Network Layer â€“ Routing Devices and Shortest Path Algorithms for Routing

159.334 Computer Networks159.334 Computer Networks

Network Layer – Routing Devices andShortest Path Algorithms for Routing

Professor Richard Harris

School of Engineering and AdvancedTechnology (SEAT)

Computer NetworksComputer Networks -- 1/1/22


Presentation Outline

Networking Devices

Dijkstra’s AlgorithmBackground

Summary of the method

Example

Bellman – Ford AlgorithmExample

Floyd’s AlgorithmExample

Dantzig’s AlgorithmExample



Objectives

You will be able to describe the various network devices including:

Hubs and repeaters

Bridges

Routers

Gateways

For the various shortest route algorithms, you will be able to:

Perform the Dijkstra algorithm for a sample communication network.

Perform a trace-back of the shortest path after applying the algorithm.

Determine the shortest route tree structure.

Develop an appreciation of the requirements for a shortest pathalgorithm.

Be able to apply the Bellman-Ford algorithm to a simple network.

Digital Networks 216.381 Computer NetworksComputer Networks -- 1/1/44


Objectives

From this lecture you will be able to:Perform the Dijkstra algorithm for a sample communicationnetwork.

Perform a trace-back of the shortest path after applying thealgorithm.

Determine the shortest route tree structure.

Develop an appreciation of the requirements for a shortest pathalgorithm.

Be able to apply the Bellman-Ford algorithm to a simple network.



Routing Devices

In a network, various network devices are used to routedata to various points in a network.

These network devices follow a hierarchical approach insupporting the network as shown below:



Repeaters

Repeaters regenerate signals in a network. They are designed for use inlocal area networks (LANs). Repeaters are Layer 1 devices; they do notinterpret any part of the data and are not capable of examining any of theaddresses in a protocol header.

Repeaters receive the signal either in electrical or optical form andregenerate the entire signal based on the results of an algorithm.

An example of a repeater is a network hub.



Function of a Repeater



Bridges - 1

A bridge is designed for use between LANs to join two different networksegments. It does NOT join two different networks (e.g., Token Ring andEthernet) together.

Large networks with many nodes should be divided into smaller networksegments with fewer nodes to prevent traffic congestion. Then, a bridge isused to interconnect these smaller network segments together.



Bridges - 2

The functions of the bridge are:Read all frames transmitted on LAN1 and accept thoseaddressed to any station on LAN2.

Using the medium access control protocol (MAC) for LAN2,retransmit each frame on LAN2.

Do the same for LAN2-to-LAN1 traffic.

The bridge makes no modification to the content or format of theframes it receives, nor does it encapsulate them with anadditional header.

The bridge should contain enough buffer space to meet peakdemands because frames may arrive faster than they can beretransmitted.

The bridge must contain addressing and routing intelligence.

A bridge may connect more than two LANs.



Learning Bridge



Bridges - BRouters

In today’s complex communication industry, bridgesoften provide additional functionality, making it difficultto draw the line between routers, bridges, repeaters.

A BRouter is one such device. It is a bridge and routerall in one.



Routers - 1

Routing is the process of choosing a path over which tosend packets. For TCP/IP, routing occurs when a hostsends IP packets, and occurs again at an IP router.

A router is a device (or software in a computer) thatdetermines the next network point to which a packetshould be forwarded to its destination.

A routing decision has to be made by consulting arouting table.



Routers - 2

131.170.16.0 131.170.16.3Default 131.170.16.1

Routing Table

131.170.8.0 131.170.8.1131.170.16.0 131.170.16.1131.170.24.0 131.170.24.1

Routing Table

131.170.16.3 131.170.16.1

131.170.16.0

131.170.24.1

131.170.24.0

131.170.8.1

131.170.8.0

Router



Routers - 3

A routing table contains entries with the IP addresses ofrouter interfaces to other networks that it cancommunicate with.

Example of a routing decision:When a host attempts communication with another host, IP firstdetermines whether the destination host is local or on a remotenetwork.

If the destination host is remote, IP then checks the routing tablefor a route to the remote host or remote network.

If no explicit route is found, IP uses its default gateway addressto deliver the packet to a router.



Routers - 4

At the router, the routing table is again consulted for a path tothe remote host or network. If a path is not found, the packet issent to the router’s default gateway address.

As each route is found, the packet is sent to the next router,called a “hop”, and finally delivered to the destination host. If aroute is not found, an error message is sent to the source host.



A Routing Example



Static Routing & Dynamic Routing - 1

Routing information is obtained in the two followingways:

Static routing

Dynamic routing

Static routing: This is a function of IP and it requiresrouting tables to be manually built and manuallyupdated. Because the routing tables are static; staticrouters do not inform each other in the event of a routechange, nor do they exchange routing information withdynamic routers.



Static Routing & Dynamic Routing - 2

Dynamic Routing: This is a function of routing protocolssuch as Routing Information Protocol (RIP), OpenShortest Path First (OSPF), Border Gateway Protocol(BGP4), Exterior Gateway Protocol (EGP) or InteriorGateway Protocol (IGP).

Dynamic routing protocols exchange routing informationperiodically or when a route change occurs.



Gateways - 1

A gateway is the network point to the entrance ofanother network.

Typically a gateway is used for protocol conversion.Examples include:

Protocol conversion between Token Ring and Ethernet.

Enabling a personal computer (PC) to communicate with amainframe computer.

Enabling different e-mail systems to communicate with eachother.

Gateways operate at many different layers depending onthe functionality required.



Gateways - 2

Today, it is rather confusing because routers can alsoprovide gateway functionality.

GATEWAY

Ethernet Network Token Ring Network



Network Interface Cards (NIC)

Also known as a network adapter or network card, it isthe device that is installed into a computer, which in turnallows the computer to be connected to a network.

The NIC is protocol-specific and has a unique machineaddress ‘burned’ into it. Theoretically, computers indifferent networks can have identical machineaddresses because there is also a network address toseparate the two nodes.



Other Network Routing Devices

These include:Modems

Cable modems

xDSL modems

ISDN routers

ATM switches


Routing Algorithms

Dijkstra and Bellman-Ford



Dijkstra's Algorithm Background

The algorithm proceeds by assigning to all nodes a label whichis either temporary or permanent. A temporary label representsan upper bound on the shortest distance from the home node tothat node; while a permanent label is the actual shortest distancefrom the home node to that node.

We also record information about predecessor nodes so that wemay find our way along the path from the home node to the finalnode of the network.

The paths traced out by the shortest route algorithm forms whatis known as a tree structure and this is a very important conceptin communications and transportation theory.



Dijkstra's Algorithm Summary

Initial step:Initialise by assigning a permanent label of zero to the home node (source). Allother node labels are declared to be temporary and are equal to the directdistance from the source node to that node. Select the minimum of thesetemporary labels and declare it permanent. In the event of a tie, choose themarbitrarily.

Step 1:Suppose that node K has been assigned a permanent label most recently. Nowconsider the remaining nodes with temporary labels. Compare, one at a time,the temporary label of each node to the sum of the permanent label of node Kand the direct distance from node K to the node under consideration. Assign theminimum of these distances as the new temporary label for that node. (If the oldtemporary label is still minimal, then it will remain unchanged during this step.)

Step 2:Select the minimum of all of the temporary labels and declare it permanent. Inthe case of ties, select just one of them and declare it permanent. If this happensto the destination node, then terminate. Otherwise go to step 1.



Shortest Path: Example - 1

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Problem: Find the shortest route from node 1to each of the other nodes.


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Shortest Path Example - 2

Step 1:Label node 1 with (0*,-) and declare it to be permanently labelled - Iuse a (*). Label the other nodes with upper bounds of ( ,-) anddeclare them to be temporary labels.

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( , ) ( , )

( , )

( , )

( , )*0




Step 2:Since i=1 was the most recent node to have been permanentlylabelled, we now consider the nodes which can be reachedfrom it, namely, nodes 2 and 3. We consider

Node 2: min( , 0+1) = 1

Node 3: min( , 0+4) = 4

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( , ) ( , )

( , )

( , )

( , )*0




The smallest temporary label is on node 2, so we nowlabel it permanently (1*, 1).

What is the meaning of the second field?

It means the node which determined the minimum value- or predecessor node.

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( ,-)

(4,1)

( ,-)

(0,-)

(1,1)




Step 4:

Now, there are still nodes left in the network with temporary labels, so we continuethe process. The most recently assigned permanent label is node 2, so we examinelinks leaving this node as before:

Node 3: Min(4, 1+3) = 4 (tie)

Node 4: Min( ,1+2) = 3

Node 5: Min(, 1+4) = 5

In each case, the predecessor node is node 2 – but we shall leave node 3 alone in thiscase.

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( ,-)

(4,1)

( ,-)

(0,-)

(1,1)




Step 5:

Now the smallest temporary label is on node 4, so this becomespermanently labelled (3*, 2).

Since nodes 3 and 5 are still temporarily labelled we must continue theprocedure.

Consider node 4, only node 5 can be reached so we check:

min(5, 3+3) = 5 so the distance remains unchanged.

The minimum temporarily labelled node is node 3 so this now becomespermanently labelled.

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(3 ,2)

(4,1)

(0,-)

(1,1)

(5 ,2)




From node 3, only node 5 can be reached so wecheck this: min(5, 4+3) = 5 (no change to the label)

The only temporary label remaining is that for node 5so we label it permanently, and now the algorithm iscomplete.

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(3 ,2)

(4,1)

(0,-)

(1,1)

(5 ,2)



The Shortest Route Tree"

We now have the shortest route between the given home node(node 1) and the destination node (node 5). We can determine theroute to be used by making use of the predecessor nodeinformation stored with the labels. The route is identified usingthe red arrows.

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(3 ,2)

(4,1)

(0,-)

(1,1)

(5 ,2)



Application of Dijkstra's Algorithm -Another Example

Consider the following directed network:

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You give it a try now!

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Application of Dijkstra's Algorithm -Solution

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The tree is, once again, given in red arrows.



Comments

You have seen how to apply the method when you haveall the information at your finger tips.

You will be shown how to develop this method and othershortest path methods for determining the shortest pathusing a distributed approach - ie you need to discoverthe information required for the computation of theshortest route tree.



Bellman-Ford Algorithm

Initialise d and p:For each node j

dj =

pj = 0

Set source distance ds = 0

Repeat the following process |N|-1 times:For each link (i,j) in G, perform relax process, where

Relax:

– If( dj > di +wij) then

• dj = di + wij

• pj = i

(Where wij is the distance between i and j)

These are initial estimates of the distance

These are initial predecessor nodes - null



Shortest Path: Example – 1 (Again!)

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d1 =

d2 =

d3 =

d4 =

d5 =



First Pass

Link 1 – 2: d2 > d1 + 1 d2 = 0 + 1 = 1 ; p2 = 1

Link 1 – 3: d3 > d1 + 4 d3 = 0 + 4 = 4 ; p3 = 1

Link 2 – 3: d3 > d2 + 3 X d3 = unchanged ; p2 = 1

Link 2 – 4: d4 > d2 + 2 d4 = 1 + 2 = 3 ; p4 = 2

Link 2 – 5: d5 > d2 + 4 d5 = 1 + 4 = 5 ; p5 = 2



SummarySummary:d1 = 0; p1 = 0

d2 = 1; p2 = 1

d3 = 4; p3 = 1

d4 = 3; p4 = 1

d5 = 5; p5 = 2



Output from 1st and 2nd passes



Output from final passes and solution



Labelling after Pass #1

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d1 = 0; p1 = 0

d2 = 1; p2 = 1 d4 = 3; p4 = 2

d3 = 4; p3 = 1 d5 = 5; p5 = 2

Documents

Network Layer â€“ Routing Devices and Shortest Path Algorithms for Routing