Spring 2008 1

Routing:Part I

Section 4.2Outline

AlgorithmsScalability

Spring 2008 2

Overview• Forwarding vs Routing

– forwarding: to select an output port based on destination address and routing table

– routing: process by which routing table is built• Network as a Graph

– Assume single admin. authority– Assume nodes are routers– Assume each link has a cost

• The Routing Problem: Find lowest cost path (sum of links) between two nodes

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36

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9

1

1D

A

FE

B

C

Spring 2008 3

Routing Protocol Issues• It may be simple to calculate least cost path if graph is

static but…– Links and routers go down– Links and routers are added– Traffic can cause links to overload– How are costs calculated?– Algorithm must be distributed in order to scale– Different routers can have different routes at same time– Rich area for research due to distributed, dynamic nature of the

problem

Spring 2008 4

Distance Vector• Each node maintains a set of triples

– (Destination, Cost, NextHop)forwarding only uses (Destination,NextHop)

• Directly connected neighbors exchange “route updates”– periodically (on the order of several seconds; called periodic

update)– whenever table changes (called triggered update)

• Each update is a list of pairs:– (Destination, Cost)

• A router modifies its routing table if it receives a “new” route– smaller cost ( “better” route)– came from the next-hop used to reach a destination

• Refresh existing routing table entries– delete an entry if it times out

Spring 2008 5

Example

Destination Cost NextHop A 1 A C 1 C D 2 C E 2 A F 2 A G 3 A

D

G

A

F

E

B

C

Table of Router B

Spring 2008 6

Routing Loops: Example 1

F detects that the link to G has failed• F sets distance to G to infinity and sends triggered update to

A• A sets distance to G to infinity since it uses F to reach G;

sends triggered update to neighbors– C ignores this update since its route to G is vai D with a cost of 2

• A receives periodic update from C with 2-hop path to G• A sets distance to G to 3 and sends a triggered update• F decides it can reach G in 4 hops via A

Network stabilizes

D

G

A

F

E

B

C

Spring 2008 7

Routing Loops: Example 2

the following depends on exact timing of events:• link from A to E fails, A advertises distance of infinity to E • C advertise a distance of 2 to E (periodic updates)• B processes update from A, then the update from C• Based on update from C

– B decides it can reach E in 3 hops; sends triggered update– A decides that it can reach E in 4 hops (Via B); sends triggered update– C decides that it can reach E in 5 hops; sends update to B

• Based on update from C– B decides it can reach E in 6 hops; sends triggered update– A decides that it can reach E in 7 hops (Via B); sends triggered update– C decides that it can reach E in 8 hops; sends update to B

• Based on update from C– cycle repeats– …..

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G

A

F

E

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C

Spring 2008 8

Routing Loops:Example 2 (continued)• Cycle stops when distances reach infinity (some

large number)

• For a period of time, no node knows that E is unreachable

• Routing tables do not stabilize

• This is known as the Count-to-infinity problem

D

G

A

F

E

B

C

Spring 2008 9

Loop-Breaking “Heuristics”

• Set infinity to 16– Assume this is the maximum number of hops in network

bounds the amount of time that it takes to count to infinity

• Split horizon– Works only for loops involving two nodes– Don’t send routes learned from a neighbor back to the neighbor

B has the route (E, 2, A) in its table it must have learned this route from A

When B sends a periodic update to A route (E, 2) is not included in update

D

G

A

F

E

B

C

Spring 2008 10

Loop-Breaking Heuristics (cont.)

• Split horizon with poison reverse– Send route back with negative information i.e. Infinite

ensures that A will not use B to get to E.B sends the route (E, ∞) to A.

D

G

A

F

E

B

C

Spring 2008 11

Loop-Breaking: What can be done ??

• B and C wait after hearing of link failure from A before advertising routes to E– each would conclude that it

really had no route to E

• However, this delays the convergence of the protocol (Distance Vector Routing)

D

G

A

F

E

BC

Spring 2008 12

Link State• Strategy

– each node sends to all other nodes information about directly connected links

• Link State Packet (LSP)– id of the node that created the LSP– cost of link to each neighbor– sequence number (SEQNO)– time-to-live (TTL) for this packet

Spring 2008 13

Link State:Reliable flooding

• when reboot, start SEQNO of all initial LSPs at 0

• generate new LSP periodically– increment SEQNO

store most recent LSP from each node• forward LSP to all nodes but one that sent it• decrement TTL of each LSP before

flooding it to neigbors– discard when TTL=0

Spring 2008 14

Link State Route Calculation:Dijkstra’s Shortest Path Algorithm

• Let– N denotes set of nodes in the graph– each node needs to execute the algorithm– l (i, j) denotes non-negative cost for edge (i, j)

l (i, j) = ∞ if no edge connects i and j– s denotes this node (i.e. the node executing the algorithm to

find the shortest path to all the other nodes in N)– for each node n != s which is a member in the set N, let C(n)

denotes cost of the path from s to node n– At each point during the execution of the algorithm, let M

denotes the set of nodes whose routes has been found so far

Spring 2008 15

Link State Route Calculation:Dijkstra’s Shortest Path Algorithm (cont.)

M = {s}for each n in N - {s}

C(n) = l(s, n) /* Costs of directly connected nodes */

while (M != N )/* Add a node */M = M union {w} such that C(w) is the minimum for all w in (N - M) for each n in (N - M) /* Recalculate costs */

C(n) = MIN(C(n), C (w) + l(w, n ))

Spring 2008 16

Route Calculation: Explanation• start with M containing s • initialize table of costs using known costs to directly

connected nodes• while M <> N

1. w: node reachable at lowest cost2. update M : add w to M3. update table of costs by considering the cost of reaching

nodes through w choose a new route to node n through w if total cost of

going from s to w and then following link from w to n is less than old route to n

• repeat until all nodes are incorporated in M

Spring 2008 17

Example: Node A Executing the Algorithm

Itrn M B Path C Path D Path E Path F Path G Path 1 {A} 2 A-B 5 A-C 1 A-D Inf. Inf. 1 A-G 2 {A,D} 2 A-B 4 A-D-C 1 A-D 2 A-D-E Inf. 1 A-G 3 {A,D,G} 2 A-B 4 A-D-C 1 A-D 2 A-D-E Inf. 1 A-G 4 {A,B,D,G} 2 A-B 4 A-D-C 1 A-D 2 A-D-E Inf. 1 A-G 5 {A,B,D,E,G} 2 A-B 3 A-D-E-C 1 A-D 2 A-D-E 4 A-D-E-F 1 A-G 6 {A,B,C,D,E 2 A-B 3 A-D-E-C 1 A-D 2 A-D-E 4 A-D-E-F 1 A-G

G} 7 {A,B,C,D,E 2 A-B 3 A-D-E-C 1 A-D 2 A-D-E 4 A-D-E-F 1 A-G

F,G}

DG

A

B C

EF

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11

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3

Spring 2008 18

Link State Routing Summary• One of the oldest algorithm for routing• Finds “Shortest Path” by developing paths in order

of increasing length– Requires each node to have complete information about

the network– Nodes exchange information with all other nodes in the

network– Known to converge quickly under static conditions– Does not generate much network traffic

Spring 2008 19

Metrics for Link Cost • Simplest method is to assign 1 to each link• Original ARPANET metric

– link cost = number of packets enqueued on each linkThis moves packets toward shortest queue not the destination!!took neither latency or bandwidth into consideration

• Newer ARPANET metric– link cost = average delay over some time period– stamp each incoming packet with its arrival time (AT)– record departure time (DT)– when link-level ACK arrives, compute

Delay = (DT - AT) + Transmit + Latency Transmit and latency are static for the link

– if timeout, reset DT to departure time for retransmission – Fine Tuning (pp 287, 289)