1. CS 5565 Network Architecture and Protocols
Lecture 18
Godmar Back

2. Announcements Project 2A due Apr 4 Project 2B due in 2 parts:
CS 5565 Spring 2012

3. Routing Algorithms

4. Routing Algorithm Classification
Global or decentralized information?
Global:
all routers have complete topology, link cost info
“link state” algorithms
Decentralized:
router knows physically-connected neighbors, link costs to neighbors
iterative process of computation, exchange of info with neighbors
“distance vector” algorithms
Static or dynamic?
Static:
routes change slowly over time
Dynamic:
routes change more quickly
periodic update
in response to link cost changes
Note: Global/decentralized classification does not say where routing computation is performed, it says what information one has when computing routes
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5. Link State Routing
Routers periodically broadcast link state information
link state messages or LSA (link state advertisement)
broadcast via sequence-number controlled flooding
All routers acquire complete connectivity + link cost information of entire network
Each router computes routing table from that obtained topology
Dijkstra’s shortest path to other routers, from computing router  this becomes forwarding table
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6. Distance Vector Algorithm (1)
Bellman-Ford Equation (dynamic programming)
Define
dx(y) := cost of least-cost path from x to y
Then
dx(y) = min {c(x,v) + dv(y) }
where min is taken over all neighbors of x
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7. Bellman-Ford Example (2)u y x w v z 2 1 3 5
Clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3
B-F equation says:
du(z) = min { c(u,v) + dv(z),
c(u,x) + dx(z),
c(u,w) + dw(z) }
= min {2 + 5,
1 + 3,
5 + 3} = 4
Node that achieves minimum is next
hop in shortest path ➜ forwarding table
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8. Distance Vector Algorithm (3)
Dx(y) = estimate of least cost from x to y
Distance vector: Dx = [Dx(y): y  N ]
Node x knows cost to each neighbor v: c(x,v)
Node x maintains Dx = [Dx(y): y  N ]
Node x also maintains its neighbors’ distance vectors (at least temporarily)
For each neighbor v, x maintains Dv = [Dv(y): y  N ]
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9. Distance Vector Algorithm (4)
Basic Idea:
Each node periodically sends its own distance vector estimate to neighbors
When a node x receives new DV estimate from neighbor, it updates its own DV using B-F equation:
Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N
Under minor, natural conditions, the estimate Dx(y) converges to actual least cost dx(y)
CS 5565 Spring 2012

10. Distance Vector Algorithm (5)
Iterative, asynchronous: each local iteration caused by:
local link cost change
DV update message from neighbor
Distributed:
each node notifies neighbors only when its DV changes
neighbors then notify their neighbors if necessary
Each node:
wait for (change in local link cost of msg from neighbor)
recompute estimates
if DV to any dest has changed, notify neighbors
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11. Example DV Routing - 1 2 5 1 1 1 - 4  2 5 4 2 2 4 - 1 1 3 5  1 -- 1 2 5 1 1 1 - 4  2 5 4 2 2 4 - 1 1 3 5  1 -
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12. Example (cont’d) Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N - 12 5 - 1 2 3 - 1 2 3  1 1 - 4  1 - 3 5 1 - 3 4  2 4 2 4 - 1 2 3 - 1 2 3 - 1  5 1 5  1 - 3 5 1 - 3 4 1 - 
time
Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N
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13. Example (cont’d) Converged after 3 iterations
What if link cost changes? 1 2 3 - 4
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14. Distance Vector: Link Cost Changes
node detects local link cost change
updates routing info, recalculates distance vector
if DV changes, notify neighbors 1 y 4 1 x z 50
At time t0, y detects the link-cost change, updates its DV,
and informs its neighbors.
At time t1, z receives the update from y and updates its table.
It computes a new least cost to x and sends its neighbors its DV.
At time t2, y receives z’s update and updates its distance table.
y’s least costs do not change and hence y does not send any
message to z.
“good
news
travels
fast”
CS 5565 Spring 2012

15. Count-To-Infinity Before change: x y z 51 50 x z y 60 y to x via z4 50 y
Before change: - 4 5 4 - 1 5 1 - 50 51 - 1 5 60 50 51 - 1 6 50 51 - 1 7 50 51 - 1 8 x y z
y to x via z
z to x via y
y to x via z
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16. Distance Vector: Link Cost Changes
good news travels fast
bad news travels slow - “count to infinity” problem!
44 iterations before algorithm stabilizes
Poisoned reverse:
If Z routes through Y to get to X :
Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)
will this completely solve count to infinity problem? x z 1 4 50 y 60
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17. Poisoned Reverse After change: x  y z x z y 60 50 1 y to x via z4 50 y
After change: - 51 50 51 - 1 5 1 - - 51 50 - 51 50 50 51 - 1 50 51 - 1 x  60 51 - 1  - 1 6 - 1 y 50 1 5 1 - 50 1 - z
y to x via z
Don’t tell z dist to x
z to x via x
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18. Comparison of LS and DV algorithms
Message complexity
LS: with n nodes, E links, O(nE) msgs sent
DV: exchange between neighbors only
convergence time varies
Speed of Convergence
LS: O(n2) algorithm requires O(nE) msgs
may have oscillations
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 node’s table used by others
error propagates thru network
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19. Hierarchical Routing Our routing study thus far - idealization
all routers identical
network “flat”
… not true in practice
scale: with 200 million destinations:
can’t store all dest’s in routing tables!
routing table exchange would swamp links!
administrative autonomy
internet = network of networks
each network admin may want to control routing in its own network
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20. Hierarchical Routing
aggregate routers into regions, “autonomous systems” (AS)
routers in same AS run same routing protocol
“intra-AS” routing protocol
routers in different AS may run different intra-AS routing protocols
Gateway router
Direct link to router in another AS
Example:
[AS1312]
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21. Interconnected ASes 3b 1d 3a 1c 2a
AS3
AS1
AS2 1a 2c 2b 1b
Intra-AS
Routing
algorithm
Inter-AS
Forwarding
table 3c
Forwarding table is configured by both intra- and inter-AS routing algorithm
Intra-AS sets entries for internal dests
Inter-AS & Intra-AS sets entries for external dests
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22. Inter-AS tasks AS1 needs:
to learn which dests are reachable through AS2 and which through AS3
to propagate this reachability info to all routers in AS1
Job of inter-AS routing!
Suppose router in AS1 receives datagram for which dest is outside of AS1
Router should forward packet towards one of the gateway routers, but which one? 3b 1d 3a 1c 2a
AS3
AS1
AS2 1a 2c 2b 1b 3c
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23. Inter-AS tasks (cont’d)
Scenario 1
Destination x is reachable through single AS
Inter-AS must propagate this information inside AS
Suppose router in AS1 receives datagram for which dest is outside of AS1
Router should forward packet towards one of the gateway routers, but which one?
Least cost path to 1c is interface l, add (x, l) to routing table
AS3 advertises route to x 3b 1d 3a 1c 2a
AS3
AS1
AS2 1a 2c 2b 1b 3c
AS2 does not advertise route to x
Spread in AS1:
use gateway 1c to get to x
CS 5565 Spring 2012

24. Hot Potato Routing Scenario 2:
Destination is reachable through multiple AS:
Hot potato routing: send packet towards closest of two routers
Suppose router in AS1 receives datagram for which dest is outside of AS1
Router should forward packet towards one of the gateway routers, but which one? 3b 1d 3a 1c 2a
AS3
AS1
AS2 1a 2c 2b 1b 3c
CS 5565 Spring 2012

25. Hot Potato Routing Scenario 2:
Destination is reachable through multiple AS:
Hot potato routing: send packet towards closest of two routers
Suppose router in AS1 receives datagram for which dest is outside of AS1
Router should forward packet towards one of the gateway routers, but which one?
1b is closer than 1c, interface k leads to 1b, so add (x, k) to routing table
AS3 advertises route to x 3b 1d 3a 1c 2a
AS3
AS1
AS2 1a 2c 2b 1b 3c
AS2 advertises route to x
Spread in AS1:
1c and 1b lead to x
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26. Summary Routing algorithms: Hierarchical Routing
Link State
Distance Vector
Hierarchical Routing
AS: autonomous systems
Next: application to Internet/IP
CS 5565 Spring 2012