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Shortest-Path Routing Reading: Sections 4.2 and 4.3.4

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Title: Shortest-Path Routing Reading: Sections 4.2 and 4.3.4


1
Shortest-Path Routing Reading Sections 4.2 and
4.3.4
  • COS 461 Computer Networks
  • Spring 2006 (MW 130-250 in Friend 109)
  • Jennifer Rexford
  • Teaching Assistant Mike Wawrzoniak
  • http//www.cs.princeton.edu/courses/archive/spring
    06/cos461/

2
Goals of Todays Lecture
  • Path selection
  • Minimum-hop and shortest-path routing
  • Dijkstra and Bellman-Ford algorithms
  • Topology change
  • Using beacons to detect topology changes
  • Propagating topology or path information
  • Routing protocols
  • Link state Open Shortest Path First
  • Distance vector Routing Information Protocol

3
What is Routing?
  • A famous quotation from RFC 791
  • A name indicates what we seek. An address
    indicates where it is. A route indicates how we
    get there. -- Jon Postel

4
Forwarding vs. Routing
  • Forwarding 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

5
Why Does Routing Matter?
  • End-to-end performance
  • Quality of the path affects user performance
  • Propagation delay, throughput, and packet loss
  • Use of network resources
  • Balance of the traffic over the routers and links
  • Avoiding congestion by directing traffic to
    lightly-loaded links
  • Transient disruptions during changes
  • Failures, maintenance, and load balancing
  • Limiting packet loss and delay during changes

6
Shortest-Path Routing
  • Path-selection model
  • Destination-based
  • Load-insensitive (e.g., static link weights)
  • Minimum hop count or sum of link weights

2
1
3
1
4
2
1
5
4
3
7
Shortest-Path Problem
  • Given network topology with link costs
  • c(x,y) link cost from node x to node y
  • Infinity if x and y are not direct neighbors
  • Compute least-cost paths to all nodes
  • From a given source u to all other nodes
  • p(v) predecessor node along path from source to v

2
1
3
1
4
u
2
1
5
p(v)
4
3
v
8
Dijkstras Shortest-Path Algorithm
  • Iterative algorithm
  • After k iterations, know least-cost path to k
    nodes
  • S nodes whose least-cost path definitively known
  • Initially, S u where u is the source node
  • Add one node to S in each iteration
  • D(v) current cost of path from source to node v
  • Initially, D(v) c(u,v) for all nodes v adjacent
    to u
  • and D(v) 8 for all other nodes v
  • Continually update D(v) as shorter paths are
    learned

9
Dijsktras Algorithm
1 Initialization 2 S u 3 for all
nodes v 4 if v adjacent to u 5
D(v) c(u,v) 6 else D(v) 8 7 8 Loop
9 find w not in S with the smallest D(w) 10
add w to S 11 update D(v) for all v
adjacent to w and not in S 12 D(v)
minD(v), D(w) c(w,v) 13 until all nodes in
S
10
Dijkstras Algorithm Example
11
Dijkstras Algorithm Example
12
Shortest-Path Tree
  • Shortest-path tree from u
  • Forwarding table at u

link
13
Link-State Routing
  • Each router keeps track of its incident links
  • Whether the link is up or down
  • The cost on the link
  • Each router broadcasts the link state
  • To give every router a complete view of the graph
  • Each router runs Dijkstras algorithm
  • To compute the shortest paths
  • and construct the forwarding table
  • Example protocols
  • Open Shortest Path First (OSPF)
  • Intermediate System Intermediate System (IS-IS)

14
Detecting Topology Changes
  • Beaconing
  • Periodic hello messages in both directions
  • Detect a failure after a few missed hellos
  • Performance trade-offs
  • Detection speed
  • Overhead on link bandwidth and CPU
  • Likelihood of false detection

hello
15
Broadcasting the Link State
  • Flooding
  • Node sends link-state information out its links
  • And then the next node sends out all of its links
  • except the one where the information arrived

X
A
X
A
C
B
D
C
B
D
(a)
(b)
X
A
X
A
C
B
D
C
B
D
(c)
(d)
16
Broadcasting the Link State
  • Reliable flooding
  • Ensure all nodes receive link-state information
  • and that they use the latest version
  • Challenges
  • Packet loss
  • Out-of-order arrival
  • Solutions
  • Acknowledgments and retransmissions
  • Sequence numbers
  • Time-to-live for each packet

17
When to Initiate Flooding
  • Topology change
  • Link or node failure
  • Link or node recovery
  • Configuration change
  • Link cost change
  • Periodically
  • Refresh the link-state information
  • Typically (say) 30 minutes
  • Corrects for possible corruption of the data

18
Convergence
  • Getting consistent routing information to all
    nodes
  • E.g., all nodes having the same link-state
    database
  • Consistent forwarding after convergence
  • All nodes have the same link-state database
  • All nodes forward packets on shortest paths
  • The next router on the path forwards to the next
    hop

2
1
3
1
4
2
1
5
4
3
19
Transient Disruptions
  • Detection delay
  • A node does not detect a failed link immediately
  • and forwards data packets into a blackhole
  • Depends on timeout for detecting lost hellos

2
1
3
1
4
2
1
5
4
3
20
Transient Disruptions
  • Inconsistent link-state database
  • Some routers know about failure before others
  • The shortest paths are no longer consistent
  • Can cause transient forwarding loops

2
2
1
1
3
3
1
1
4
4
2
2
1
1
5
4
4
3
3
21
Convergence Delay
  • Sources of convergence delay
  • Detection latency
  • Flooding of link-state information
  • Shortest-path computation
  • Creating the forwarding table
  • Performance during convergence period
  • Lost packets due to blackholes and TTL expiry
  • Looping packets consuming resources
  • Out-of-order packets reaching the destination
  • Very bad for VoIP, online gaming, and video

22
Reducing Convergence Delay
  • Faster detection
  • Smaller hello timers
  • Link-layer technologies that can detect failures
  • Faster flooding
  • Flooding immediately
  • Sending link-state packets with high-priority
  • Faster computation
  • Faster processors on the routers
  • Incremental Dijkstra algorithm
  • Faster forwarding-table update
  • Data structures supporting incremental updates

23
Scaling Link-State Routing
  • Overhead of link-state routing
  • Flooding link-state packets throughout the
    network
  • Running Dijkstras shortest-path algorithm
  • Introducing hierarchy through areas

Area 1
Area 0
area border router
Area 4
24
Bellman-Ford Algorithm
  • Define distances at each node x
  • dx(y) cost of least-cost path from x to y
  • Update distances based on neighbors
  • dx(y) min c(x,v) dv(y) over all neighbors v

2
v
y
1
3
1
4
x
z
u
2
1
5
t
du(z) minc(u,v) dv(z),
c(u,w) dw(z)
w
4
3
s
25
Distance Vector Algorithm
  • c(x,v) cost for direct link from x to v
  • Node x maintains costs of direct links c(x,v)
  • Dx(y) estimate of least cost from x to y
  • Node x maintains distance vector Dx Dx(y) y ?
    N
  • Node x maintains its neighbors distance vectors
  • For each neighbor v, x maintains Dv Dv(y) y ?
    N
  • Each node v periodically sends Dv to its
    neighbors
  • And neighbors update their own distance vectors
  • Dx(y) ? minvc(x,v) Dv(y) for each node y ?
    N
  • Over time, the distance vector Dx converges

26
Distance Vector Algorithm
Each node
  • Iterative, asynchronous each local iteration
    caused by
  • Local link cost change
  • Distance vector update message from neighbor
  • Distributed
  • Each node notifies neighbors only when its DV
    changes
  • Neighbors then notify their neighbors if necessary

27
Distance Vector Example Step 0
Optimum 1-hop paths
Table for A Table for A Table for A
Dst Cst Hop
A 0 A
B 4 B
C ?
D ?
E 2 E
F 6 F
Table for B Table for B Table for B
Dst Cst Hop
A 4 A
B 0 B
C ?
D 3 D
E ?
F 1 F
E
C
3
1
F
1
2
6
1
D
3
A
4
B
Table for C Table for C Table for C
Dst Cst Hop
A ?
B ?
C 0 C
D 1 D
E ?
F 1 F
Table for D Table for D Table for D
Dst Cst Hop
A ?
B 3 B
C 1 C
D 0 D
E ?
F ?
Table for E Table for E Table for E
Dst Cst Hop
A 2 A
B ?
C ?
D ?
E 0 E
F 3 F
Table for F Table for F Table for F
Dst Cst Hop
A 6 A
B 1 B
C 1 C
D ?
E 3 E
F 0 F
28
Distance Vector Example Step 2
Optimum 2-hop paths
Table for A Table for A Table for A
Dst Cst Hop
A 0 A
B 4 B
C 7 F
D 7 B
E 2 E
F 5 E
Table for B Table for B Table for B
Dst Cst Hop
A 4 A
B 0 B
C 2 F
D 3 D
E 4 F
F 1 F
E
C
3
1
F
1
2
6
1
D
3
A
4
B
Table for C Table for C Table for C
Dst Cst Hop
A 7 F
B 2 F
C 0 C
D 1 D
E 4 F
F 1 F
Table for D Table for D Table for D
Dst Cst Hop
A 7 B
B 3 B
C 1 C
D 0 D
E ?
F 2 C
Table for E Table for E Table for E
Dst Cst Hop
A 2 A
B 4 F
C 4 F
D ?
E 0 E
F 3 F
Table for F Table for F Table for F
Dst Cst Hop
A 5 B
B 1 B
C 1 C
D 2 C
E 3 E
F 0 F
29
Distance Vector Example Step 3
Optimum 3-hop paths
Table for A Table for A Table for A
Dst Cst Hop
A 0 A
B 4 B
C 6 E
D 7 B
E 2 E
F 5 E
Table for B Table for B Table for B
Dst Cst Hop
A 4 A
B 0 B
C 2 F
D 3 D
E 4 F
F 1 F
E
C
3
1
F
1
2
6
1
D
3
A
4
B
Table for C Table for C Table for C
Dst Cst Hop
A 6 F
B 2 F
C 0 C
D 1 D
E 4 F
F 1 F
Table for D Table for D Table for D
Dst Cst Hop
A 7 B
B 3 B
C 1 C
D 0 D
E 5 C
F 2 C
Table for E Table for E Table for E
Dst Cst Hop
A 2 A
B 4 F
C 4 F
D 5 F
E 0 E
F 3 F
Table for F Table for F Table for F
Dst Cst Hop
A 5 B
B 1 B
C 1 C
D 2 C
E 3 E
F 0 F
30
Distance Vector Link Cost Changes
  • Link cost changes
  • Node detects local link cost change
  • Updates the distance table
  • If cost change in least cost path, notify
    neighbors

algorithm terminates
good news travels fast
31
Distance Vector Link Cost Changes
  • Link cost changes
  • Good news travels fast
  • Bad news travels slow - count to infinity
    problem!

algorithm continues on!
32
Distance Vector Poison Reverse
  • If Z routes through Y to get to X
  • Z tells Y its (Zs) distance to X is infinite (so
    Y wont route to X via Z)
  • Still, can have problems when more than 2 routers
    are involved

algorithm terminates
33
Routing Information Protocol (RIP)
  • 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., used in the Princeton campus network

34
Comparison of LS and DV algorithms
  • Message complexity
  • LS with n nodes, E links, O(nE) messages sent
  • DV exchange between neighbors only
  • Convergence time varies
  • Speed of Convergence
  • LS O(n2) algorithm requires O(nE) messages
  • DV convergence time varies
  • May be routing loops
  • 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
  • DV node can advertise incorrect path cost
  • Each nodes table used by others (error
    propagates)

35
Conclusions
  • Routing is a distributed algorithm
  • React to changes in the topology
  • Compute the shortest paths
  • Two main shortest-path algorithms
  • Dijkstra ? link-state routing (e.g., OSPF and
    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 policy-based path-vector routing
  • Reading Section 4.3.3
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