recitation 6e

Recitation 6: Routing on the Internet

Hung-Bin (Bing) Chang and Yu-Yu Lin

Electrical Engineering Department University of California (UCLA), USA,[email protected] and [email protected]

Prof. Izhak Rubin (UCLA) EE 132B 2014 Fall 1 / 15

Outline

1 Introduction

2 Distance Vector Routing

3 Link State RoutingDijkstras Algorithm


Introduction

Routing on the Internet

DefinitionIn its simplest terms, routing is choosing a path over which datapackets will be sent. On the internet, this function is performed bylayer 3 (IP) of the OSI model.Each router attaches to two or more physical networks andforwards IP datagrams among them.Except for destinations on directly attached networks, hosts pass allIP datagrams to routers which will forward them to their finaldestinations.

Two main classes of routing algorithms:Distance vector routingLink state routing (or called shortest path first, SPF)


Distance Vector Routing


When a router boots up, it initializes its routing table to contain anentry for each directly connected network.When a report arrives at router K from router J, K examines theset of destinations reported and the distance to each.

If J knows a shorter way to a destination, or if J lists a destinationthat K does not have in its table, K replaces its table entry.

Bellman-Ford algorithm.



Distance Vector Routing - Contd

The process of interchanging information between neighboringrouters continues until convergence is achieved.Advantages:

Because routers do not need to maintain the state of all links in thenetwork, it typically consumes less overhead at the expense oflimited visibility.

Disadvantages:Does not scale well to large networks (volume of informationexchange can be huge)Slow response time


Link State Routing

Link State (Shortest Path First, SPF) Routing

Algorithm requires each participating router to have completetopology information.The easiest way to think of the topology information is to imaginethat every router has a map that shows all other routers and thenetworks to which they connect.Instead of sending messages that contain lists of destinations, arouter participating in an SPF algorithm performs two tasks:

Actively tests the status of neighboring routersIt periodically propagates link status information to all neighboringrouters.


Link State Routing

SPF Routing - Contd

A status message does NOT specify routes, it simply reportswhether communication is possible between pairs of routersWhenever a link status message arrives, a router uses theinformation to update its map of the network by marking links asup or down.Whenever link status changes, the router re-computes routesusing the well-known Dijkstras Algorithm.Advantages:

Routers perform route computation locally guaranteed to converge.Disadvantage:

Maintaining link-state information for the entire area typicallyrequires much overhead.


Link State Routing Dijkstras Algorithm

Dijkstras Algorithm - Introduction

The communication network can be modeled as a graph.The nodes of the graph are the routers.The edges of the graph represent a link.Each communication link is assigned a weight. A weightrepresents parameters such as:

Physical distance = Shortest pathCost = Cheapest pathQueueing delay (congestion level) = Fastest path



Dijkstras Algorithm - Problem Statement

Problem: Given a source node, find the path with the least weightto every node in the graph.Notations

w(i , j) = weight associated with edge (i , j)d(i , j) = distance from node i to node j

We pick a node to be our source node. We want to find theshortest path from our source node to destination nodes.Each node (other than source node) is associated with two labels:

Preceding node on the shortest path to the sourceDistance to the source



Dijkstras Algorithm - Some Definitions

The algorithm labels nodes as either permanent (P) set ortemporary (T ) set.

When a node is labeled as temporary (T ) set, it is tentative. Thepreceding node and distance to the source are only estimates.When a node is labeled as permanent (P) set, the preceding nodeand distance to the source are the true final values.The algorithm then proceeds to select the least cost edgeconnecting a node with a permanent label to a node with atemporary label.

Notations:

h(i, j) =

w(i, j) , if i and j are directly connected by an edge,

0 , if i = j ,

+ , otherwise.



Dijkstras Algorithm

Step 1:Set P = {1} (i.e., Node 1 is the source node)Set T = {2, 3, . . . }j = 2, 3, . . . , set d(1, j) = h(1, j)

Step 2: Find i T where d(1, i) = minjT{d(1, j)}.Set T = T {i}Set P = P + {i}If T = , it is done!

Step 3: j T :d(1, j) = min{d(1, j),d(1, i) + h(i , j)}Go to step 2



Example 1

Step 1:

P = {1}T = {2, 3, 4}d(1, 2) = 3,d(1, 4) =0.5,d(1, 3) =

Step 2:

i = 4P = {1, 4},T = {2, 3}d(1, 2) = min{3, 0.5 +} =3d(1, 3) = min{, 0.5 + 8} =8.5

3 4

80.5

2

1

4

3

3 4

80.5

2

1

4

3

(1, 3)

(1, 0.5)

(1, )

3 4

80.5

2

1

4

3

(1, 3)

(1, 0.5)

(4, 8.5)

Step 1

Step 2

Figure : Dijkstras algorithm



Example 1 - Contd

Step 3:

i = 2P = {1, 2, 4}T = {3}d(1, 2) = min{3, 0.5 +} =3d(1, 3) = min{8.5, 3+4} = 7

Step 4:

i = 3P = {1, 2, 3, 4}

3 4

80.5

2

1

4

3

(1, 3)

(1, 0.5)

(2, 7)

Step 3

3 4

80.5

2

1

4

3

(1, 3)

(1, 0.5)

(2, 7)

Step 4

Figure : Dijkstras algorithm



Example 2

State the differences between distance-vector and link-statebased routing algorithms.Use Dijkstras algorithm, showing all steps, to derive the shortestpath tree rooted at node A for the network graph with indicatedlink weights as shown below.

B

A

C

E

F

D

G

Figure : An example for Dijkstras algorithm



Example 2 - Sol.

Table : Dijkstras Algorithm

A (0,A) (0,A) (0,A) (0,A) (0,A) (0,A) (0,A)B (, null) (2, A) (2,A) (2,A) (2,A) (2,A) (2,A)C (, null) (5, A) (5, A) (5,A) (5,A) (5,A) (5,A)D (, null) (, null) (6,B) (6,B) (6,B) (6,B) (6,B)E (, null) (, null) (12,B) (12,B) (8,D) (8,D) (8,D)F (, null) (, null) (, null) (19,C) (19,C) (12,E) (12,E)G (, null) (, null) (, null) (, null) (24,D) (24,D) (17,F)

B

A

C

E

F

D

G

Figure : Shortest Path TreeProf. Izhak Rubin (UCLA) EE 132B 2014 Fall 15 / 15

IntroductionDistance Vector RoutingLink State RoutingDijkstra's Algorithm

recitation 6e

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