1. Chapter 4: outline 4.1 introduction
4.2 virtual circuit and datagram networks
4.3 what’s inside a router
4.4 IP: Internet Protocol
datagram format
IPv4 addressing
ICMP
IPv6
4.5 routing algorithms
link state
distance vector
hierarchical routing
4.6 routing in the Internet
RIP
OSPF
BGP
4.7 broadcast and multicast routing
Network Layer

2. Interplay between routing, forwarding
routing algorithm determines
end-end-path through network
routing algorithm
forwarding table determines
local forwarding at this router
local forwarding table
dest address
output link
address-range 1
address-range 2
address-range 3
address-range 4 3 2 1
IP destination address in
arriving packet’s header 1 2 3
Network Layer

3. Graph abstraction z x u y w v 5 2 3 1 graph: G = (N,E)
N = set of routers = { u, v, w, x, y, z }
E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }
Network Layer

4. Graph abstraction: costs
c(x,x’) = cost of link (x,x’)
e.g., c(w,z) = 5
cost is inversely related to bandwidth,
or proportionally related to congestion
- high bandwidth, low congestion: cost 1
- low bandwidth, high congestion: high cost u y x w v z 2 1 3 5
cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)
key question: what is the least-cost path between u and z ?
routing algorithm: algorithm that finds that least cost path
Network Layer

5. Routing Algorithm classification
[Classification 1] Global or Decentralized information?
Global:
all routers have complete topology and link cost info.
“link state (LS)” algorithms
Decentralized:
router only knows physically-connected neighbors and link costs to neighbors
“distance vector (DV)” algorithms
Network Layer

6. Routing Algorithm classification
[Classification 2] Static or Dynamic?
Static:
Manual setup
Network administrator usually setups the route
routes does not change, or change slowly over time
Dynamic:
routes change more quickly
periodic update
in response to link cost changes
LS and DV algorithms
Network Layer

7. Routing Algorithm classification
Static routing
Manually configuration routing table
Single “permanent” route is configured for each source to destination pair
Routes usually determined using a least cost algorithm
Route fixed, at least until a change in network topology
Can’t react dynamically to network change such as router’s crash
Practically, fixed routing is much used within a local domain

8. Routing Algorithm classification
Dynamic route
Network protocol adjusts automatically for topology or traffic changes
Unix hosts can run routing daemon routed or gated
Routing
Table
Routing
Table
Routing
Protocol
Routing
Protocol
Update Routing Information

9. Routing Algorithm classification
[Classification 3] Source or Hop-by-Hop?
Source routing:
Source will determine the entire route
Routers only act as store-forward devices
Hop-by-hop:
Routers determine the path based on theirs’ own information
LS and DV algorithms
Network Layer

10. Chapter 4: outline 4.1 introduction
4.2 virtual circuit and datagram networks
4.3 what’s inside a router
4.4 IP: Internet Protocol
datagram format
IPv4 addressing
ICMP
IPv6
4.5 routing algorithms
link state
distance vector
hierarchical routing
4.6 routing in the Internet
RIP
OSPF
BGP
4.7 broadcast and multicast routing
Network Layer

11. Flooding “Link State”
Each node floods “link status” to the entire routers
Packet sent by source router to every neighbor
Incoming packet resent to all outgoing links except source link
Duplicate packets already transmitted are discarded
Prevent endless retransmission
All routers get information to build routing table
High traffic load
Use the link state to build a shortest path map to every node
Also known as Shortest Path First (SPF) algorithm
Network Layer

12. Link State Algorithm - Overview
Exchange its connection and cost to its neighbors
All nodes will have same info
Each router computes the set of optimum path to all destination (using a Shortest Path - Dijkstra's algorithm) W X Y Z
link state
link state
link state
Network Layer

13. Link State Algorithm - Overview
Each router initially begins with directly connected network
Link state flooding (broadcast)
Determine full knowledge of distant routers and their connection R1
exchange link
state packets R2 R4
build topological
database
Routing
Table R3
compute SPF
update routing
table
Network Layer

14. Link State Algorithm - Overview
On the topology change, send the change information to other routers
All information will converge R1 R4
topology
change R2 R3
Network Layer

15. A Link-State Routing Algorithm
Dijkstra’s algorithm
net topology, link costs known to all nodes
computes the least cost paths from one node (‘source”) to all other nodes
Result: forwarding table for that node
iterative: 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(v): current value of cost of path from source to dest. V
p(v): predecessor node along path from source to v
N': set of nodes whose least cost path definitively known
Network Layer

16. Dijsktra’s Algorithm (see this, not one in the book)
Inside node u u y x w v z 2 1 3 5
0 Pre-calculation:
c(u,v)
c(u,x)
c(u,y)
c(u,w)
c(u,z) 2 1 ∞ 5
link cost
value
c(v,u)
c(v,x)
c(v,y)
c(v,w)
c(v,z) 2 ∞ 3
link cost
value
c(x,u)
c(x,v)
c(x,y)
c(x,w)
c(x,z) 1 2 3 ∞
link cost
value
c(y,u)
c(y,v)
c(y,x)
c(y,w)
c(y,z) ∞ 1 2
link cost
value
c(w,u)
c(w,v)
c(w,x)
c(w,y)
c(w,z) 5 3 1
link cost
value
c(z,u)
c(z,v)
c(z,x)
c(z,y)
c(z,w) ∞ 2 5
link cost
value
Network Layer

17. Dijsktra’s Algorithm (see this, not one in the book)
Inside node u u y x w v z 2 1 3 5
1 Initialization:
2 N' = {u}
3 for all nodes v
if v adjacent to u
then D(v) = c(u,v), p(v)=u
else D(v) = ∞ 7
8 Loop
9 find e not in N' such that D(e) is a minimum
10 add e to N'
11 update D(n) for all n (not in N') adjacent to e: if (D(e) + c(e,n) < D(n)) {
D(n) = D(e) + c(e,n), p(n) = e }
15 /* new cost to n is either old cost to n or
shortest path cost to e plus cost from e to n */
17 until all nodes in N'
Network Layer

18. Dijkstra’s algorithm: example
Step 1 2 3 4 5 N' u ux
uxy
uxyv
uxyvw
uxyvwz
D(v),p(v)
2,u
D(w),p(w)
5,u
4,x
3,y
D(x),p(x)
1,u
D(y),p(y) ∞
2,x
D(z),p(z) ∞
4,y
D(n) = min( D(n), D(e) + c(e,n) ) u y x w v z 2 1 3 5
[Example]
Step1: D(w) = min(D(w), D(x) + c(x,w)) = min(5, 1 + 3) = D(y) = min(D(y), D(x) + c(x,y)) = min(∞, 1 + 1) = 2
Step2: D(w) = min(D(w), D(y) + c(y,w)) = min(4, 2 + 1) = 3
Network Layer

19. Dijkstra’s algorithm: example
resulting shortest-path tree from u: u y x w v z
“resulting forwarding table” in u: v x y w z
(u,v)
(u,x)
destination
link
Network Layer

20. Dijkstra’s algorithm: another example
D(v)
p(v)
D(w)
p(w)
D(x)
p(x)
D(y)
p(y)
D(z)
p(z)
Step N' u ∞
7,u
3,u
5,u 1 uw ∞
11,w
6,w
5,u 2
uwx
14,x
11,w
6,w 3
uwxv
14,x
10,v 4
uwxvy
12,y 5
uwxvyz w 3 4 v x u 5 7 y 8 z 2 9
notes:
construct shortest path tree by tracing predecessor nodes
Network Layer

21. Dijkstra’s algorithm, discussion
oscillations possible:
link cost
amount of carried traffic
Initial traffic
z  w: 1 traffic
x  w: 1 traffic
y  w: e traffic
routers execute their LS routing algorithm with the same periodicity
Solution:
ensure that not all routers run the LS algorithm at the same time.
Network Layer

22. Chapter 4: outline 4.1 introduction
4.2 virtual circuit and datagram networks
4.3 what’s inside a router
4.4 IP: Internet Protocol
datagram format
IPv4 addressing
ICMP
IPv6
4.5 routing algorithms
link state
distance vector
hierarchical routing
4.6 routing in the Internet
RIP
OSPF
BGP
4.7 broadcast and multicast routing
Network Layer

23. Distance vector algorithm
At Node i, for the destination j via all other neighbor nodes
let
dx(y) := cost of least-cost path from x to y
then
dx(y) = min {c(x,v) + dv(y) }
a, 22.7
b, 28.1
c, 15.1
di(j) =
where a, b, c are the i‘s neighbors
Bellman-Ford equation (dynamic programming) v
cost from neighbor v to destination y
cost to neighbor v
min taken over all neighbors v of x
Network Layer

24. Bellman-Ford example Assume that router u knows…
dv(z) = 5, dx(z) = 3, dw(z) = 3 u y x w v z 2 1 3 5
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 achieving minimum” is the next hop in shortest path and it will be used in forwarding table
Network Layer

25. Distance vector algorithm
Dx(y) = estimate of least cost from x to y
x maintains “distance vector”  Dx = [Dx(y): y є N ]
node x:
knows “exact” cost to each neighbor v: c(x,v)
maintains its neighbors’ distance vectors.
For each neighbor v, x maintains Dv = [Dv(y): y є N ]
Network Layer

26. Distance vector algorithm
key idea:
from time-to-time, each node sends its own distance vector (DV) estimate to neighbors
when 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 natural conditions, the estimate Dx(y) will converge to the actual cost dx(y)
Network Layer

27. Distance vector algorithm
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 or msg from neighbor)
recompute estimates
if DV to any dest has changed, notify neighbors
Network Layer

28. z y x Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2
node x
table
cost to
cost to
x y z
x y z x x 2 3 y
from ∞ ∞ ∞
from y z z ∞ ∞ ∞
node y
table
cost to x z 1 2 7 y
x y z x ∞ ∞ ∞ y
from z ∞ ∞ ∞
node z
table
cost to
x y z x
∞ ∞ ∞
from y ∞ ∞ ∞ z 7 1
time
Network Layer

29. z y x Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2
node x
table
cost to
cost to
cost to
x y z
x y z
x y z x x 2 3 x y
from y ∞ ∞ ∞
from y
from z z ∞ ∞ ∞ z
node y
table
cost to
cost to x z 1 2 7 y
cost to
x y z
x y z
x y z x ∞ ∞ ∞ x x y y
from
from y
from z z ∞ ∞ ∞ z
node z
table
cost to
cost to
cost to
x y z
x y z
x y z
Dz(x) = min{c(z,x) Dx(x), c(z,y) + Dy(x)}
= min{7+0 , 1+2} = 3 x x x
∞ ∞ ∞ y
from y y
from
from ∞ ∞ ∞ z z z 7 1
time
time
Network Layer

30. Distance vector: link cost changes
SKIP!!
Distance vector: link cost changes
link cost changes:
node detects local link cost change
updates routing info, recalculates distance vector
if DV changes, notify neighbors x z 1 4 50 y
“good
news
travels
fast”
t0 : y detects link-cost change, updates its DV, informs its neighbors.
t1 : z receives update from y, updates its table, computes new least cost to x , sends its neighbors its DV.
t2 : y receives z’s update, updates its distance table. y’s least costs do not change, so y does not send a message to z.
Network Layer

31. Distance vector: link cost changes
SKIP!!
Distance vector: link cost changes
link cost changes:
node detects local link cost change
bad news travels slow - “count to infinity” problem!
44 iterations before algorithm stabilizes x z 1 4 50 y 60
At time t0, y detects the link-cost change, updates its DV,
and informs its neighbors.
Dy(x) = min{c(y,x)+Dx(x), c(y,z)+Dz(x)} = min{60+0, 1+5} = 6
 “Routing Loop” occurs (from y to x: y send to z and z send to y)
At time t1, z receives the update from y and updates its table.
Dz(x) = min{c(z,x)+Dx(x), c(z,y)+Dy(x)} = min{50+0, 1+6} = 7
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 DV, and inform its neighbor
Dy(x) = min{c(y,x)+Dx(x), c(y,z)+Dz(x)} = min{60+0, 1+7} = 8 …
Network Layer

32. Distance vector: link cost changes
SKIP!!
Distance vector: link cost changes
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
Network Layer

33. Comparison of LS and DV algorithms
robustness: what happens if router malfunctions?
LS:
node can advertise incorrect link cost
each node computes only its own table
Incorrect link cost will be delivered after a (long) periodic time.
DV:
DV node can advertise incorrect path cost
incorrect cost delivered immediately
each node’s table used by others
error propagate thru network
message complexity
LS: with n nodes, E links, O(nE) msgs sent
Link State Flooding  Fast Convergence
DV: exchange between neighbors only
convergence time varies (and slow)
Weak point
LS: O(n2) algorithm requires O(nE) msgs  fast
may have oscillations
DV: convergence time varies (and slow)
may be routing loops
count-to-infinity problem
Network Layer

34. Chapter 4: outline 4.1 introduction
4.2 virtual circuit and datagram networks
4.3 what’s inside a router
4.4 IP: Internet Protocol
datagram format
IPv4 addressing
ICMP
IPv6
4.5 routing algorithms
link state
distance vector
hierarchical routing
4.6 routing in the Internet
RIP
OSPF
BGP
4.7 broadcast and multicast routing
Network Layer

35. Hierarchical routing our routing study thus far - idealization
all routers identical
network “flat”
… not true in practice
scale: with 600 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
Network Layer

36. 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 can run different intra-AS routing protocol
gateway router:
at “edge” of its own AS
has link to router in another AS
Network Layer

37. 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 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
Network Layer

38. Inter-AS tasks
suppose router in AS1 receives datagram destined outside of AS1:
router should forward packet to gateway router, but which one?
AS1 must:
learn which dests are reachable through AS2, which through AS3
propagate this reachability info to all routers in AS1
job of inter-AS routing! 3c 3a 3b 2c
AS3
other
networks
AS1 1c 1a 1d 1b 2a 2b
other
networks
AS2
Network Layer

39. Example: setting forwarding table in router 1d
suppose AS1 learns (via inter-AS protocol) that subnet x reachable via AS3 (gateway 1c), but not via AS2
inter-AS protocol propagates reachability info to all internal routers
router 1d determines from intra-AS routing info that its interface I is on the least cost path to 1c
installs forwarding table entry (x,I) … x 3c 3a 3b 2c
AS3
other
networks
AS1 1c 1a 1d 1b 2a 2b
other
networks I
AS2
Network Layer

40. Example: choosing among multiple ASes
now suppose AS1 learns from inter-AS protocol that subnet x is reachable from AS3 and from AS2.
to configure forwarding table, router 1d must determine which gateway it should forward packets towards for dest x
this is also job of inter-AS routing protocol! … x 3c …… 3a 3b 2c
AS3
other
networks
AS1 1c 1a 1d 1b 2a 2b
other
networks
AS2 ?
Network Layer

41. Example: choosing among multiple ASes
now suppose AS1 learns from inter-AS protocol that subnet x is reachable from AS3 and from AS2.
Before Inter-AS routing algorithm select one of two gateways, which gateways does the router 1d send a packet destined to subnet x?
Just send it to gateway 1b (more closer one.)
hot potato routing: send packet towards the closest of two gateways.
the AS gets rid of the packet (the hot potato) as quickly as possible (more precisely, as inexpensively as possible).
This is done by having a router send the packet to the gateway router that has the smallest router-to-gateway cost among all gateways with a path to the destination.
Network Layer

42. Internet Routing Architecture
IGP: Interior Gateway Protocols
- RIP, OSPF, IGRP
EGP: Exterior Gateway Protocols
- BGP(Boarder Gateway Protocol)
Autonomous
System
IGP
EGP/BGP
IGP
EGP/BGP
IGP
Autonomous
System
BGP4
BGP4
Autonomous
System
IGP
IGP
BGP4
Autonomous
System
EGP/BGP
EGP/BGP
EGP/BGP
EGP/BGP
IGP
IGP
IGP
IGP
Autonomous
System
Network Layer