Chapter 5 Network Layer

Transcription

1 Chapter Network Layer

2 Network layer Physical layer: moe bit seqence between two adjacent nodes Data link: reliable transmission between two adjacent nodes Network: gides packets from the sorce to destination, along a path that may comprise a nmber of roters and links. Application transport Data link

3 Network layer transport segment from sending to receiing host on sending side encapslate segments into datagrams on receing side, delier segments to transport layer layer protocols in eery host, roter roter examines header fields in all IP datagrams passing throgh it application transport data link data link data link data link data link data link data link data link data link data link data link data link application transport data link

4 Network layer A roter is a box with inpt and otpt links. It has access to the roting table When a packet arries at a roter, the roter examines header fields of the packets and forwards the packets according to its roting table Roting: determine the best rote/path from sorce to destination. After that, roting tables can be constrcted roting algorithm roting table header ale otpt link application transport data link Sorce 0 ale in arriing packet s header 0 application transport data link Destination

5 Roting Algorithm The roting problem can be represented sing a graph. Graph: G = (N,E) x w y z N = set of roters = {,, w, x, y, z } A set of link lengths/costs between these nodes: {d i,j, i, j ϵ S}, d i,j = if there is no link from i to j. Cost/distance of path (x, x, x,, x p ) = dx,x + dx,x + + dx p-,x p 0 Qestion: What s the least-cost/shortest distance path between and z? Roting algorithm: algorithm that finds least-cost/shortest path

6 Roting Algorithm "Good" roting algorithm:. simplicity. robstness to node/link failres. stability (fast adaptation to topology and traffic changes) 4. optimality (low delay and high throghpt). fairness. Most of roting algorithms are distribted algorithms: roting decisions are made at each node in a cooperatie manner. Information is exchanged with neighbors. Bellman-Ford algorithm is a distribted algorithm.

7 Initial condition: At step h=0, node i has the estimate d 0 (i)=, for all i S with i¹ D and that d 0 (D)=0. The nodes adertise these estimates to their neighbors. At step h : Node j pdates its estimate of its distance to D to some ale d h (j) and adertises that ale to its neighbors. At step h+: Bellman-Ford Algorithm Node i examines the message that it jst receied from its neighbors at the preios step h, e.g., j might be a neighbor of i, that is d(i,j)< and j informs i at step h that the shortest estimated distance from j to D is eqal to d h (j). Node i gets similar messages from all its neighbors. Node i then know that if it chooses to send a packet to D by first sending it to its neighbor j, then the distance that the packet will trael to reach D is estimated to be d(i,j)+d h (j). Since node i can choose the neighbor to which it sends the message destined to D, node i estimates the shortest distance to D as d h+ (i) = min{d(i,j)+d h (j), j S}.

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9 . The shortest path length from node i to the destination node is the sm of the length of the arc to the node following i and the shortest path length from that node to the destination node.. Algorithm: Bellman-Ford Algorithm ( =)

10 Bellman-Ford Algorithm Example: Gien a digraph G(N,A) with the following specifications. N={,,,4,,6} A={(,)=, (,)=, (,)=, (,)=, (4,)=6, (4,)=, (,)=, (,4)=, (6,4)=, (6,)=} a) Draw and label the arcs of the digraph. b) Discss how the Bellman-Ford algorithm can be sed to determine the shortest path from any node to a destination node on the digraph. c) Find the shortest paths from each of the other nodes to destination node on this digraph sing the Bellman-Ford algorithm.

11 Soltion: Bellman-Ford Algorithm (a) The labeled digraph is as follows: 6 4 6

12 Bellman-Ford Algorithm (b) The Bellman-Ford algorithm can be implemented on the aboe diagram.. Label each node i with (d i, j) where d i (the first element of the label) is the distance from node i to the destination node throgh the neighboring node j.. Initialization: label node i with (d i0,.) where. Shortest distance labeling of all nodes: for each sccessie rn h > 0, determine j which minimizes d i h+ =d(i,j)+d jh, and pdate label at each node i with (d i h+,j). 4. Repeat step ntil no change of any d i occrs.

13 Bellman-Ford Algorithm (c) The exection reslts of Bellman-Ford algorithm on the aboe digraph is shown in the following table From table, we can get all the shortest paths: -> -> -> 4 -> -> -> -> -> -> -> 6 -> -> -> ->

14 Link-State Roting Algorithm Network topology, link costs known to all nodes accomplished ia link state broadcast all nodes hae same info Then each roter ses Dijkstra s algorithm To compte its least cost paths to all other nodes yields forwarding table for that node iteratie: after k iterations, know least cost path to k destinations Notation: c(x,y): link cost from node x to y; = if not direct neighbors D(): crrent ale of cost of path from sorce to destination p(): predecessor node along path from sorce to N': set of nodes whose least cost path definitiely known 4

15 Dijkstra s Algorithm at node Notations: c(x,y): link cost from node x to y Initialization: N' = {} for all nodes 4 if adjacent to then D() = c(,) 6 else D() = 7 8 Loop 9 find w not in N' sch that D(w) is a minimm 0 add w to N' D(): crrent ale of cost of path from sorce to destination p(): predecessor node along path from sorce to N': set of nodes whose least cost path definitiely known pdate D() for all adjacent to w and not in N' : D() = min( D(), D(w) + c(w,) ) /* new cost to is either old cost to or known 4 shortest path cost to w pls cost from w to */ ntil all nodes in N'

16 Step 0: Initialization x w y z Sorce = node Roting algorithm is rn at node to find the least cost paths to all the other nodes. Becase no direct connection Step 0 4 N' x xy xy xyw xywz D(),p(),,, D(w),p(w), 4,x,y,y D(x),p(x), D(y),p(y),x D(z),p(z) 4,y 4,y 4,y 4-6

17 Iteration D() = min( D(), D(w) + c(w, )) x w y z - Smallest cost in row 0 and node x is not in N - Then, add x to N Step 0 D(x) = 4 N' x xy xy xyw xywz D() = min(, + ) = D(w) = min(, + ) = 4 D(),p() D(w),p(w) D(x),p(x) D(y),p(y) D(z),p(z),,,, 4, x, x C(x, ) D(y) = min(, + ) = 4-7

18 Iteration x w y z D() = min( D(), D(w) + c(w, )) Compte for the neighbors of y that are not in N D(w) = min(4, + )= D(z) = min(, + ) = 4 Lower cost à change Step 0 4 N' x xy xy xyw xywz D(),p(),, D(w),p(w), 4,x D(x),p(x), D(y),p(y), x D(z),p(z),,y 4, y 4-8

19 Iteration D() = min( D(), D(w) + c(w, )) x w y z D(w) = min(, + ) = Step 0 4 N' x xy xy xyw xywz D(),p(),,, D(w),p(w), 4,x,y D(x),p(x), D(y),p(y),x D(z),p(z) 4,y,y 4,y 4-9

20 Iteration 4 D() = min( D(), D(w) + c(w, )) x w y z D(z) = min(4, + ) = 4 Step 0 4 N' x xy xy xyw D(),p(),,, D(w),p(w), 4,x,y,y D(x),p(x), D(y),p(y),x D(z),p(z) 4,y 4,y 4,y 4-0

21 Iteration D() = min( D(), D(w) + c(w, )) x w y z D(z) = min(4, 4 + 0) = 4 Step 0 4 N' x xy xy xyw xywz D(),p(),,, D(w),p(w), 4,x,y,y D(x),p(x), D(y),p(y),x D(z),p(z) 4,y 4,y 4,y 4-

22 Reslting shortest-path tree from : w x y z To : To x: x To y: xy To w: xyw To z: xyz Reslting forwarding table in : destination x y w z Next-hop node x x x x cost 4

23 Dijkstra s algorithm: example D() p() D(w) p(w) D(x) p(x) D(y) p(y) D(z) p(z) Step N' 0 7,,, w 6,w,,w wx 6,w,w 4,x wx 0, 4,x 4 wxy,y wxyz x w 9 Notes: constrct shortest path tree by tracing predecessor nodes w y z 7 4

24 Adantage: The algorithm is ery flexible to the choice of initial estimates d j0. It can be exected at each node i in parallel with eery other nodes. Disadantage: The roting ses only one path per original-destination pair, thereby potentially limiting the throghpt; its capability to adapt the changing traffic conditions is limited by its ssceptibility to oscillations, which is de to the abrpt traffic shifts reslting when some of the shortest paths change de to changes in link lengths. Example: Optimal Roting 0bps R Bbps R 0 A D A D 0bps R +e 0bps R +e

25 Optimal Roting Sorce A is attached to two roters. Initially, A sends all its traffic to D ia node R. The delay along link (R, D) is eqal to 0 and delay along link (R, D) is eqal to +e. These roters adertise these delays to node A which then finds ot that the preferred path to D starts with R and not with R. Sorce A then sends all its traffic to R and not with R. 0bps R A D Bbps R 0+e As a reslt, the sitation alternates between the two paths. A better roting strategy wold consist in sorce A sending half of its traffic to R and the other half to R. Optimal roting can eliminate both of these disadantages. It directs traffic exclsiely along paths which are shortest with respect to some link lengths that depend on the traffic flows carried by the links.

26 Optimal Roting E.g. The gien inpt r is to be diided into the two path flows l & l, so as to minimize a cost fnction (based on M M approximation) High capacity C r origin l l Low capacity C destination

27 Optimal Roting

28 Optimal Roting

29 Optimal Roting

30 Optimal Roting * l l * * l l * 0 r C - CC C + C The figre shows the optimal soltion for r in the range [0, C +C ) for possible inpts.