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Routing

Lesson 10NETS2150/2850http://www.ug.cs.usyd.edu.au/~nets2150/

School of Information Technologies

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Lesson Outline• Know the characteristics of unicast routing

protocol• Understand various ways of routing

—Routing Strategies

• Experiment with common routing algorithms—Dijsktra’s Algorithm of OSPF—Bellman-Ford Algorithm of RIP

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Routing

Graph abstraction for routing algorithms:

• graph nodes are routers

• graph edges are physical links—link cost/weight:

delay, $ cost or congestion level

Goal: find “good” path thru network from source to

destination.

Routing protocol

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• “good” path:—typically means

minimum cost path

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Routing in Packet Switched Network• Routing protocol establish mutually consistent

routing tables in every router• Characteristics of routing protocol:

—Correctness—Simplicity—Robustness

—Stability—Fairness—Optimality—Efficiency

application

transportnetworkdata linkphysical

application

transportnetworkdata linkphysical

1. Send data 2. Receive data

networkdata linkphysical

Packet switching network

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Performance Criteria• How to select “best” path?• Used for selection of path

—Minimum hop—Least cost

IP routing table

Destination Gateway Netmask Iface

129.78.8.0 0.0.0.0 255.255.252.0 eth0

127.0.0.0 0.0.0.0 255.0.0.0 lo

0.0.0.0 129.78.11.254 0.0.0.0 eth0

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Example Packet Switched Network

Link cost

•Shortest path VS•Least-cost path

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Routing Strategies• Fixed• Flooding• Random• Adaptive

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Fixed Routing• Single permanent path for each source to

destination pair• Path fixed, at least until a change in

network topology

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Fixed RoutingTables

Network Topology

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Flooding• Packet sent by node to every neighbour

and the neighbour sends to its neighbours• 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• To bound the flood, max hop count is

included in the packets

If (Packet’s hop count = = max_hop_count) discard!

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Flooding Example

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Properties of Flooding• All possible routes are tried

—Very robust

• At least one packet will have taken minimum hop count or “best” route

• All nodes are visited• The common approach used to distribute

routing information, like a node’s link costs to neighbours

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Random Routing• Node selects one outgoing path for

retransmission of incoming packet• Selection can be random or round robin• Can select outgoing path based on

probability calculation• Path is typically not “best” one• Used in ‘hot potato routing’

— nodes have no buffer to store packets— packets routed to any path of the lowest

delay

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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

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Adaptive Routing - Advantages• Improved performance• Aids congestion control by

exercising load balancing across different alternative paths

• But, it is complex—Reacting too quickly can cause

oscillation—Too slowly, may not be relevant

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Routing Algorithm classificationGlobal or decentralised information?Global:• all routers have complete topology, link cost info• Known as “link state” algorithms• E.g. Dijkstra’s AlgorithmDecentralised: • router knows physically-connected neighbours,

i.e link costs to neighbours• iterative process of computation, exchange of

info with neighbours• Known as “distance vector” algorithms• E.g. Bellman-Ford Algorithm

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Routing Algorithms• Given network of nodes connected by bi-

directional links• Each link has a cost in each direction and

may be different• Cost of path between two nodes is sum of

costs of links traversed• For each pair of nodes, find a path with

the least cost

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Dijkstra’s Algorithm Definitions• Find shortest paths from given source node to all

other nodes, by developing paths in order of increasing path length

• N = set of nodes in the network• s = source node• T = set of nodes so far incorporated by the

algorithm• w(i, j) = link cost from node i to node j

—w(i, i) = 0—w(i, j) = if the two nodes are not directly connected—w(i, j) 0 if the two nodes are directly connected

• L(n) = cost of least-cost path from node s to node n

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Dijkstra’s Algorithm• Step 1 [Initialization]

—T = {s} Set of nodes so far incorporated consists of only source node

—L(n) = w(s, n) for n ≠ s

• Step 2 [Get Next Node]—Find neighbouring node, x, not in T with least-cost path

from s — Incorporate node x into T

• Step 3 [Update Least-Cost Paths]—L(n) = min[L(n), L(x) + w(x, n)] for all n T

• Algorithm terminates when all nodes have been added to T

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Dijkstra’s Algorithm Notes• At termination, value L(x) associated with

each node x is cost of least-cost path from s to x.

• One iteration of steps 2 and 3 adds one new node to T—Defines least cost path from s to that node

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T = {A,D}

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T = {A,D,B}

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T = {A,D,B,E}

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T = {A,D,B,E,C}

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T = {A,D,B,E,C,F}

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Results of Example Dijkstra’s Algorithm

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T L(B) Path L(C) Path L(D) Path L(E) Path L(F) Path

1 {A} 2 A–B 5 A-C 1 A–D - -

2 {A,D} 2 A–B 4 A-D-C 1 A–D 3 A-D-E -

3 {A,D,B} 2 A–B 4 A-D-C 1 A–D 3 A-D-E -

4 {A,D,B,E}

2 A–B 4 A-D-C 1 A–D 3 A-D-E 5 A-D-E-F

5 {A,D,B,E,C}

2 A–B 4 A-D-C 1 A–D 3 A-D-E 5 A-D-E-F

6 {A,D,B,E,C,F}

2 A–B 4 A-D-C 1 A–D 3 A-D-E 5 A-D-E-F

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Bellman-Ford Algorithm Definitions• Find shortest paths from given node considering

at most one hop away• Then, find the shortest paths with a constraint of

paths of at most two hops. Then 3 hops, and so on…

• s = source node• w(i, j) = link cost from node i to node j

—w(i, i) = 0—w(i, j) = if the two nodes are not directly connected—w(i, j) 0 if the two nodes are directly connected

• h = maximum number of hops (links) in path• Lh(n) = cost of least-cost path from s to n, at

most h hops away

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Bellman-Ford Algorithm• Step 1 [Initialization]

—Lh(s) = 0, for all h

—L0(n) = , for n s

• Step 2 [Update] —For each successive h > 0 and each node n:

• If Lh(n) > minj[Lh(j) + w(j,n)] Then

– Lh+1(n)=minj[Lh(j)+w(j,n)]

• Connect n with predecessor node j that achieves minimum cost

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h = 1

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h = 2

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h = 3

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h = 4

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Results of Example Bellman-Ford Algorithm

hop

Lh(B) Path

Lh(C) Path Lh(D) Path Lh(E) Path Lh(F) Path

1 2 A–B 5 A-C 1 A–D - -

2 2 A–B 4 A-D-C 1 A–D 3 A-D-E 10 A-C-F

3 2 A–B 4 A-D-C 1 A–D 3 A-D-E 5 A-D-E-F

4 2 A–B 4 A-D-C 1 A–D 3 A-D-E 5 A-D-E-F

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Algorithms Comparison• Results from two algorithms agree• Information gathered

—Bellman-Ford• Each node can maintain set of costs and paths for every

other node• Only exchange information with direct neighbours• Can update costs and paths based on information from

neighbours and knowledge of link costs• Used as part of the Routing Information Protocol (RIP)

—Dijkstra• Each node needs complete topology• Must know link costs of all links in network• Must exchange information with all other nodes• Used as part of Open Shortest Path First Protocol (OSPF)

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OSPF Protocol

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Example: ImageStream’s TransPort™ router

Physical Spec:• 533 MHz VIA C3 processor• 128 MB SDRAM• Runs on Linux• Three onboard 10/100

Ethernet ports• 1 or 2 T1/E1 ports

Software spec:• PPP, Cisco HDLC &

frame relay• ATM• PPPoE & PPPoA• Routing procotols:

—RIP, RIP II, OSPF, IS-IS & BGP4

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Summary• Routing is the process of finding a path

from a source to every destination in the network

• Different routing strategies available• Common adaptive routing:

—Dijsktra’s algorithm—Bellman-Ford algorithm

• Read Stallings Section 12.2 and 12.3• Next: Functions of internetwork layer

protocol