# Lecture 1 Internet

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```					Lecture 8 Overview
Graph abstraction
5
v   3       w
2                   5
u           2                   z
3   1
1                       2
x           y
Graph: G = (N,E)                                      1

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) }

Graph abstraction is useful in other network contexts

Example: P2P, where N is set of peers and E is set of TCP connections

CPE 401/601 Lecture 8 : Routing Algorithms                                           2
Graph abstraction: costs
5                                 • c(x,x’) = cost of link (x,x’)
v      3       w
2                          5            - e.g., c(w,z) = 5
u            2                         z
3     1
1                                         • cost could always be 1, or
x              y       2
inversely related to bandwidth, or
1
inversely related to congestion

Cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)

Routing algorithm: algorithm that finds least-cost path

CPE 401/601 Lecture 8 : Routing Algorithms                                                3
Routing Algorithm classification
• Global or decentralized information?
– all routers have complete topology,

• Decentralized: distance vector algorithms
– router knows physically-connected neighbors
– iterative process of computation,
• exchange of info with neighbors
CPE 401/601 Lecture 8 : Routing Algorithms            4
Routing Algorithm classification
• Static or dynamic?

• Static:
– routes change slowly over time

• Dynamic:
– routes change more quickly
• periodic update
• in response to link cost changes

CPE 401/601 Lecture 8 : Routing Algorithms            5
Dijkstra’s algorithm
– Topology, link costs known to all nodes
– all nodes have same info
• Compute least cost paths from source node to
all other nodes
– produces forwarding table for that node
• Iterative:
– after k iterations, know least cost path to k dests
CPE 401/601 Lecture 8 : Routing Algorithms                    6
Dijkstra’s Algorithm
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
CPE 401/601 Lecture 8 : Routing Algorithms   7
Dijsktra’s Algorithm
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
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‘
CPE 401/601 Lecture 8 : Routing Algorithms               8
Dijkstra’s algorithm, discussion
• Oscillations possible:
– e.g., link cost = amount of carried traffic

A                             A                       A                       A
1               1+e         2+e              0       0                       2+e
2+e                       0
D                       B      D                     B   D                   B   D
0       0                                                                                    B
1+e 1                   0 0                     1+e 1
0               e              0             0           1         1+e           0           e
C                              C                      C                        C
1
1
e                          … recompute              … recompute         … recompute
initially                     routing

CPE 401/601 Lecture 8 : Routing Algorithms                                                               9
Distance Vector Algorithm
Bellman-Ford Equation
• dynamic programming
Define
• dx(y) := cost of least-cost path from x to y

Then
• dx (y) = minv {c(x,v) + dv(y) }
• where min is taken over all neighbors v of x

CPE 401/601 Lecture 8 : Routing Algorithms       10
Bellman-Ford example
5
Clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3
v       3       w
2                            5
u            2               1            z    B-F equation says:
3
1                                 2            du(z) = min { c(u,v) + dv(z),
x               y
1                                         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
CPE 401/601 Lecture 8 : Routing Algorithms                                               11
Distance vector algorithm
• Basic idea:
– From time-to-time, each node sends its own
distance vector estimate to neighbors
– Asynchronous
• When a node x receives new DV estimate
from neighbor, it updates its own DV using B-F
Dx(y) ← minv{c(x,v) + Dv(y)}     for each node y ∊ N

• Under minor, natural conditions, the estimate
Dx(y) converge to the actual least cost dx(y)
CPE 401/601 Lecture 8 : Routing Algorithms                         12
Distance Vector Algorithm
• Iterative, asynchronous:                         Each node:
– each local iteration caused by
cost or msg from neighbor)
• DV update message from
neighbor
• Distributed:                               recompute estimates

– each node notifies neighbors
only when its DV changes             if DV to any dest has
changed, notify neighbors
– neighbors then notify their
neighbors if necessary
CPE 401/601 Lecture 8 : Routing Algorithms                           13
y
– node detects local link cost change                                   4        1
x                    z
– updates routing info, recalculates                                        50
distance vector
– if DV changes, notify neighbors
“good         and informs its neighbors.
news At time t1, z receives the update from y and updates its table.
travels It computes a new least cost to x and sends its neighbors its DV.
fast”   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.
CPE 401/601 Lecture 8 : Routing Algorithms                                                 14
y
4        1
– good news travels fast                                 x                z
50
• “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?
CPE 401/601 Lecture 8 : Routing Algorithms                                          15
LS vs DV
• Message complexity
– LS: with n nodes, E links, O(nE) msgs sent
– DV: exchange between neighbors only

• Speed of Convergence
– LS: O(n2) algorithm
• may have oscillations
– DV: convergence time varies
• may be routing loops
• count-to-infinity problem
CPE 401/601 Lecture 8 : Routing Algorithms           16
LS vs DV
• Robustness: what happens if router
malfunctions?
• LS:
– each node computes only its own table
• DV:
– DV node can advertise incorrect path cost
– each node’s table used by others
• error propagate thru network

CPE 401/601 Lecture 8 : Routing Algorithms          17
Lecture 9
Routing in the Internet

CPE 401 / 601

Computer Network Systems

slides modified from J. Dave Hollinger
slides are are modified fromKurose & K. Ross
Hierarchical Routing
• scale
– with 200 million destinations
– can’t store all dests in routing tables!
– routing table exchange would swamp links!

– internet = network of networks
– each network admin may want to control routing
in its own network

CPE 401/601 Lecture 9 : Routing in the Internet           19
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
– Direct link to router in another AS
CPE 401/601 Lecture 9 : Routing in the Internet               20
Interconnected ASes
• 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

3c
3a                                          2c
3b                                                  2a
AS3                                                  2b
1c
AS2
1a                  1b
Intra-AS      Inter-AS
AS1                   Routing       Routing
1d                                      algorithm     algorithm

Forwarding
table

CPE 401/601 Lecture 9 : Routing in the Internet                                            21
• 1a in AS1 receives datagram destined outside of AS1
– should forward packet to gateway router, but which one?
• AS1 must:
– learn which dests are reachable through AS2 and AS3
– propagate this reachability info to all routers in AS1
– Job of inter-AS routing!

3c
3a                                    2c
3b                                            2a
AS3                                            2b
1c
AS2
1a            1b
1d         AS1
CPE 401/601 Lecture 9 : Routing in the Internet                              22
Example: Forwarding table in 1d
• AS1 learns (via inter-AS protocol) that subnet x is
reachable via AS3 (gateway 1c) but not via AS2
• inter-AS protocol propagates info to 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)

3c
…             x
3a                                        2c
3b                                                2a
AS3                                                   2b
1c
AS2
1a                1b
1d            AS1

CPE 401/601 Lecture 9 : Routing in the Internet                                       23
Example: Multiple ASes
• now suppose AS1 learns from inter-AS protocol that
subnet x is reachable from both AS3 and AS2
• to configure forwarding table, router 1d must
determine towards which gateway it should forward
packets for dest x.
– this is also job of inter-AS routing protocol!

x
3c
3a                                         2c
3b                                                 2a
AS3                                                 2b
1c
AS2
1a                 1b
1d            AS1

CPE 401/601 Lecture 9 : Routing in the Internet                                       24
Example: Multiple ASes
• now suppose AS1 learns from inter-AS protocol that
subnet x is reachable from both AS3 and AS2
• to configure forwarding table, router 1d must
determine towards which gateway it should forward
packets for dest x.
– this is also job of inter-AS routing protocol!
• hot potato routing: send packet towards closest of
two routers
Use routing info                                Determine from
Learn from inter-AS                                      Hot potato routing:    forwarding table the
from intra-AS
protocol that subnet                                    Choose the gateway      Interface i that leads
protocol to determine
x is reachable via                                         that has the       to least-cost gateway.
costs of least-cost
multiple gateways                                       smallest least cost         Enter (x,i) in
paths to each
of the gateways                                 forwarding table

CPE 401/601 Lecture 9 : Routing in the Internet                                                   25
Intra-AS Routing
Intra-AS Routing
• known as Interior Gateway Protocols (IGP)

• most common Intra-AS routing protocols:

– RIP: Routing Information Protocol

– OSPF: Open Shortest Path First

– IGRP: Interior Gateway Routing Protocol
• Cisco proprietary

CPE 401/601 Lecture 9 : Routing in the Internet    27
Routing Information Protocol
• distance vector algorithm
• distance metric: # of hops
– max = 15 hops

From router A to subnets:
u                       v              destination hops
u         1
A               B        w             v         2
w         2
x         3
x          y         3
z       C               D
y              z         2

CPE 401/601 Lecture 9 : Routing Information Protocol                           28
• distance vectors:
– exchanged among neighbors every 30 sec via
Response Message

– list of up to 25 destination subnets within AS

CPE 401/601 Lecture 9 : Routing Information Protocol      29
RIP: Example
z
w                              x                                y
A                           D            B

C
Routing/Forwarding table in D
Destination Network        Next Router                          Number of hops to dest
w                                       A               2
y                                       B               2
z                                       B               7
x                                       --              1
….                                      ….              ....

CPE 401/601 Lecture 9 : Routing Information Protocol                                30
RIP: Example
Dest       Next hops
x            - 1                        from A to D
z           C 4
….          … ...
z
w                           x                                     y
A                           D               B

Routing/Forwarding table in D   C
Destination Network        Next Router                        Num. of hops to dest.
w                                         A                     2
y                                         B                     2
z                                         B A                   7 5
x                                         --                    1
….                                        ….                    ....
CPE 401/601 Lecture 9 : Routing Information Protocol                                 31
– routes via neighbor invalidated
• if tables changed
– link failure info propagates to entire net
– poison reverse used to prevent ping-pong loops
• infinite distance = 16 hops

CPE 401/601 Lecture 9 : Routing Information Protocol      32
RIP Table processing
• RIP routing tables managed by application-
level process called route-d (daemon)
periodically repeated
routed                            routed

Transprt                                                   Transprt
(UDP)                                                     (UDP)
network           forwarding               forwarding      network
(IP)             table                     table            (IP)
physical                                                   physical
CPE 401/601 Lecture 9 : Routing Information Protocol                              33
Open Shortest Path First (OSPF)
Open Shortest Path First
– LS packet dissemination
– topology map at each node
– route computation using Dijkstra’s algorithm
neighbor router
– via flooding
– carried in OSPF messages directly over IP
CPE 401/601 Lecture 9 : Open Shortest Path First        35
• security: all OSPF messages authenticated
– to prevent malicious intrusion
• 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 uses same topology data base as OSPF
• hierarchical OSPF in large domains

CPE 401/601 Lecture 9 : Open Shortest Path First                         36
Hierarchical OSPF

CPE 401/601 Lecture 9 : Open Shortest Path First   37
Hierarchical OSPF
• two-level hierarchy: local area, backbone
• each nodes has detailed area topology
• know only direction 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
• boundary routers: connect to other AS’s
CPE 401/601 Lecture 9 : Open Shortest Path First             38
Border Gateway Protocol (BGP)
Border Gateway Protocol(BGP)
• De facto standard for Internet inter-AS routing
• allows subnet to advertise its existence to rest
of Internet: “I am here”
• BGP provides each AS a means to:
– Obtain subnet reachability information from
neighboring ASs
– Propagate reachability information to all AS-
internal routers
– Determine “good” routes to subnets based on
reachability information and policy
CPE 401/601 Lecture 9 : Border Gateway Protocol         40
BGP basics
• Pairs of routers (BGP peers) exchange routing info
over semi-permanent TCP connections: BGP sessions
– BGP sessions need not correspond to physical links
• when AS2 advertises a prefix to AS1:
– AS2 promises it will forward datagrams towards that prefix

eBGP session
3c
iBGP session
3a                                        2c
3b                                                 2a
AS3                                                  2b
1c
AS2
1a               1b
AS1         1d
CPE 401/601 Lecture 9 : Border Gateway Protocol                                   41
Distributing reachability info
• using eBGP session between 3a and 1c, AS3 sends
prefix reachability info to AS1
– 1c can then use iBGP do distribute new prefix info to all
routers in AS1
– 1b can then re-advertise new reachability info to AS2 over
1b-to-2a eBGP session

eBGP session
3c
iBGP session
3a                                        2c
3b                                                 2a
AS3                                                  2b
1c
AS2
1a               1b
AS1         1d
CPE 401/601 Lecture 9 : Border Gateway Protocol                                   42

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