Download - EE 122 : Shortest Path Routing
![Page 1: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/1.jpg)
1
EE 122: Shortest Path RoutingIon Stoica
TAs: Junda Liu, DK Moon, David Zatshttp://inst.eecs.berkeley.edu/~ee122/fa09
(Materials with thanks to Vern Paxson, Jennifer Rexford,and colleagues at UC Berkeley)
![Page 2: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/2.jpg)
2
What is Routing?
Routing implements the core function of a network:
It ensures that information accepted for transfer at a source node is delivered to the correct set of destination nodes, at reasonable levels of performance.
![Page 3: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/3.jpg)
3
Internet Routing Internet organized as a two level hierarchy First level – autonomous systems (AS’s)
AS – region of network under a single administrative domain
AS’s run an intra-domain routing protocols Distance Vector, e.g., Routing Information Protocol (RIP) Link State, e.g., Open Shortest Path First (OSPF)
Between AS’s runs inter-domain routing protocols, e.g., Border Gateway Routing (BGP) De facto standard today, BGP-4
![Page 4: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/4.jpg)
4
Example
AS-1
AS-2
AS-3
Interior routerBGP router
![Page 5: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/5.jpg)
5
Forwarding vs. RoutingForwarding: “data plane”
Directing a data packet to an outgoing link Individual router using a forwarding table
Routing: “control plane” Computing paths the packets will follow Routers talking amongst themselves Individual router creating a forwarding table
![Page 6: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/6.jpg)
6
Routing requires knowledge of the network structure Centralized global state
Single entity knows the complete network structure Can calculate all routes centrally Problems with this approach?
Distributed global state Every router knows the complete network structure Independently calculates routes Problems with this approach?
Distributed no-global state Every router knows only about its neighboring routers Independently calculates routes Problems with this approach?
Know Thy Network
Link State RoutingE.g. Algorithm: Dijkstra
E.g. Protocol: OSPF
Distance Vector RoutingE.g. Algorithm: Bellman-Ford
E.g. Protocol: RIP
![Page 7: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/7.jpg)
7
Modeling a Network
Modeled as a graph Routers nodes Link edges
Possible edge costs delay congestion level
Goal of Routing Determine a “good” path through the network from source
to destination Good usually means the shortest path
A
ED
CB
F
2
2
13
1
1
2
53
5
![Page 8: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/8.jpg)
8
Link State: Control Traffic Each node floods its local information to every other node in
the network Each node ends up knowing the entire network topology
use Dijkstra to compute the shortest path to every other node
Host A
Host BHost E
Host D
Host C
N1 N2
N3
N4
N5
N7N6
![Page 9: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/9.jpg)
9
Link State: Node State
Host A
Host BHost E
Host D
Host C
N1 N2
N3
N4
N5
N7N6
A
B E
DC
A
B E
DC A
B E
DC
A
B E
DC
A
B E
DC
A
B E
DC
A
B E
DC
![Page 10: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/10.jpg)
10
Notationc(i,j): link cost from node i
to j; cost infinite if not direct neighbors; ≥ 0
D(v): current value of cost of path from source to destination v
p(v): predecessor node along path from source to v, that is next to v
S: set of nodes whose least cost path definitively known
A
ED
CB
F
2
2
13
1
1
2
53
5
Source
![Page 11: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/11.jpg)
11
Dijsktra’s Algorithm1 Initialization: 2 S = {A};3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(A,v); 6 else D(v) = ;7 8 Loop 9 find w not in S such that D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 if D(w) + c(w,v) < D(v) then // w gives us a shorter path to v than we’ve found so far 13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
c(i,j): link cost from node i to j D(v): current cost source v p(v): predecessor node along
path from source to v, that is next to v
S: set of nodes whose least cost path definitively known
![Page 12: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/12.jpg)
12
Example: Dijkstra’s AlgorithmStep
012345
start SA
D(B),p(B)2,A
D(C),p(C)5,A
D(D),p(D)1,A
D(E),p(E) D(F),p(F)
A
ED
CB
F
22
13
1
1
2
53
5
1 Initialization: 2 S = {A};3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(A,v); 6 else D(v) = ;…
![Page 13: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/13.jpg)
13
Example: Dijkstra’s AlgorithmStep
012345
start SA
D(B),p(B)2,A
D(C),p(C)5,A
…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
A
ED
CB
F
22
13
1
1
2
53
5
D(D),p(D)1,A
D(E),p(E) D(F),p(F)
![Page 14: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/14.jpg)
14
Example: Dijkstra’s AlgorithmStep
012345
start SA
AD
D(B),p(B)2,A
D(C),p(C)5,A
D(D),p(D)1,A
D(E),p(E) D(F),p(F)
A
ED
CB
F
22
13
1
1
2
53
5
…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
![Page 15: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/15.jpg)
15
Example: Dijkstra’s AlgorithmStep
012345
start SA
AD
D(B),p(B)2,A
D(C),p(C)5,A4,D
D(D),p(D)1,A
D(E),p(E)
2,D
D(F),p(F)
A
ED
CB
F
22
13
1
1
2
53
5
…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
![Page 16: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/16.jpg)
16
Example: Dijkstra’s AlgorithmStep
012345
start SA
ADADE
D(B),p(B)2,A
D(C),p(C)5,A4,D3,E
D(D),p(D)1,A
D(E),p(E)
2,D
D(F),p(F)
4,E
A
ED
CB
F
22
13
1
1
2
53
5…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
![Page 17: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/17.jpg)
17
Example: Dijkstra’s AlgorithmStep
012345
start SA
ADADE
ADEB
D(B),p(B)2,A
D(C),p(C)5,A4,D3,E
D(D),p(D)1,A
D(E),p(E)
2,D
D(F),p(F)
4,E
A
ED
CB
F
22
13
1
1
2
53
5…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
![Page 18: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/18.jpg)
18
Example: Dijkstra’s AlgorithmStep
012345
start SA
ADADE
ADEBADEBC
D(B),p(B)2,A
D(C),p(C)5,A4,D3,E
D(D),p(D)1,A
D(E),p(E)
2,D
D(F),p(F)
4,E
A
ED
CB
F
22
13
1
1
2
53
5…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
![Page 19: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/19.jpg)
19
Example: Dijkstra’s AlgorithmStep
012345
start SA
ADADE
ADEBADEBC
ADEBCF
D(B),p(B)2,A
D(C),p(C)5,A4,D3,E
D(D),p(D)1,A
D(E),p(E)
2,D
D(F),p(F)
4,E
A
ED
CB
F
22
13
1
1
2
53
5…8 Loop 9 find w not in S s.t. D(w) is a minimum; 10 add w to S; 11 update D(v) for all v adjacent to w and not in S: 12 If D(w) + c(w,v) < D(v) then13 D(v) = D(w) + c(w,v); p(v) = w;14 until all nodes in S;
![Page 20: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/20.jpg)
20
Example: Dijkstra’s AlgorithmStep
012345
start SA
ADADE
ADEBADEBC
ADEBCF
D(B),p(B)2,A
D(C),p(C)5,A4,D3,E
D(D),p(D)1,A
D(E),p(E)
2,D
D(F),p(F)
4,E
A
ED
CB
F
22
13
1
1
2
53
5To determine path A C (say), work backward from C via p(v)
![Page 21: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/21.jpg)
21
• Running Dijkstra at node A gives the shortest path from A to all destinations
• We then construct the forwarding table
The Forwarding Table
A
ED
CB
F
22
13
1
1
2
53
5Destination Link
B (A,B)
C (A,D)
D (A,D)
E (A,D)
F (A,D)
![Page 22: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/22.jpg)
22
Complexity
How much processing does running the Dijkstra algorithm take?
Assume a network consisting of N nodes Each iteration: need to check all nodes, w, not in S N(N+1)/2 comparisons: O(N2) More efficient implementations possible: O(N log(N))
![Page 23: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/23.jpg)
23
Obtaining Global State Flooding
Each router sends link-state information out its links The next node sends it out through all of its links
except the one where the information arrived Note: need to remember previous msgs & suppress
duplicates!X A
C B D
(a)
X A
C B D
(b)
X A
C B D
(c)
X A
C B D
(d)
![Page 24: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/24.jpg)
24
Flooding the Link State Reliable flooding
Ensure all nodes receive link-state information Ensure all nodes use the latest version
Challenges Packet loss Out-of-order arrival
Solutions Acknowledgments and retransmissions Sequence numbers Time-to-live for each packet
![Page 25: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/25.jpg)
25
When to Initiate Flooding Topology change
Link or node failure Link or node recovery
Configuration change Link cost change See next slide for hazards of dynamic link
costs based on current load Periodically
Refresh the link-state information Typically (say) 30 minutes Corrects for possible corruption of the data
![Page 26: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/26.jpg)
26
Oscillations Assume link cost = amount of carried traffic
A
D
C
B1 1+e
e0
e1 1
0 0
initially
A
D
C
B2+e 0
001+e 1
… recomputerouting
A
D
C
B0 2+e
1+e10 0
… recompute
A
D
C
B2+e 0
e01+e 1
… recompute
How can you avoid oscillations?
![Page 27: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/27.jpg)
27
5 Minute Break
Questions Before We Proceed?
![Page 28: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/28.jpg)
28
Distance Vector Routing Each router knows the links to its immediate
neighbors Does not flood this information to the whole network
Each router has some idea about the shortest path to each destination E.g.: Router A: “I can get to router B with cost 11 via
next hop router D” Routers exchange this information with their
neighboring routers Again, no flooding the whole network
Routers update their idea of the best path using info from neighbors
![Page 29: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/29.jpg)
29
Information Flow in Distance Vector
Host A
Host BHost E
Host D
Host C
N1 N2
N3
N4
N5
N7N6
![Page 30: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/30.jpg)
30
Bellman-Ford Algorithm INPUT:
Link costs to each neighbor Not full topology
OUTPUT: Next hop to each destination and the
corresponding cost Does not give the complete path to the
destination
![Page 31: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/31.jpg)
Bellman-Ford - Overview Each router maintains a table
Row for each possible destination Column for each directly-attached
neighbor to node Entry in row Y and column Z of node
X best known distance from X to Y, via Z as next hop = DZ(X,Y)
A C12
7
B D3
1
B CB 2 8C 3 7D 4 8
Node A
Neighbor (next-hop)
Destinations DC(A, D)
![Page 32: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/32.jpg)
Bellman-Ford - Overview Each router maintains a table
Row for each possible destination Column for each directly-attached
neighbor to node Entry in row Y and column Z of node
X best known distance from X to Y, via Z as next hop = DZ(X,Y)
A C12
7
B D3
1
B CB 2 8C 3 7D 4 8
Node A
Smallest distance in row Y = shortestDistance of A to Y, D(A, Y)
![Page 33: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/33.jpg)
33
Bellman-Ford - Overview Each router maintains a table
Row for each possible destination Column for each directly-attached
neighbor to node Entry in row Y and column Z of node
X best known distance from X to Y, via Z as next hop = DZ(X,Y)
Each local iteration caused by: Local link cost change Message from neighbor
Notify neighbors only if least cost path to any destination changes Neighbors then notify their neighbors
if necessary
wait for (change in local link cost or msg from neighbor)
recompute distance table
if least cost path to any dest has changed, notify neighbors
Each node:
![Page 34: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/34.jpg)
34
Distance Vector Algorithm (cont’d)
1 Initialization: 2 for all neighbors V do3 if V adjacent to A 4 D(A, V) = c(A,V);5 else 6 D(A, V) = ∞;7 send D(A, Y) to all neighbors loop: 8 wait (until A sees a link cost change to neighbor V /* case 1 */9 or until A receives update from neighbor V) /* case 2 */10 if (c(A,V) changes by ±d) /* case 1 */11 for all destinations Y that go through V do 12 DV(A,Y) = DV(A,Y) ± d 13 else if (update D(V, Y) received from V) /* case 2 */ /* shortest path from V to some Y has changed */ 14 DV(A,Y) = DV(A,V) + D(V, Y); /* may also change D(A,Y) */15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever
c(i,j): link cost from node i to j DZ(A,V): cost from A to V via Z D(A,V): cost of A’s best path to V
![Page 35: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/35.jpg)
Example:1st Iteration (C A)
A C12
7
B D3
1
B CB 2 8C ∞ 7D ∞ 8
Node A
A C DA 2 ∞ ∞C ∞ 1 ∞D ∞ ∞ 3
Node B
Node C
A B DA 7 ∞ ∞B ∞ 1 ∞D ∞ ∞ 1
B CA ∞ ∞B 3 ∞C ∞ 1
Node D7 loop: …13 else if (update D(A, Y) from C) 14 DC(A,Y) = DC(A,C) + D(C, Y);15 if (new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever
DC(A, B) = DC(A,C) + D(C, B) = 7 + 1 = 8
DC(A, D) = DC(A,C) + D(C, D) = 7 + 1 = 8
![Page 36: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/36.jpg)
Example: 1st Iteration (B A)
A C12
7
B D3
1
B CB 2 8C 3 7D 5 8
Node A
A C DA 2 ∞ ∞C ∞ 1 ∞D ∞ ∞ 3
Node B
Node C
A B DA 7 ∞ ∞B ∞ 1D ∞ ∞ 1
Node D7 loop: …13 else if (update D(A, Y) from B) 14 DB(A,Y) = DB(A,B) + D(B, Y);15 if (new min. for destination Y)16 send D(A, Y) to all neighbors 17 forever
DB(A, C) = DB(A,B) + D(B, C) = 2 + 1 = 3
DB(A, D) = DB(A,B) + D(B, D) = 2 + 3 = 5
B CA ∞ ∞B 3 ∞C ∞ 1
![Page 37: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/37.jpg)
Example: End of 1st Iteration
A C12
7
B D3
1
B CB 2 8C 3 7D 5 8
Node A Node B
Node C
A B DA 7 3 ∞B 9 1 4D ∞ 4 1
Node D
B CA 5 8B 3 2C 4 1
End of 1st Iteration All nodes knows the best two-hop
paths
A C DA 2 3 ∞C 9 1 4D ∞ 2 3
![Page 38: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/38.jpg)
Example: 2nd Iteration (A B)
A C12
7
B D3
1
B CB 2 8C 3 7D 5 8
Node A Node B
Node C
A B DA 7 3 ∞B 9 1 4D ∞ 4 1
Node D
B CA 5 8B 3 2C 4 1
A C DA 2 3 ∞C 5 1 4D 7 2 3
7 loop: …13 else if (update D(B, Y) from A) 14 DA(B,Y) = DA(B,A) + D(A, Y);15 if (new min. for destination Y)16 send D(B, Y) to all neighbors 17 forever
DA(B, C) = DA(B,A) + D(A, C) = 2 + 3 = 5
DA(B, D) = DA(B,A) + D(A, D) = 2 + 5 = 7
![Page 39: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/39.jpg)
Example: End of 2nd Iteration
A C12
7
B D3
1
B CB 2 8C 3 7D 4 8
Node A
A C DA 2 3 11C 5 1 4D 7 2 3
Node B
Node C
A B DA 7 3 6B 9 1 4D 12 4 1
Node D
B CA 5 4B 3 2C 4 1
End of 2nd Iteration All nodes knows the best three-hop paths
![Page 40: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/40.jpg)
Example: End of 3rd Iteration
A C12
7
B D3
1
B CB 2 8C 3 7D 4 8
Node A
A C DA 2 3 6C 5 1 4D 7 2 3
Node B
Node C
A B DA 7 3 5B 9 1 4D 11 4 1
Node D
B CA 5 4B 3 2C 4 1
End of 2nd Iteration: Algorithm
Converges!
![Page 41: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/41.jpg)
41
Distance Vector: Link Cost Changes
A C14
50
B1
“goodnews travelsfast”
A CA 4 6C 9 1
Node B
A BA 50 5B 54 1
Node C
Link cost changes heretime
Algorithm terminates
loop: 8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) /10 if (c(A,V) changes by ±d) /* case 1 */11 for all destinations Y that go through V do 12 DV(A,Y) = DV(A,Y) ± d 13 else if (update D(V, Y) received from V) /* case 2 */14 DV(A,Y) = DV(A,V) + D(V, Y); 15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever
A CA 1 6C 9 1
A BA 50 5B 54 1
A CA 1 6C 9 1
A BA 50 2B 51 1
A CA 1 3C 3 1
A BA 50 2B 51 1
![Page 42: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/42.jpg)
42
Distance Vector: Count to Infinity Problem
A C14
50
B60
“badnews travelsslowly”
Node B
Node C
Link cost changes here time
…
loop: 8 wait (until A sees a link cost change to neighbor V9 or until A receives update from neighbor V) /10 if (c(A,V) changes by ±d) /* case 1 */11 for all destinations Y that go through V do 12 DV(A,Y) = DV(A,Y) ± d 13 else if (update D(V, Y) received from V) /* case 2 */14 DV(A,Y) = DV(A,V) + D(V, Y); 15 if (there is a new minimum for destination Y)16 send D(A, Y) to all neighbors 17 forever
A CA 4 6C 9 1
A BA 50 5B 54 1
A CA 60 6C 9 1
A BA 50 5B 54 1
A CA 60 6C 9 1
A BA 50 7B 101 1
A CA 60 8C 9 1
A BA 50 7B 101 1
![Page 43: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/43.jpg)
43
Distance Vector: Poisoned Reverse
A C14
50
B60• If B routes through C to get to A:
- B tells C its (B’s) distance to A is infinite (so C won’t route to A via B)
- Will this completely solve count to infinity problem?
Node B
Node C
Link cost changes here; C updates D(C, A) = 60 as B has advertised D(B, A) = ∞
timeAlgorithm terminates
A CA 4 6C 9 1
A BA 50 5B ∞ 1
A CA 60 6C 9 1
A BA 50 5B ∞ 1
A CA 60 6C 9 1
A BA 50 ∞B ∞ 1
A CA 60 51C 9 1
A BA 50 ∞B ∞ 1
A CA 60 51C 9 1
A BA 50 ∞B ∞ 1
![Page 44: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/44.jpg)
44
Routing Information Protocol (RIP)
Simple distance-vector protocol Nodes send distance vectors every 30 seconds … or, when an update causes a change in routing
Link costs in RIP All links have cost 1 Valid distances of 1 through 15 … with 16 representing infinity Small “infinity” smaller “counting to infinity” problem
RIP is limited to fairly small networks E.g., campus
![Page 45: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/45.jpg)
45
Link State vs. Distance VectorPer-node message
complexity: LS: O(e) messages
e: number of edges DV: O(d) messages,
many times d is node’s degree
Complexity/Convergence LS: O(N log N)
computation Requires global flooding
DV: convergence time varies Count-to-infinity problem
Robustness: what happens if router malfunctions?
LS: Node can advertise
incorrect link cost Each node computes only
its own table DV:
Node can advertise incorrect path cost
Each node’s table used by others; errors propagate through network
![Page 46: EE 122 : Shortest Path Routing](https://reader035.vdocuments.net/reader035/viewer/2022062410/56816384550346895dd46910/html5/thumbnails/46.jpg)
46
Summary Routing is a distributed algorithm
Different from forwarding React to changes in the topology Compute the shortest paths
Two main shortest-path algorithms Dijkstra link-state routing (e.g., OSPF, IS-IS) Bellman-Ford distance-vector routing (e.g., RIP)
Convergence process Changing from one topology to another Transient periods of inconsistency across routers
Next time: BGP Reading: K&R 4.6.3