Computer Networks Group Universität Paderborn Computer Networks Chapter 6: Routing Holger Karl.

Computer Networks GroupUniversität Paderborn

Computer NetworksChapter 6: Routing

Holger Karl

WS 05/06, v 1.1 Computer Networks - Routing 2

Goals of this chapter

Building larger networks by simply interconnecting LANs is limited, it does not scale

To build larger networks, the following questions have to be explicitly solved:

What are good paths that a packet should take to get from a source node to a destination node?

How to represent these paths by routing tables and how to construct them efficiently?

How to use routing tables (once constructed) efficiently? How to organize larger networks with respect to an addressing

structure that allows efficient & compact routing tables?

In addition, we will look at how the Internet’s routing structure looks like as a case study


Overview

From spanning trees to routing tables Computing routing tables Hierarchical routing Addressing Case study: IP routing, forwarding, & addressing


Goal: Build LARGE networks

The “internetworking” mechanisms described in previous chapter can help packets to reach their destination

Hubs: broadcast; switch: send to directly connected network Bridge: Flooding causes problems; spanning tree solves some of

them

Can we directly extend these mechanisms to large networks (millions or more nodes)?

Flooding clearly not a good idea Need some structure to decide where a packet should go A single spanning tree is not good, can introduce considerable

detours


Desirable: Shortest paths!

Instead of a single spanning tree for an entire network, provide shortest paths

Given a source and destination node for a packet, what is the shortest way to deliver the packet?

What does “shortest” mean? Fewest hops? Smallest delivery time? Lowest cost?

Choice to make: to which neighbor to forward a packet?


Destination

Forwarding table of W

Routing tables expressing costs

Routing table: For a given node and all its direct neighbors, express cost to send to any destination

Construct from routing table: Forwarding table

For a given node and any destination, express to which neighbor a packet should be passed on to minimize cost

Trivial to construct from routing table, but smaller and quicker to search

M P Z

U 2 3 4

V 3 2 3

X 4 3 2

Y 4 4 3

Destination

Neig

hb

or

Routing table of W

M P Z

U (2) V (2) X (2)


Properties for routing algorithms

Routing algorithm = an algorithm to compute routing tables Properties/classifications

Correct, simple Centralized/distributed Robustness

Can compensate quickly for failing links

Non-adaptive/adaptive to current situation of a network Also called: static/dynamic routing

Stable – will converge to an equilibrium over time Optimality (in throughput, delay, … or some other metric) Fairness


Overview

From spanning trees to routing tables Computing routing tables

Link-state routing algorithms Distance-vector routing algorithms

Hierarchical routing Addressing Case study: IP routing, forwarding, & addressing


Computing routing tables – A centralized view

Given a graph G=(V,E) and a cost function c : E! Real Compute, for each node v 2 V, the routing table to each

destination u 2 V Such that for each pair (v,u), the path (v, s1, …, sn, u) with

the minimal smallest cost can be derived easily from the routing table

By simply choosing the neighbor with the smallest entry Cost of a path is the sum of the costs of its edges

“All pairs-shortest path problem” Approach: Compute shortest paths from a given node to all

possible destination nodes; do that for all nodes in the network “Shortest path tree” NOT a minimum spanning tree computation


Centralized shortest path – Dijkstra

Given graph G=(V,E), cost c : E! real, source node A Algorithm can be applied to any source node, of course

Compute shortest paths to all destinations (and their cost)

Dijkstra’s algorithm Label each node with distance to source node A (or 1, if not known) Label each node as either tentative or permanent

Only nodes labeled permanent have final distance estimates

Label each node with its predecessor in the path towards the source Or mark as “unknown”

Initially, all labels are (1, tentative, unknown)


Centralized shortest path – Dijkstra

Initial action: Make node A permanent Whenever a node X is changed from tentative to

permanent with label (cX, permanent, W): For all neighbors Y of X with label (1, tentative, - ):

Replace label of Y by (cX + c(X,Y), tentative, X) First time a path is found for node Y

For all neighbors Y of X with label (cY, tentative, U):If cX + c(X,Y) < cY, replace label by (cX + c(X,Y), tentative, X)

A better path to Y has been found, via X instead of via U

Once relabeling step is complete, search (in entire graph) tentative node with smallest cost – and make it permanent

This is the closest node to A which is still uncertain, for any other node a still cheaper path might be found

Proceed until all nodes are labeled as “permanent”


Centralized routing – Dijkstra – Example


Centralized vs. distributed algorithms – Link-state routing

Dijkstra’s algorithm nice and well But how to obtain centralized view of the entire network to

be able to apply Dijkstra’s algorithm? Assumption: only direct neighbors know the (current) cost of a link

or know whether a link has failed/been restored/upgraded/…

Solution: Have each node distribute this information – state of all its links – in the entire network

Then, all nodes know entire network topology & can apply Dijkstra’s algorithm

Distribution itself can happen via flooding

! Link-state routing Intuition: Little information (about direct neighbors) is spread over

large distances (to the entire network)


Overview

From spanning trees to routing tables Computing routing tables

Link-state routing algorithms Distance-vector routing algorithms

Hierarchical routing Addressing Case study: IP routing, forwarding, & addressing


Alternative approach: Distance-vector routing

Alternative idea to link state routing: Distribute lot’s of information over short distances

Distribute everything a node currently knows (or believes) about the entire network topology, but only to direct neighbors

This information is represented by the routing table (containing outgoing link and cost)

If reduced to cost only, also called a distance vector

Invented by Bellman & Ford (1957)

After receiving a routing table from a neighbor, compare whether it contains “good news”, i.e., a shorter route than the one currently known

Assumption: each router knows cost to each of its direct neighbors

In practice: It suffices to exchange distance vectors


Distance-vector routing – Formally

Suppose that node X Has distance vector (x1, … xn) for each of the n possible

destinations in the network Receives distance vector (y1, … , yn) from its neighbor Y

Has cost cXY to reach neighbor Y

Then: Node X compares, for every destination i,xi < yi + cXY

i.e., is it cheaper to go first to Y and then to i rather than to go to node i directly?

If yes, replace outgoing link for node i by y, update cost to yi + cXY

Algorithms keeps iterating


Distance-vector routing – Example

This is the (current version of)

routing table!

8

10

12

6


Overview



Solution for LARGE networks?

What happens to routings when networks grow? Routing tables become longer and longer, requiring more memory Searching through routing/forwarding tables takes more and more

time, reducing throughput of a router/increasing delay Run-time of routing algorithms becomes larger

But: does a given node really care about details of the route “far away”?

Suppose you send a packet to an Australian university – do you care which route it takes from one campus router to the next?

It suffices to get the packet towards Australia For local packets, a router better should care!

! Hierarchical routing


Hierarchical routing – Regions

Group nodes/routers into regions Routers know

How to reach each node/router in their own region How to reach each other region

Perspectiveof one router


Routing within and between regions

A router perceives all routers in a “foreign” region as the same node, does not distinguish routing tables

Packet destined to own region: routed as normal Packet destined to other region: get it to the region, don’t

worry about details of routing there Once a packet enters its destination region, router knows about

the details how to reach the destination node

Necessary: Router must be able to easily infer the target region from packet’s destination!

Requires adequate addressing structure for a quick address ! region mapping

Treated a few slides later


Price of hierarchy

Hierarchical routing good for algorithm runtime, memory required for routing tables, next-hop lookup times, …

What is the price to pay?

Routes become non-optimal Since no longer all the details of the network are represented,

routing algorithms might miss optimization potential Can this overhead be bounded? Is it acceptable in practice?


Only regions? Or multiple levels of hierarchy?

If network becomes REALLY big, these two levels of hierarchy might again not suffice

Group regions into clusters, clusters into domains, domains into conglomerates, … (or whatever terminology pleases you)

Obvious question: How many levels of hierarchy? How many entities should be grouped together to form the next-

level conglomerate structure?

Good rule of thumb: For n nodes, use ln n levels of hierarchy

Requires e ln n entries in each routing table

Then: Good balance between routing overhead and smaller routing table sizes


Gateways between networks

Gateways are those nodes that connect to peer conglomerates

Such conglomerates arefairly independent of eachother

Different routing protocolscan be used – an interiorgateway protocol in each conglomerate

Between gateways, yet another protocol is conceivable – an exterior gateway protocol – operating only on the “gateway graph”

Because of autonomy, the name autonomous system is used

Gateways


Broadcast & multicast

Broadcast routing: Make sure every node receives a copy of a given packet

Unrestricted flooding is one (not particularly good) implementation option

Better: Construct minimum spanning tree, copy each packet going in on a given edge to all other tree edges

Related: Construction of minimal connected dominating set

Multicast routing: Ensure that each node of an explicitly given subset of all nodes receives a copy of a given packet

Algorithmically: Steiner tree problem, NP complete Several approximations, e.g., Takahashi & Matsuyama Various network constructions, tree-based or mesh-based

approaches


Overview



Addressing – Failure of simple addresses

Think back to the MAC/LLC layer: Each device has a globally unique MAC address

Why is there then a need to talk about some other addressing scheme?

How did spanning tree algorithm for bridges work? Each bridge had to store a separate entry for each device to

which is was routing packets Lot’s of memory, CPU overhead (for searching)

! Clearly, this does not scale to large networks


Addressing and hierarchical routing

“Flat” addresses – addresses that express no structure – do not work well together with hierarchical routing

Necessary: Addresses that express/respect the hierarchical routing structure

Essentially, something like: Group-IDn:Group-IDn-1:…:Group-ID1:Device-ID

Hierarchical addresses – addresses are relative to higher groups

Perspectiveof one routerPerspectiveof one router


Overview


IP addressing Growing pains: Subnetting, classless addressing Inter- and intra-domain routing in IP


Addressing case study: Internet IP addresses

IP addresses (traditionally) distinguish only two levels of hierarchies

Network interfaces/hosts Note: “hosts” is somewhat incorrect since their interfaces are actually

addressed; still common terminology Networks

Different sizes of networks conjectured, defined as three classes ! Classful addressing

Network classes: Big – medium – small (class A, B, and C) Routers have to know about all other networks (or at least about a

router that knows about all of them as a default solution to send a packet)

An IP address is 32 bits, split into a network part (with three possible lengths) and an interface/host part

Usually written as dotted decimal, four decimals between 0 and 255


Classful IP addressing

In addition to three network classes A, B, and C, there is class D for multicast; class E as “reserved”

Encodes network class of this address

128 NWs; 16 M hosts

16K NWs; 64K hosts

2M NWs; 256 hosts


Some reserved IP addresses

Some IP addresses are set aside for special uses Not all of the network/host combinations are available


Forwarding using IP addresses/IP routing tables

A router is in charge of its “own” network, has to known how to handle packets for all destinations within

Upon a packet arrival, check if packet is destined for own network

If no: Look at “network” bits of the destination address, look up corresponding outgoing link, forward packet to that router

If no outgoing link known, use a “default”, fallback peer router

If yes: Look at “host” bits of the destination address, look up corresponding outgoing link, forward packet to that host

Basically, fairly straightforward, two-level hierarchical forwarding and routing


An IPv4 packet header


Overview




Growing pains…

How does IP hold up when networks grow? Two main problems ensue

Class A and B networks can contain MANY hosts, too many for a router to easily deal with ! subnetting

Network classes waste a lot of addresses Example: Organization with 2000 hosts requires a class B address,

wasting 64K-2K ¼ 62.000 host addresses!

! Classless addressing


Subnetting

Suppose an organization has a class B address but is organized into several LANs

Example: university with different departments

Main router does not really want to bother with all the nodes in the individual departments but wants to look only at whole networks

Obvious case for hierarchical routing and addressing – how to put hierarchies into existing IP addresses?


Subnetting – Hierarchies in addresses

Manipulating the class bits to introduce more hierarchy levels is not practical

Idea: have more hierarchy levels implicitly Introduce a subnet, represented by “borrowing” bits from the host

part of the IP address Local router has to know where to apply this split – needs a

subnet mask Represented as u.x.y.u/#bits or as bit pattern needed to mask out

the host bits

Original host part


Forwarding with subnetting in place

Forwarding when packet is not destined to “own” network: as above; send to router in charge

Subnetting not visible outside the network!

Packet is destined to own network: Router checks list of subnets belonging to the current network Either another router/outgoing link is known ! send packet there Or this router itself is in charge of the packet’s subnetwork ! send

packet directly to the host in charge Or nothing is known ! Send to default router

In effect: subnetting has introduced another hierarchy level between networks and hosts as in the traditional internet addressing


Classless Interdomain Routing (CIDR)

To solve second problem (running out of addresses because large chunks of addresses are allocated in big networks), essentially a similar idea is used

Just like in subnetting, break out bits from the host part to form networks of a more suitable size

But: Make these networks visible to other routers! No extension in the IP packets needed But more information in the routing tables has to be stored Lookup and forwarding algorithms become more complicated


Overview




Autonomous systems in the IP world

Large organizations can own multiple networks that are under a single administrative control

Forming an autonomous system or a routing domain

Autonomous system form yet another level of aggregating routing information

Gives raise to inter- and intra-domain routing

Inter-domain routing is hard One organization might not be interested in carrying a competitor’s

traffic, … Routing metrics of different domains cannot be compared; only

reachability can be expressed Scale – currently, inter-domain routers have to know about

140.000 networks


Structure of autonomous systems in the IP

Resulting structure Stub AS: Only a single connection to other AS; only carries local

traffic Multihomed AS: Has connections to multiple other ASs but refuses

to carry non-local traffic for anybody else Transit AS: Multiple connections, does carry both local and transit

traffic – typical example of an Internet service provider (ISP)

Backbone service provider 2

Backbone service provider 1Consumer

ISP 1

ConsumerISP 2

Largecompany

Smallcompany 1

Smallcompany 2

Peering point


Intra-domain routing: OSPF

Internet’s most prevalent intra-domain (=interior gateway) routing protocol: Open Shortest Path First

Main properties Open, variety of routing distances, dynamic algorithm Routing based on traffic type (e.g., real-time traffic uses different

paths) – different metrics for a link for different traffic Load balancing: also put some packets on the 2nd, 3rd best path Hierarchical routing, “areas” as additional level, some security in

place, support tunneled routers

Essential operation: Compute shortest paths on graph abstraction of an autonomous system

Link state algorithm Link state information reliably flooded, sequence numbers,

triggered or periodically, with time to live


Inter-domain routing: BGPv4

Routing between domains: Border Gateway Protocols (BGP)

Routing complicated by politics, e.g., only route packets for paying customers, do not route transit traffic, …

Legal constraints, e.g.: Traffic originating and ending in Canada must not leave Canada while in transit!

BGP’s perspective: only autonomous systems and their connections

Only talk about reachability, “optimal” is a vain hope

Operation: Distance vector protocol But not only keep track of cost via a given neighbor, but store

entire paths to destination ASs More robust, solves problems like count to infinity Infernally complicated protocol…


Example: Routing table sizes for Internet AS

http://www.mcvax.org/~jhma/routing/bgp-hist.html


Bridging addressing gap: ARP

What happens once a packet arrives at its destination network / LAN?

How to turn an IP address (which is all that is known about the destination) into a MAC address that corresponds to the MAC address?

Simple solution: Yell! Broadcast on the LAN, asking which node has IP address x Node answers with its MAC address Router can then address packet to that MAC address

Address Resolution Protocol (ARP)


Some internetworking issues

Other things to watch out for Fragmentation Connection-oriented vs. connection-less networks Tunneling Dynamic Host Configuration Protocol (DHCP) IP version 6 Multicasting Network Address Translation Virtual Circuits Routing for Quality of Service support QoS concepts: Integrated and Differentiated Services ATM / Label switching / MPLS Routing in ad hoc networks, peer-to-peer networks …

… but are not covered here due to lack of time


Conclusion

Routing in large networks not only requires adequate routing algorithms for general graphs

Also an appropriate, hierarchical network structure is required

Network structure has to be reflected in the addressing structure

Flat addresses would result in prohibitive overhead

Different metrics and goals have to be fulfilled, in particular in inter-domain routing where optimality is only a single aspect


Some IP design principles – A historical side remark

RFC 1958, based on papers from mid-80s: Make sure it works – before writing the standard Keep it simple Make clear choices Exploit modularity Expect heterogeneity Avoid static options and parameters Look for a good design; it need not be perfect (80-20 rule) Be strict when sending and tolerant when receiving Think about scalability Consider performance and cost

Computer Networks Group Universität Paderborn Computer Networks Chapter 6: Routing Holger Karl.

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