Lecture 20
Routing in Data Networks
Eytan Modiano
Eytan Modiano
Slide 1
Routing
? Must choose routes for various origin destination pairs (O/D pairs)
or for various sessions
– Datagram routing: route chosen on a packet by packet basis
Using datagram routing is an easy way to split paths
– Virtual circuit routing: route chosen a session by session basis
– Static routing: route chosen in a prearranged way based on O/D pairs
Eytan Modiano
Slide 2
Routing is a global problem
5 units 5 units
All links
have
capacity
10 units
Either session
alone is best
routed through
center path, but
both cannot
go through
center.
? Static routing is not desirable
All links
have
capacity
10 units
10 units 15 units
Both sessions
must split their
traffic between
two paths.
? Datagam routing is a natural way to split the traffic
– How?
Eytan Modiano
Slide 3
Shortest Path routing
? Each link has a cost that reflects
– The length of the link
– Delay on the link
– Congestion
– $$ cost
? Cost may change with time
? The length of the route is the sum of the costs along the route
? The shortest path is the path with minimum length
? Shortest Path algorithms
– Bellman-Ford: centralized and distributed versions
– Dijkstra’s algorithm
– Many others
Eytan Modiano
Slide 4
Directed graphs (digraphs)
? A directed graph (digraph) G = (N,A) is a finite nonempty set of nodes N and
a set of ordered node pairs A called directed arcs.
1
2
3
4
N = {1,2,3,4}
A = {(1,2), (2,1),(1,4),
(4,2), (4,3),(3,2)}
? Directed walk: (4,2,1,4,3,2)
? Directed path: (4,2,1)
? Directed cycle: (4,2,1,4)
? Data networks are best represented with digraphs, although typically links
tend to be bi-directional (cost may differ in each direction)
– For simplicity we will use bi-directional links of equal costs in our examples
Eytan Modiano
Slide 5
Bellman Ford algorithm
? Finds the shortest paths, from a given source node, say node 1, to all
other nodes.
? General idea:
– First find the shortest single arc path,
– Then the shortest path of at most two arcs, etc.
– Let dij=∞ if (i,j) is not an arc.
? Let Di(h) be the shortest distance from 1 to i using at most h arcs.
– Di(1) = d1i ; i≠1 D1(1) = 0
– Di(h+1) = min {j} [Dj(h) + dji] ;i≠1 D1(h+1) = 0
? If all weights are positive, algorithm terminates in N-1 steps.
Eytan Modiano
Slide 6
Bellman Ford - example
Eytan Modiano
Slide 7
Eytan Modiano
Slide 8
Distributed Bellman Ford
? Link costs may change over time
– Changes in traffic conditions
– Link failures
– Mobility
? Each node maintains its own routing table
– Need to update table regularly to reflect changes in network
? Let Di be the shortest distance from node i to the destination
– Di = min {j} [Dj + dij] : update equation
? Each node (i) regularly updates the values of Di using the update equation
– Each node maintains the values of dij to its neighbors, as well as values of Dj
received from its neighbors
– Uses those to compute Di and send new value of Di to its neighbors
– If no changes occur in the network, algorithm will converge to shortest paths in
no more than N steps
Eytan Modiano
Slide 9
Slow reaction to link failures
? Start with D3=1 and D2=100
– After one iteration node 2 receives D3=1 and
D2 = min [1+1, 100] = 2
? In practice, link lengths occasionally change
– Suppose link between 3 and 1fails (I.e., d31=infinity)
– Node 3 will update D3 = d32 + D2 = 3
– In the next step node 2 will update: D2 = d23+D3 = 4
– It will take nearly 100 iterations before node 2 converges on the correct route
to node 1
? Possible solutions:
– Propagate route information as well
– Wait before rerouting along a path with increasing cost
Node next to failed link should announce D=infinity for some time to prevent loops
3 2
1
1
1
1
100
Eytan Modiano
Slide 10
Instability
1
1
1
1
1
1
ε
Destination
ε
1+
2+
3+
ε
ε
ε
3
2
1
2
3
4
1
5
6
7
8
Assume d is equal to the flow on (i,j) Note that D
ij
D = 3
D = 5
D = 6
D = 6
D = 6
D = 5+2
D = 3+
2
3
4
5
6
7
8
ε
ε
6
5
= D + 0
As routes change due to traffic conditions, they affect the
Loadings on the links, hence routes may oscillate
Eytan Modiano
Slide 11
Instability
? Having a bias independent of flow in the arc distances helps to
prevent this problem.
? Asynchronous updates also helps.
Assume d is equal to the flow on (i,j) Note that D
now has a counter clockwise shortest path
1
1
1
1
1
1
ε
Destination
ε
1
2
ε
ε
ε
4+
3+
2+
2
3
4
1
5
6
7
8
ij
D = 3
D = 3
D = 3
D = 3
D = 3
D = 3
D = 2
2
3
4
5
6
7
8
2
1
1+
Eytan Modiano
Slide 12
Dijkstra's algorithm
? Find the shortest path from a given source node to all other nodes
– Requires non-negative arc weights
? Algorithm works in stages:
– Stage k: the k closest nodes to the source have been found
– Stage k+1: Given k closest nodes to the source node, find k+1st.
? Key observation: the path to the k+1st closest nodes includes only nodes
from among the k closest nodes
? Let M be the set of nodes already incorporated by the algorithm
– Start with Dn = dsn for all n (Dn = shortest path distance from node n to the
source node
– Repeat until M=N
Find node w?M which has the next least cost distance to the source node
Add w to M
Update distances: Dn = min [ Dn, Dw + dwn] (for all nodes n ?M)
– Notice that the update of Dn need only be done for nodes not already in M and
that the update only requires the computation of a new distance by going
through the newly added node w.
Eytan Modiano
Slide 13
Dijkstra example
Eytan Modiano
Slide 14
Dijkstra’s algorithm implementation
? Centralized version: Single node gets topology information and
computes the routes
– Routes can then be broadcast to the rest of the network
? Distributed version: each node i broadcasts {dij all j} to all nodes
of the network; all nodes can then calculate shortest paths to each
other node
– Open Shortest Path First (OSPF) protocol used in the internet
Eytan Modiano
Slide 15
Routing in the Internet
? Autonomous systems (AS)
– Internet is divided into AS’s each under the control of a single
authority
? Routing protocol can be classified in two categories
– Interior protocols - operate within an AS
– Exterior protocols - operate between AS’s
? Interior protocols
– Typically use shortest path algorithms
Distance vector - based on distributed Bellman-ford
link state protocols - Based on “distributed” Dijkstra’s
Eytan Modiano
Slide 16
Distance vector protocols
? Based on distributed Bellman-Ford
– Nodes exchange routing table information with their neighbors
? Examples:
– Routing information protocols (RIP)
Metric used is hop-count (dij=1)
Routing information exchanged every 30 seconds
– Interior Gateway Routing Protocol (IGRP)
CISCO proprietary
Metric takes load into account
Dij ~ 1/(μ?λ) (estimate delay through link)
Update every 90 seconds
Multi-path routing capability
Eytan Modiano
Slide 17
Link State Protocols
? Based on Dijkstra’s Shortest path algorithm
– Avoids loops
– Routers monitor the state of their outgoing links
– Routers broadcast the state of their links within the AS
– Every node knows the status of all links and can calculate all routes
using dijkstra’s algorithm
Nonetheless, nodes only send packet to the next node along the route with
the packets destination address. The next node will look-up the address in
the routing table
? Example: Open Shortest Path First (OSPF) commonly used in the
internet
? Link State protocols typically generate less “control” traffic than
Distance-vector
Eytan Modiano
Slide 18
Inter-Domain routing
? Used to route packets across different AS’s
? Options:
– Static routing - manually configured routes
– Distance-vector routing
Exterior Gateway Protocol (EGP)
Border Gateway Protocol (BGP)
? Issues
– What cost “metric” to use for Distance-Vector routing
Policy issues: Network provider A may not want B’s packets routed through
its network or two network providers may have an agreement
Cost issues: Network providers may charge each other for dlivery of packets
Eytan Modiano
Slide 19
Bridges, Routers and Gateways
? A Bridge is used to connect multiple LAN segments
– Layer 2 routing (Ethernet)
– Does not know IP address
– Varying levels of sophistication
Simple bridges just forward packets
smart bridges start looking like routers
? A Router is used to route connect between different networks using
network layer address
– Within or between Autonomous Systems
– Using same protocol (e.g., IP, ATM)
? A Gateway connects between networks using different protocols
– Protocol conversion
– Address resolution
? These definitions are often mixed and seem to evolve!
Eytan Modiano
Slide 20
Ethernet A
Ethernet B
Bridge
IP
Router
Small company
Gateway
Service
provider’s
ATM
backbone
ATM switches
(routers)
Gateway
Another provider’s
Frame Relay
Backbone
Bridges, routers and gateways