Interplay between routing and
forwarding
routing algorithm
Routing Algorithms and Routing
in the Internet
local forwarding table
header value output link
0100
0101
0111
1001
3
2
2
1
value in arriving
packet’s header
1
0111
3 2
Network Layer
4-1
Graph abstraction
Network Layer
Graph abstraction: costs
5
2
u
v
2
1
Graph: G = (N,E)
x
5
3
w
3
1
5
z
1
• c(x,x’) = cost of link (x,x’)
3
w
3
5
z
1
- e.g., c(w,z) = 5
• cost could always be 1, or
inversely related to bandwidth,
or inversely related to
congestion
Cost of path (x1, x2 , x3,…, x p ) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)
E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }
x
1
y
2
Question: What’s the least-cost path between u and z ?
Remark: Graph abstraction is useful in other network contexts
Routing algorithm: algorithm that finds least-cost path
Example: P2P, where N is set of peers and E is set of TCP connections
Network Layer
v
2
1
2
y
2
u
N = set of routers = { u, v, w, x, y, z }
4-3
Network Layer
Routing Algorithm classification
A Link-State Routing Algorithm
Global or decentralized
information?
Dijkstra’s algorithm
Global:
❒
❒
❒
❒
❒
Static or dynamic?
Static:
❒
all routers have complete
topology, link cost info
❒ routes change slowly over
“link state” algorithms
Dynamic:
Decentralized:
router knows physicallyconnected neighbors, link
costs to neighbors
iterative process of
computation, exchange of info
with neighbors
4-2
time
❍
❒ routes change more quickly
❍
❍
net topology, link costs known
to all nodes
❍
❒
periodic update
in response to link cost
changes
❒
Network Layer
4-5
all nodes have same info
computes least cost paths
from one node (‘source”) to all
other nodes
❍
“distance vector” algorithms
accomplished via “link
state broadcast”
gives forwarding table for
that node
4-4
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
iterative: after k iterations,
know least cost path to k
dest.’s
Network Layer
4-6
1
Dijsktra’s Algorithm
Dijkstra’s algorithm: example
1 Initialization:
2 N' = {u}
3 for all nodes v
4
if v adjacent to u
5
then D(v) = c(u,v)
6
else D(v) = ∞
7
8 Loop
9 find w not in N' such that D(w) is a minimum
10 add w to N'
11 update D(v) for all v adjacent to w and not in N' :
12
D(v) = min( D(v), D(w) + c(w,v) )
13 /* new cost to v is either old cost to v or known
14 shortest path cost to w plus cost from w to v */
15 until all nodes in N'
Step
0
1
2
3
4
5
N'
u
ux
uxy
uxyv
uxyvw
uxyvwz
D(v),p(v) D(w),p(w)
2,u
5,u
2,u
4,x
2,u
3,y
3,y
D(x),p(x)
1,u
D(y),p(y)
∞
2,x
D(z),p(z)
∞
∞
4,y
4,y
4,y
5
2
u
2
1
Network Layer
v
x
3
w
3
1
5
z
1
y
2
4-7
Network Layer
4-8
Distance Vector Algorithm (1)
Dijkstra’s algorithm, discussion
Algorithm complexity: n nodes
❒
each iteration: need to check all nodes, w, not in N
❒
n(n+1)/2 comparisons: O(n2)
❒
more efficient implementations possible: O(nlogn)
Bellman-Ford Equation (dynamic programming)
Define
dx(y) := cost of least-cost path from x to y
Oscillations possible:
D
1
Then
e.g., link cost = amount of carried traffic
❒
1
0
A
0 0
C
1+e
e
A
2+e
B
D
0
1+e 1
C
1
e
0
0
B
… recompute
routing
initially
0
D
1
A
0 0
C
2+e
B
1+e
… recompute
2+e
D
0
A
1+e 1
C
0
e
B
… recompute
Network Layer
2
u
v
2
3
w
3
z
1
B-F equation says:
x
1
y
2
Network Layer
❒ Dx(y) = estimate of least cost from x to y
❒ Distance vector: Dx = [Dx (y): y є N ]
❒ Node x knows cost to each neighbor v:
du(z) = min { c(u,v) + d v(z),
c(u,x) + dx(z),
c(u,w) + d w(z) }
= min {2 + 5,
1 + 3,
5 + 3} = 4
Node that achieves minimum is next
hop in shortest path ➜ forwarding table
1
Network Layer 4-10
Distance Vector Algorithm (3)
Clearly, dv(z) = 5, d x(z) = 3, d w(z) = 3
5
where min is taken over all neighbors of x
4-9
Bellman-Ford example (2)
5
dx(y) = min {c(x,v) + dv(y) }
c(x,v)
❒ Node x maintains Dx = [Dx(y): y є N ]
❒ Node x also maintains its neighbors’
distance vectors
❍
4-11
For each neighbor v, x maintains
Dv = [Dv(y): y є N ]
Network Layer 4-12
2
Distance vector algorithm (4)
Distance Vector Algorithm (5)
Iterative, asynchronous:
Basic idea:
❒
❒
Each node:
each local iteration caused
by:
Each node periodically sends its own distance
vector estimate to neighbors
❒
wait for (change in local link
❒ local link cost change
When node 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
cost of msg from neighbor)
❒ DV update message from
neighbor
recompute estimates
Distributed:
❒ each node notifies
Under minor, natural conditions, the estimate
Dx(y) converge the actual least cost d x(y)
if DV to any dest has
changed, notify neighbors
neighbors only when its
DV changes
❍
neighbors then notify
their neighbors if
necessary
Network Layer 4-13
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
x y z
x ∞∞ ∞
y ∞∞ ∞
z 71 0
from
from
from
from
x 0 2 7
y 2 0 1
z 7 1 0
cost to
x y z
x 0 2 7
y 2 0 1
z 3 1 0
❒
❒
❒
good news travels fast
bad news travels slow - “count
to infinity” problem!
2
x
x 0 2 3
y 2 0 1
z 3 1 0
time
4
y
7
1
50
❒
50
1
z
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.
Network Layer 4-15
Network Layer 4-16
Comparison of LS and DV algorithms
❒
1
z
44 iterations before
algorithm stabilizes: see text
❒
LS: with n nodes, E links, O(nE)
msgs sent
❍
❒
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?
Network Layer 4-17
Robustness: what happens if
router malfunctions?
LS:
DV: exchange between
neighbors only
❍
❍
convergence time varies
Speed of Convergence
If Z routes through Y to get
to X :
❍
“good
news
travels
fast”
Message complexity
y
y
❒ if DV changes, notify neighbors
z
Poissoned reverse:
❒
x
distance vector
cost to
x y z
x
4
❒ updates routing info, recalculates
x 0 2 3
y 2 0 1
z 3 1 0
60
1
❒ node detects local link cost change
Distance Vector: link cost changes
Link cost changes:
Distance Vector: link cost changes
Link cost changes:
x 0 2 3
y 2 0 1
z 3 1 0
cost to
x y z
from
from
from
x ∞ ∞ ∞
y 2 0 1
z ∞∞ ∞
node z table
cost to
x y z
x 0 2 3
y 2 0 1
z 7 1 0
cost to
x y z
cost to
x y z
from
from
x 0 2 7
y ∞∞ ∞
z ∞∞ ∞
node y table
cost to
x y z
cost to
x y z
Network Layer 4-14
DV:
LS: O(n2 ) algorithm requires
O(nE) msgs
❍
❍ may have oscillations
DV: convergence time varies
❍
❍
may be routing loops
❍
count-to-infinity problem
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
• error propagate thru network
Network Layer 4-18
3
Hierarchical Routing
Hierarchical Routing
Our routing study thus far - idealization
❒
all routers identical
❒
network “flat”
aggregate routers
into regions,
“autonomous systems”
(AS)
❒
… not true in practice
scale: with 200 million
destinations:
❒ internet = network of
networks
❒ can’t store all dest’s in
routing tables!
❒ each network admin may
❍
want to control routing in its
own network
❒ routing table exchange
would swamp links!
❍
Network Layer 4-19
❒
3c
3b
3a
AS3
1a
2a
1c
1d
1b
Intra-AS
Routing
algorithm
2c
AS2
AS1
2b
Inter-AS
Routing
algorithm
Forwarding
table
configured by both intraand inter-AS routing
algorithm
❍
❍
routers in different
AS can run different
intra-AS routing
protocol
Network Layer 4-20
Intra-AS sets entries for
internal dests
Inter-AS & Intra-As sets
entries for external dests
AS1 needs:
Suppose router in AS1
receives datagram for
which dest is outside
of AS1
❍
❒ Forwarding table is
Direct link to router
in another AS
“intra-AS” routing
protocol
Inter-AS tasks
Interconnected ASes
❒
routers in same AS
run same routing
protocol
❒
administrative autonomy
Gateway router
Router should forward
packet towards on of
the gateway routers,
but which one?
1.
to learn which dests
are reachable
through AS2 and
which through AS3
2.
to propagate this
reachability info to
all routers in AS1
Job of inter-AS routing!
3c
3b
3a
AS3
1a
2a
1c
1d
1b
2c
AS2
2b
AS1
Network Layer 4-21
Example: Setting forwarding table
in router 1d
❒ Suppose AS1 learns from the inter-AS
protocol that subnet x is reachable from
AS3 (gateway 1c) but not from AS2.
❒ Inter-AS protocol propagates reachability
Network Layer 4-22
Example: Choosing among multiple ASes
❒ Now suppose AS1 learns from the inter-AS protocol that
subnet x is reachable from AS3 and from AS2.
❒ To configure forwarding table, router 1d must determine
towards which gateway it should forward packets for dest x.
❒ This is also the job on inter-AS routing protocol!
❒ Hot potato routing: send packet towards closest of two
routers.
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.
❒ Puts in forwarding table entry
(x,I).
Network Layer 4-23
Learn from inter-AS
protocol that subnet
x is reachable via
multiple gateways
Use routing info
from intra-AS
protocol to
determine
costs of least-cost
paths to each
of the gateways
Hot potato routing:
Choose the
gateway
that has the
smallest least cost
Determine from
forwarding table the
interface I that leads
to least-cost gateway.
Enter (x,I) in
forwarding table
Network Layer 4-24
4
Intra-AS Routing
RIP ( Routing Information Protocol)
❒
Also known as Interior Gateway Protocols (IGP)
❒
Distance vector algorithm
❒
Most common Intra-AS routing protocols:
❒
Included in BSD-UNIX Distribution in 1982
❒
Distance metric: # of hops (max = 15 hops)
❍
RIP: Routing Information Protocol
❍
OSPF: Open Shortest Path First
❍
u
IGRP: Interior Gateway Routing Protocol (Cisco
proprietary)
z
destination hops
u
1
v
2
w
2
x
3
y
3
z
2
v
A
B
C
D
w
x
y
Network Layer 4-25
RIP advertisements
Network Layer 4-26
RIP: Example
z
❒ Distance vectors: exchanged among
w
neighbors every 30 sec via Response
Message (also called advertisement)
A
x
D
B
y
C
❒ Each advertisement: list of up to 25
Destination Network
destination nets within AS
w
y
z
x
….
Next Router
Num. of hops to dest.
A
B
B
--
2
2
7
1
….
....
Routing table in D
Network Layer 4-27
RIP: Example
Dest
w
x
z
….
Next
C
…
w
hops
4
...
A
RIP: Link Failure and Recovery
Advertisement
from A to D
z
x
Network Layer 4-28
D
B
y
If no advertisement heard after 180 sec -->
neighbor/link declared dead
❍
routes via neighbor invalidated
❍
new advertisements sent to neighbors
❍
Destination Network
w
y
z
x
….
C
Next Router
A
B
B A
-Routing….
table in D
Num. of hops to dest.
2
2
7 5
1
....
Network Layer 4-29
❍
❍
neighbors in turn send out new advertisements (if
tables changed)
link failure info quickly propagates to entire net
poison reverse used to prevent ping-pong loops
(infinite distance = 16 hops)
Network Layer 4-30
5
RIP Table processing
❒
❒
OSPF (Open Shortest Path First)
RIP routing tables managed by application-level
process called route-d (daemon)
❒
“open”: publicly available
❒
Uses Link State algorithm
advertisements sent in UDP packets, periodically
repeated
routed
Transprt
(UDP)
network
(IP)
link
forwarding
table
routed
forwarding
table
physical
Transprt
(UDP)
network
(IP)
link
physical
❒
❒
❍
LS packet dissemination
❍
Topology map at each node
❍
Route computation using Dijkstra’s algorithm
OSPF advertisement carries one entry per neighbor
router
Advertisements disseminated to entire AS (via
flooding)
❍
Network Layer 4-31
OSPF “advanced” features (not in RIP)
❒
❒
❒
❒
Multiple same-cost paths allowed (only one path in
RIP)
For each link, multiple cost metrics for different
TOS (e.g., satellite link cost set “low” for best
effort; high for real time)
Integrated uni- and multicast support:
Multicast OSPF (MOSPF) uses same topology data
base as OSPF
Hierarchical OSPF in large domains.
Network Layer 4-33
Hierarchical OSPF
❒
❍
❒
❒
Network Layer 4-34
Internet inter-AS routing: BGP
Two-level hierarchy: local area, backbone.
❍
❒
Hierarchical OSPF
Security: all OSPF messages authenticated (to
prevent malicious intrusion)
❍
❒
Carried in OSPF messages directly over IP (rather than TCP
Network Layer 4-32
or UDP
❒ BGP (Border Gateway Protocol):
Link-state advertisements only in area
facto standard
each nodes has detailed area topology; only know
direction (shortest path) to nets in other areas.
Area border routers: “summarize” distances to
nets in own area, advertise to other Area Border
routers.
Backbone routers: run OSPF routing limited to
backbone.
the de
❒ BGP provides each AS a means to:
1.
Obtain subnet reachability information from
neighboring ASs.
2.
Propagate the reachability information to all
routers internal to the AS.
3.
Determine “good” routes to subnets based on
reachability information and policy.
❒ Allows a subnet to advertise its existence
Boundary routers: connect to other AS’s.
Network Layer 4-35
to rest of the Internet: “I am here”Network Layer
4-36
6
BGP basics
Distributing reachability info
❒ Pairs of routers (BGP peers) exchange routing info over semi-
❒ With eBGP session between 3a and 1c, AS3 sends prefix
❒ Note that BGP sessions do not correspond to physical links.
❒ 1c can then use iBGP do distribute this new prefix reach
permanent TCP conctns: BGP sessions
❒ When AS2 advertises a prefix to AS1, AS2 is promising it
will forward any datagrams destined to that prefix towards
the prefix.
❍
AS2 can aggregate prefixes in its advertisement
3c
3b
3a
AS3
1a
AS1
2a
1c
1d
1b
reachability info to AS1.
info to all routers in AS1
❒ 1b can then re-advertise the new reach info to AS2 over
the 1b-to-2a eBGP session
❒ When router learns about a new prefix, it creates an entry
for the prefix in its forwarding table.
3c
2c
AS2
3a
AS3
3b
2b
1a
AS1
eBGP session
1c
1d
2c
2a
AS2
1b
eBGP session
iBGP session
iBGP session
Network Layer 4-38
Network Layer 4-37
Path attributes & BGP routes
❒
When advertising a prefix, advert includes BGP
attributes.
❍
❒
❍
BGP route selection
❒ Router may learn about more than 1 route
to some prefix. Router must select route.
❒ Elimination rules:
Two important attributes:
❍
❒
prefix + attributes = “route”
2b
AS-PATH: contains the ASs through which the advert
for the prefix passed: AS 67 AS 17
1.
Local preference value attribute: policy
decision
NEXT-HOP: Indicates the specific internal-AS router to
next-hop AS. (There may be multiple links from current
AS to next-hop-AS.)
2.
Shortest AS-PATH
3.
Closest NEXT-HOP router: hot potato routing
4.
Additional criteria
When gateway router receives route advert, uses
import policy to accept/decline.
Network Layer 4-39
BGP messages
❒
❒
Network Layer 4-40
BGP routing policy
BGP messages exchanged using TCP.
BGP messages:
❍
❍
❍
❍
legend:
B
W
OPEN: opens TCP connection to peer and
authenticates sender
UPDATE: advertises new path (or withdraws old)
provider
network
X
A
customer
network:
C
Y
Figure 4.5
-BGPnew: a simple BGP scenario
KEEPALIVE keeps connection alive in absence of
UPDATES; also ACKs OPEN request
❒
A,B,C are provider networks
❒
X,W,Y are customer (of provider networks)
NOTIFICATION: reports errors in previous msg;
also used to close connection
❒
X is dual-homed: attached to two networks
Network Layer 4-41
❍
X does not want to route from B via X to C
❍
.. so X will not advertise to B a route to C
Network Layer 4-42
7
Why different Intra- and Inter-AS routing
?
BGP routing policy (2)
legend:
B
W
provider
network
X
A
customer
network:
C
A advertises to B the path AW
❒
B advertises to X the path BAW
❒
Should B advertise to C the path BAW?
❍
B wants to force C to route to w via A
❍
B wants to route only to/from its customers!
Inter-AS: admin wants control over how its traffic
routed, who routes through its net.
Intra-AS: single admin, so no policy decisions needed
Scale:
❒
No way! B gets no “revenue” for routing CBAW since neither
W nor C are B’s customers
❍
❒
❒
Y
Figure 4.5
-BGPnew: a simple BGP scenario
❒
Policy:
Network Layer 4-43
hierarchical routing saves table size, reduced update
traffic
Performance:
❒
Intra-AS: can focus on performance
❒
Inter-AS: policy may dominate over performance
Network Layer 4-44
8