitiel knon 9 Netork Laer -9
2 Dijkstra s algorithm: eample (Step ) Step N' D(),p() D(),p() D(),p() D(),p() D(),p() 0,,, 6,,, 6,,, 0,,, pdate D(m) for all n adjacent to m and not in N' : D(n) = min( D(n), D(m) + c(m,n) ) N () pdate D() D()=min(D(), D()+c(,)) =min(, 0+)= notation: 8 D(n): crrent ale of cost of path sorce to n N': set of nodes hose least cost path definitiel knon 9 Netork Laer -9 Dijkstra s algorithm: eample (Step ) Step N' D(),p() D(),p() D(),p() D(),p() D(),p() 0,,, 6,,, 6,,, 0,,, destination link (,) (,) (,) (,) (,) notes: 8 constrct shortest path tree b tracing predecessor nodes ties can eist (can be broken arbitraril) 9 Netork Laer -9 Dijkstra s algorithm: an eample Dijkstra s algorithm: eample () Step 0 N' D(),p(),,, D(),p(),,,, D(),p(), D(),p(), destination D(),p(),,, link (,) (,) (,) (,) (,) reslting shortest-path tree : reslting forarding in : destination link (,) (,) (,) (,) (,) Netork Laer -96 Netork Laer -9
3 Chapter : otline Distance ector algorithm. introdction. irtal circit and datagram netorks. hat s inside a roter. IP: Internet Protocol datagram format IP addressing ICMP IP6. roting algorithms link state distance ector hierarchical roting.6 roting in the Internet RIP OSPF GP. broadcast and mlticast roting ellman-ford eqation (dnamic programming) let d () := least-cost path to then d () = min {c(,) + d () } cost neighbor to destination neighbor min taken oer all neighbors of Netork Laer -98 Netork Laer -99 ellman-ford eample clearl, d () =, d () =, d () = -F eqation sas: d () = min { c(,) + d (), c(,) + d (), c(,) + d () } = min { +, +, + } = node achieing minimm is net hop in shortest path, sed in forarding Distance ector algorithm D () = estimate of least cost to maintains distance ector D = [D (): є N ] node : knos each neighbor : c(,) maintains its neighbors distance ectors. For each neighbor, maintains D = [D (): є N ] Netork Laer -00 Netork Laer -0
4 Distance ector algorithm ke idea: time-to-time, each node sends its on distance ector estimate to neighbors hen receies ne DV estimate neighbor, it pdates its on DV sing -F eqation: D () min {c(,) + D ()} for each node N nder minor, natral conditions, the estimate D () conerge to the actal least cost d () Distance ector algorithm iteratie, asnchronos: each local iteration cased b: local link cost change DV pdate message neighbor distribted: each node notifies neighbors onl hen its DV changes neighbors then notif their neighbors if necessar each node: ait for (change in local link cost or msg neighbor) recompte estimates D () min {c(,) + D ()} if DV to an dest has changed, notif neighbors Netork Laer -0 Netork Laer -0 node node 0 0 D () = min{c(,) + D (), c(,) + D ()} = min{+0, +} = D () = min{c(,) + D (), c(,) + D ()} = min{+, +0} = node node 0 D () = min{c(,) + D (), c(,) + D ()} = min{+0, +} = D () = min{c(,) + D (), c(,) + D ()} = min{+, +0} = node 0 time Netork Laer -0 node time Netork Laer -0
5 Distance ector: link cost changes () link cost changes: node detects local link cost change pdates roting info, recalclates distance ector if DV changes, notif neighbors 0 Distance ector: link cost changes () link cost changes: node detects local link cost change bad nes traels slo - cont to infinit problem! iterations before algorithm stabilies 60 0 good nes traels fast algorithm terminates algorithm contines on! Netork Laer -06 Netork Laer -0 Distance ector: cont to infinit Distance ector: Poison Reerse If Z rotes throgh Y to get to X : Z tells Y its (Z s) distance to X is infinite (so Y on t rote to X ia Z) Still, can hae problems hen more than roters are inoled 60 0 algorithm terminates Netork Laer -08 Netork Laer -09
6 Comparison of LS and DV algorithms Chapter : otline. introdction. irtal circit and datagram netorks. hat s inside a roter. IP: Internet Protocol datagram format IP addressing ICMP IP6. roting algorithms link state distance ector hierarchical roting.6 roting in the Internet RIP OSPF GP. broadcast and mlticast roting Netork Laer -0 Netork Laer - Hierarchical roting or roting std ths far - idealiation all roters identical netork flat not tre in practice scale: ith 600 million destinations: can t store all dest s in roting s! roting echange old samp links! administratie atonom internet = netork of netorks each netork admin ma ant to control roting in its on netork Hierarchical roting aggregate roters into regions, atonomos sstems (S) roters in same S rn same roting protocol intra-s roting protocol roters in different S can rn different intra- S roting protocol gatea roter: at edge of its on S has link to roter in an S Netork Laer - Netork Laer - 6
7 Interconnected Ses c a b S a c d b Intra-S Roting algorithm S Forarding Inter-S Roting algorithm c a b S forarding configred b both intraand inter-s roting algorithm intra-s sets entries for internal dests inter-s & intra-s sets entries for eternal dests Netork Laer - Inter-S tasks sppose roter in S receies datagram destined otside of S: roter shold forard packet to gatea roter, bt hich one? netorks c a b S c a S d b S mst:. learn hich dests are reachable throgh S, hich throgh S. propagate this reachabilit info to all roters in S job of inter-s roting! c a b S netorks Netork Laer - Eample: setting forarding in roter d sppose S learns (ia inter-s protocol) that sbnet reachable ia S (gatea c), bt not ia S inter-s protocol propagates reachabilit info to all internal roters roter d determines intra-s roting info that its interface I is on the least cost path to c installs forarding entr (,I) netorks c a b S c a S d b c a b S netorks Netork Laer -6 Eample: choosing among mltiple Ses no sppose S learns inter-s protocol that sbnet is reachable S and S. to configre forarding, roter d mst determine hich gatea it shold forard packets toards for dest this is also job of inter-s roting protocol! netorks c a b S c a S d? b c a b S netorks Netork Laer -
8 Eample: choosing among mltiple Ses no sppose S learns inter-s protocol that sbnet is reachable S and S. to configre forarding, roter d mst determine toards hich gatea it shold forard packets for dest this is also job of inter-s roting protocol! hot potato roting: send packet toards closest of to roters. learn inter-s protocol that sbnet is reachable ia mltiple gateas se roting info intra-s protocol to determine costs of least-cost paths to each of the gateas hot potato roting: choose the gatea that has the smallest least cost determine forarding the interface I that leads to least-cost gatea. Enter (,I) in forarding Chapter : otline. introdction. irtal circit and datagram netorks. hat s inside a roter. IP: Internet Protocol datagram format IP addressing ICMP IP6. roting algorithms link state distance ector hierarchical roting.6 roting in the Internet RIP OSPF GP. broadcast and mlticast roting Netork Laer -8 Netork Laer -9 Intra-S Roting also knon as interior gatea protocols (IGP) most common intra-s roting protocols: RIP: Roting Information Protocol OSPF: Open Shortest Path First IGRP: Interior Gatea Roting Protocol (Cisco proprietar) Netork Laer -0 RIP ( Roting Information Protocol) distance ector algorithm distance metric: # hops (ma = hops), each link has cost DVs echanged ith neighbors eer 0 sec in response message (aka adertisement) each adertisement: list of p to destination sbnets (in IP addressing sense) C D roter to destination sbnets: sbnet hops Netork Laer - 8
9 RIP: eample D RIP: eample -to-d adertisement dest net hops - - C.... D C roting in roter D destination sbnet net roter # hops to dest C roting in roter D destination sbnet net roter # hops to dest Netork Laer - Netork Laer - RIP: link failre, recoer if no adertisement heard after 80 sec --> neighbor/ link declared dead rotes ia neighbor inalidated ne adertisements sent to neighbors neighbors in trn send ot ne adertisements (if s changed) link failre info qickl (?) propagates to entire net poison reerse sed to preent ping-pong loops (infinite distance = 6 hops) RIP processing RIP roting s managed b application-leel process called rote-d (daemon) adertisements sent in UDP packets, periodicall repeated transport (UDP) netork (IP) link phsical roted forarding forarding roted transprt (UDP) netork (IP) link phsical Netork Laer - Netork Laer - 9
10 OSPF (Open Shortest Path First) open : pblicl aailable ses link state algorithm LS packet dissemination topolog map at each node rote comptation sing Dijkstra s algorithm OSPF adertisement carries one entr per neighbor adertisements flooded to entire S carried in OSPF messages directl oer IP (rather than TCP or UDP IS-IS roting protocol: nearl identical to OSPF OSPF adanced featres (not in RIP) secrit: all OSPF messages athenticated (to preent malicios intrsion) mltiple same-cost paths alloed (onl one path in RIP) for each link, mltiple cost metrics for different TOS (e.g., satellite link cost set lo for best effort ToS; high for real time ToS) integrated ni- and mlticast spport: Mlticast OSPF (MOSPF) ses same topolog data base as OSPF hierarchical OSPF in large domains. Netork Laer -6 Netork Laer - Hierarchical OSPF Hierarchical OSPF area area border roters backbone area bondar roter internal roters backbone roter area to-leel hierarch: local area, backbone. link-state adertisements onl in area each nodes has detailed area topolog; onl kno direction (shortest path) to nets in areas. area border roters: smmarie distances to nets in on area, adertise to rea order roters. backbone roters: rn OSPF roting limited to backbone. bondar roters: connect to S s. Netork Laer -8 Netork Laer -9 0
11 Internet inter-s roting: GP GP (order Gatea Protocol): the de facto inter-domain roting protocol gle that holds the Internet together GP proides each S a means to: egp: obtain sbnet reachabilit information neighboring Ss. igp: propagate reachabilit information to all Sinternal roters. determine good rotes to netorks based on reachabilit information and polic. allos sbnet to adertise its eistence to rest of Internet: I am here Netork Laer -0 GP basics GP session: to GP roters ( peers ) echange GP messages: adertising paths to different destination netork prefies ( path ector protocol) echanged oer semi-permanent TCP connections hen S adertises a prefi to S: S promises it ill forard datagrams toards that prefi S can aggregate prefies in its adertisement netorks c GP a message b S c a S d b c a b S netorks Netork Laer - GP basics: distribting path information sing egp session beteen a and c, S sends prefi reachabilit info to S. c can then se igp do distribte ne prefi info to all roters in S b can then re-adertise ne reachabilit info to S oer bto-a egp session hen roter learns of ne prefi, it creates entr for prefi in its forarding. netorks a b S c a S d egp session igp session b c a b S netorks Netork Laer - Path attribtes and GP rotes adertised prefi incldes GP attribtes prefi + attribtes = rote to important attribtes: S-PTH: contains Ss throgh hich prefi adertisement has passed: e.g., S 6, S NEXT-HOP: indicates specific internal-s roter to nethop S. (ma be mltiple links crrent S to nethop-s) gatea roter receiing rote adertisement ses import polic to accept/decline e.g., neer rote throgh S polic-based roting Netork Laer -
12 GP rote selection roter ma learn abot more than rote to destination S, selects rote based on:. local preference ale attribte: polic decision. shortest S-PTH. closest NEXT-HOP roter: hot potato roting. additional criteria GP messages GP messages echanged beteen peers oer TCP connection GP messages: OPEN: opens TCP connection to peer and athenticates sender UPDTE: adertises ne path (or ithdras old) KEEPLIVE: keeps connection alie in absence of UPDTES; also CKs OPEN reqest NOTIFICTION: reports errors in preios msg; also sed to close connection Netork Laer - Netork Laer - GP roting polic GP roting polic () W C X legend: proider netork cstomer netork: W C X legend: proider netork cstomer netork:,,c are proider netorks X,W,Y are cstomer (of proider netorks) X is dal-homed: attached to to netorks X does not ant to rote ia X to C.. so X ill not adertise to a rote to C Y Y adertises path W to adertises path W to X Shold adertise path W to C? No a! gets no reene for roting CW since neither W nor C are s cstomers ants to force C to rote to ia ants to rote onl to/ its cstomers! Netork Laer -6 Netork Laer -
13 Wh different Intra-, Inter-S roting? polic: inter-s: admin ants control oer ho its traffic roted, ho rotes throgh its net. intra-s: single admin, so no polic decisions needed scale: hierarchical roting saes sie, redced pdate traffic performance: intra-s: can focs on performance inter-s: polic ma dominate oer performance Chapter : otline. introdction. irtal circit and datagram netorks. hat s inside a roter. IP: Internet Protocol datagram format IP addressing ICMP IP6. roting algorithms link state distance ector hierarchical roting.6 roting in the Internet RIP OSPF GP. broadcast and mlticast roting Netork Laer -8 Netork Laer -9 roadcast and mlticast roting One to man commnications roadcast deliering a packet sent a sorce node to all nodes in the netork Mlticast a single sorce node to send a cop of a packet to a sbset of the netork nodes. roadcast delier packets sorce to all nodes sorce dplication is inefficient: dplicate R R R sorce dplication dplicate creation/transmission R R R R R in-netork dplication dplicate sorce dplication: ho does sorce determine recipient addresses? Netork Laer -0 Netork Laer -
14 In-netork dplication flooding: hen node receies broadcast packet, sends cop to all neighbors problems: ccles & broadcast storm controlled flooding: node onl broadcasts pkt if it hasn t broadcast same packet before node keeps track of packet ids alread broadacsted or reerse path forarding (RPF): onl forard packet if it arried on shortest path beteen node and sorce spanning tree: no redndant packets receied b an node Spanning tree first constrct a spanning tree nodes then forard/make copies onl along spanning tree F c E D (a) broadcast initiated at G F c E D G (b) broadcast initiated at D Netork Laer - Netork Laer - Spanning tree: creation center node each node sends nicast join message to center node message forarded ntil it arries at a node alread belonging to spanning tree F c E D G (a) stepise constrction of spanning tree (center: E) F c E D (b) constrcted spanning tree G Netork Laer - Mlticast goal: sending a packet to a grop of members enefits of mlticast better bandidth tiliation less host/roter processing qicker participation pplications Video/dio broadcast (One sender) Video conferencing (Man senders) Real time nes distribtion Interactie gaming Netork Laer -
15 Internet mlticast Senders transmit IP datagrams to a "host grop" Host grop identified b a class D IP address Members of host grop cold be present anhere in the Internet Members join and leae the grop and indicate this to the roters Roters listen to all mlticast addresses and se mlticast roting protocols to manage grops Roting protocols: DVMRP: distance ector mlticast roting protocol, RFC0 PIM: protocol independent mlticast Netork Laer -6 Chapter : done!. introdction. irtal circit and datagram netorks. hat s inside a roter. IP: Internet Protocol datagram format, IP addressing, ICMP, IP6. roting algorithms link state, distance ector, hierarchical roting.6 roting in the Internet RIP, OSPF, GP. broadcast and mlticast roting nderstand principles behind netork laer serices: netork laer serice models, forarding erss roting ho a roter orks, roting (path selection), broadcast, mlticast instantiation, implementation in the Internet Netork Laer - note on these slides Part of PPT slides ere adopted Prof. Natalija Vlajic earl CSE corse and the rest ere adopted the book Compter Netorking: Top Don pproach 6 th Edition b Jim Krose and Keith Ross Compter Netorking: Top Don pproach 6 th edition Jim Krose, Keith Ross ddison-wesle March 0 ll material copright J.F Krose and K.W. Ross, ll Rights Resered Introdction -8
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