Data Communication and Networks

Lecture 8

Networks:(Routing)

October 23, 2003

Joseph Conron

Computer Science Department

New York University

jconron@cs.nyu.edu

Some Perspective on Routing …..

When we wish to take a long trip by car, we consult a road map.

The road map shows the possible routes to our destination.

It might show us the shortest distance, but, it can’t always tell us what we really want to know: What is the fastest route! Why is this not always obvious?

Question: What’s the difference between you and network packet?

Packets are Dumb, Students are Smart!

We adapt to traffic conditions as we go. Packets depend on routers to choose how they

get their destination. Routers have maps just like we do. These are

called routing tables. What we want to know is:

How to these tables get constructed/updated? How are routes chosen using these tables?

Network Information Source and Update Timing Routing decisions usually based on knowledge of

network (not always) Distributed routing

Nodes use local knowledge May collect info from adjacent nodes May collect info from all nodes on a potential route

Central routing Collect info from all nodes

Update timing When is network info held by nodes updated Fixed - never updated Adaptive - regular updates

Routing StrategiesFixedFloodingRandomAdaptive

Fixed RoutingSingle permanent route for each source to

destination pairDetermine routes using a least cost

algorithm (chapter 12.3)Route fixed, at least until a change in

network topology

Fixed RoutingTables

Flooding No network info required Packet sent by node to every neighbor Incoming packets retransmitted on every link

except incoming link Eventually a number of copies will arrive at

destination Each packet is uniquely numbered so duplicates

can be discarded Nodes can remember packets already forwarded

to keep network load in bounds Can include a hop count in packets

Flooding Example

Properties of FloodingAll possible routes are tried

Very robust

At least one packet will have taken minimum hop count route Can be used to set up virtual circuit

All nodes are visited Useful to distribute information (e.g. routing)

Random RoutingNode selects one outgoing path for

retransmission of incoming packetSelection can be random or round robinCan select outgoing path based on

probability calculationNo network info neededRoute is typically not least cost nor

minimum hop

Adaptive Routing Used by almost all packet switching networks Routing decisions change as conditions on the

network change Failure Congestion

Requires info about network Decisions more complex Tradeoff between quality of network info and

overhead Reacting too quickly can cause oscillation Too slowly to be relevant

Adaptive Routing - AdvantagesImproved performanceAid congestion control (See chapter 13)Complex system

May not realize theoretical benefits

ClassificationBased on information sources

Local (isolated)Route to outgoing link with shortest queueCan include bias for each destination Rarely used - do not make use of easily available info

Adjacent nodes All nodes

Isolated Adaptive Routing

ARPANET Routing Strategies(1)First Generation

1969 Distributed adaptive Estimated delay as performance criterion Bellman-Ford algorithm (chapter 12.3) Node exchanges delay vector with neighbors Update routing table based on incoming info Doesn't consider line speed, just queue length Queue length not a good measurement of delay Responds slowly to congestion

ARPANET Routing Strategies(2)Second Generation

1979 Uses delay as performance criterion Delay measured directly Uses Dijkstra’s algorithm (Chapter 12.3) Good under light and medium loads Under heavy loads, little correlation between

reported delays and those experienced

ARPANET Routing Strategies(3)Third Generation

1987 Link cost calculations changed Measure average delay over last 10 seconds Normalize based on current value and previous

results

Static Vs. Dynamic Routing

Routes are static if they do not change. Route table is loaded once at startup and all

changes are manual Computers at the network edge use static

routing.

Routes are dynamic if the routing table information can change over time (without human intervention. Internet routers use dynamic routing.

Routing Table Example

Dynamic Routing and Routers

To insure that routers know how to reach all possible destinations, routers exchange information using a routing protocol.

But, we cannot expect every router to know about every other router. Too much Internet traffic would be generated. Tables would be huge (106 routers) Algorithms to choose “best” path would never

terminate.

How to handle this?

Autonomous Systems (AS) Routers are divided into groups known as an

autonomous systems (AS). ASs communicate using an Exterior Routing

Protocol (Intra-AS Routing) Routers within an AS communicate using an

Interior Routing Protocol (Inter-AS Routing)

Interior and Exterior Routing

Why different Intra and Inter-AS routing ?

Policy: Inter-AS: admin wants control over how its traffic routed,

who routes through its net. Intra-AS: single admin, so no policy decisions neededScale: hierarchical routing saves table size, reduced update trafficPerformance: Intra-AS: can focus on performance Inter-AS: policy may dominate over performance

Routing Algorithms

Graph abstraction for routing algorithms:

graph nodes are routers

graph edges are physical links link cost: delay, $

cost, or congestion level

Goal: determine “good” path

(sequence of routers) thru network from source to

dest.

Routing protocol

A

ED

CB

F

2

2

13

1

1

2

53

5

“good” path: typically means

minimum cost path other def’s possible

Routing Algorithm classification

Static or dynamic?

Static: routes change slowly over time

Dynamic: routes change more quickly

periodic updatein response to link cost changes

Routing Algorithm classification

Global or decentralized?

• 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

A Link-State Routing Algorithm

Dijkstra’s algorithm

net topology, link costs known to all nodes accomplished via “link state broadcast” all nodes have same info

computes least cost paths from one node (‘source”) to all other nodes gives routing table for that node

Iterative after k iterations, know least cost path to k

dest.’s

A Link-State Routing Algorithm

Notation:• c(i,j): link cost from node i to j. cost infinite 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, that is next v

• N: set of nodes whose least cost path definitively known

Dijsktra’s Algorithm

1 Initialization: 2 N = {A} 3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(A,v) 6 else D(v) = infty 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

Dijkstra’s algorithm: example

Step012345

start NA

ADADE

ADEBADEBC

ADEBCF

D(B),p(B)2,A2,A2,A

D(C),p(C)5,A4,D3,E3,E

D(D),p(D)1,A

D(E),p(E)infinity

2,D

D(F),p(F)infinityinfinity

4,E4,E4,E

A

ED

CB

F

2

2

13

1

1

2

53

5

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(n**2) more efficient implementations possible: O(nlogn)

Oscillations possible: e.g., link cost = amount of carried traffic

A

D

C

B1 1+e

e0

e

1 1

0 0

A

D

C

B2+e 0

001+e1

A

D

C

B0 2+e

1+e10 0

A

D

C

B2+e 0

e01+e1

initially… recompute

routing… recompute … recompute

Distance Vector Routing Algorithm

iterative: continues until no nodes

exchange info. self-terminating: no

“signal” to stop

asynchronous: nodes need not

exchange info/iterate in lock step!

distributed: each node

communicates only with directly-attached neighbors

Distance Table data structure

each node has its own row for each possible destination column for each directly-attached

neighbor to node example: in node X, for dest. Y via

neighbor Z:

D (Y,Z)X

distance from X toY, via Z as next hop

c(X,Z) + min {D (Y,w)}Z

w

=

=

Distance Table: example

A

E D

CB7

8

1

2

1

2

D ()

A

B

C

D

A

1

7

6

4

B

14

8

9

11

D

5

5

4

2

Ecost to destination via

dest

inat

ion

D (C,D)E

c(E,D) + min {D (C,w)}D

w== 2+2 = 4

D (A,D)E

c(E,D) + min {D (A,w)}D

w== 2+3 = 5

D (A,B)E

c(E,B) + min {D (A,w)}B

w== 8+6 = 14

loop!

loop!

Distance table gives routing table

D ()

A

B

C

D

A

1

7

6

4

B

14

8

9

11

D

5

5

4

2

Ecost to destination via

dest

inat

ion

A

B

C

D

A,1

D,5

D,4

D,2

Outgoing link to use, cost

dest

inat

ion

Distance table Routing table

Distance Vector Routing: overview

Iterative, asynchronous: each local iteration caused by:

local link cost change message from neighbor:

its least cost path change from neighbor

Distributed: each node notifies

neighbors only when its least cost path to any destination changes neighbors then notify

their neighbors if necessary

wait for (change in local link cost of msg from neighbor)

recompute distance table

if least cost path to any dest

has changed, notify neighbors

Each node:

Distance Vector Algorithm:

1 Initialization: 2 for all adjacent nodes v: 3 D (*,v) = infty /* the * operator means "for all rows" */ 4 D (v,v) = c(X,v) 5 for all destinations, y 6 send min D (y,w) to each neighbor /* w over all X's neighbors */

XX

Xw

At all nodes, X:

Distance Vector Algorithm (cont.):

8 loop 9 wait (until I see a link cost change to neighbor V 10 or until I receive update from neighbor V) 11 12 if (c(X,V) changes by d) 13 /* change cost to all dest's via neighbor v by d */ 14 /* note: d could be positive or negative */ 15 for all destinations y: D (y,V) = D (y,V) + d 16 17 else if (update received from V wrt destination Y) 18 /* shortest path from V to some Y has changed */ 19 /* V has sent a new value for its min DV(Y,w) */ 20 /* call this received new value is "newval" */ 21 for the single destination y: D (Y,V) = c(X,V) + newval 22 23 if we have a new min D (Y,w)for any destination Y 24 send new value of min D (Y,w) to all neighbors 25 26 forever

w

XX

XX

X

w

w

Distance Vector Algorithm: example

X Z12

7

Y

Distance Vector Algorithm: example

X Z12

7

Y

D (Y,Z)X

c(X,Z) + min {D (Y,w)}w=

= 7+1 = 8

Z

D (Z,Y)X

c(X,Y) + min {D (Z,w)}w=

= 2+1 = 3

Y

Distance Vector: link cost changes

Link cost changes: node detects local link cost

change updates distance table (line 15) if cost change in least cost path,

notify neighbors (lines 23,24)

X Z14

50

Y1

algorithmterminates“good

news travelsfast”

Distance Vector: link cost changes

Link cost changes: good news travels fast bad news travels slow -

“count to infinity” problem! X Z14

50

Y60

algorithmcontinues

on!

Distance Vector: 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

14

50

Y60

algorithmterminates

Comparison of LS and DV algorithms

Message complexity LS: with n nodes, E links, O(nE) msgs sent

each DV: exchange between neighbors only

convergence time varies

Speed of Convergence LS: O(n**2) algorithm requires O(nE) msgs

may have oscillations DV: convergence time varies

may be routing loops count-to-infinity problem

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

DV:– DV node can advertise incorrect path cost– each node’s table used by others

• error propagates thru network

RIP ( Routing Information Protocol)

Distance vector algorithm Included in BSD-UNIX Distribution in 1982 Distance metric: # of hops (max = 15 hops)

Can you guess why?

Distance vectors: exchanged every 30 sec via Response Message (also called advertisement)

Each advertisement: route to up to 25 destination nets

OSPF (Open Shortest Path First)

“open”: publicly available Uses Link State algorithm

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)