Routing in Communication Networks

Routing: Network layer protocol that guides information units to correct destinations. A complex collection of decision rules that work somewhat independently.

- Determination of allowable path set for each origin - destination pair

- Broadcast of routing related information to all network nodes

- Determination of particular path per arrived call.

Routing Types

Virtual circuit routing

Datagram routing

Characteristics

Performance indices

Throughput

Delay

Under light load: throughput = offered load

Under heavy load: throughput = offered load - rejected load

Routing interacts with flow control to maintain the performance

Traffic experiences delay depending on routing

Flow control rejects a portion of load depending on delay

Routing Types Revisited

Virtual circuit vs. datagram

Centralized vs. distributed

Static vs. adaptive

Hierarchical vs. non hierarchical

Broadcasting

Send information from a node to all nodes in networks (e.g., announcing equipment and link failures)

Send information from a node to some selected subset of nodes

Examples of broadcasting method: Flooding

A node send a packet to all of its neighbors.

Each neighbor sends the received packet to its neighbors and so on.

Loop back should be eliminated.

Multiple transmissions must be eliminated.

Not efficient.

Example: Spanning Tree

Connected sub-graph of network including all nodes

No cycles

Packets transmitted over spanning tree

More efficient than flooding

Packets transmitted N-1 times (N = number of nodes)

Routing Examples Shortest path routing

Each link has a link length (> 0).Path length is the sum of link lengths over the path.Shortest path routing routes each packet over a minimum length path (i.e.,a greedy algorithm).Minimum hop routing: If every link has a unit link cost.

Optimal routingRoutes are determined for all OD pairs simultaneously for the good of entire network.Can eliminate potential oscillations in the shortest path routing.

Hot potato routingMinimize buffer requirements.Arrived packets are routed on an out-going link from the list of links.Packets may get out of sequence.Packets may experience long delay.

Cut-through routing

Minimizes delay.

Packets are allowed to go out on an out-going link as soon as initial few bits arrive.

Error checking and ARQ cannot be done.

Link reservation is needed while transmitting a packet.

Speed mismatch among links can create overflows/congestions.

ARPANET routingAdaptive and distributed datagram routingShortest path routing based on link delay as link lengthShortest paths are calculated using Bellman-Ford algorithm.Link lengths are updated every 10 seconds.

TYMNET routingCentralized and adaptive virtual circuit routingSupervisor determines the routing for all nodes.Shortest lath routing based on link load as link length

SNA routingNetwork manager chooses virtual paths for each OD pair

Circuit switched routingLike virtual circuit routingTypically implemented with hierarchy

Interconnected Network Routing

Involves gateways, routers, and bridges between networks

Non hierarchical routing

Control becomes complex.

Much information needs be stored at each node.

Hierarchical routing

long distance routing

Routing within sub-network

Lower information storage at potentially lower performance

Graphical Model for Routing

Use of Graph Theoretic Model Undirected graph G = (N, A)N = finite non empty set of nodesA = collection of pairs of distinct nodes from N called arc.

N = {1,2,3,4}A = {(1,2), (2,3), (4,1), (2,4)}

Note:No loopNo multiple arcs between the same pair of nodesA node is also called a vertex.An arc is also called an edge, link, or branch.

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Definition:

A walk is a sequence of nodes (n1, n2, n3,…,nl) such that (n1, n2) (n2, n3),…(nl-1, nl)

are each an arc in G.

Definition:

A path is a walk with no repeated node.

Definition:

A cycle is a path with no repeated node expect for n1 = nl.

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Definition

A graph is connected if from each node i, there is a path to any other nodes j.

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Lemma: Let G = (N,A) is a graph. S N and S N. Then G is connected if for any such S there is at least one arc (i, j) with i S and j S.

Definition: g= (n, a) is a sub-graph of G=(N,A) if g is a graph and n N and a A.

Definition: A tree is a connected graph with no cycle.

Definition: A spanning tree of a graph G is a sub-graph of G that is a tree and that includes all nodes of G.

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Minimum Weight Spanning Tree (MST)

For G = (N,A), let each arc (i, j) has some weight wij. We want to find a spanning tree with the minimum sum of arc weights.

Definition

Any sub-tree of an MST is called a fragment.

Definition

An arc having one node in a fragment and the other one outside the fragment is called an outgoing arc.

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Start with each node being a fragment. Order the arc weights in an ascending order w1, w2, w3, …,w|A|.. At each iteration, add an arc that has the minimum weight out of all arcs that are outgoing from all of the fragments.

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Kruskal’s algorithm can be made distributed if MST is unique. (Each fragment adds the minimum weight outgoing arc and includes the fragment on the other side of that arc.)

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For a graph G = (N,A), let N be a finite non empty set of nodes and let A be a collection of ordered pairs of distinct nodes from N. (There is no loop as before.)

Definition Given a digraph G = (N, A), a graph G´=(N´, A´) is (undirected) associated

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Walk, path, cycle in a digraph are those of the associated graph.Definition

(n1, n2, n3, …, nl ) is a directed walk in G if (ni, ni+1) is a directed arc in A for i=1, 2, 3,…, l-1.

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G= (N, A) is strongly connected if for each pair i N and j N, there is a directed path from i to j.

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G is connected if the associated graph is connected.

Definition

For a given digraph G = (N, A), assign to each arc (i, j), some number dij as the length of the arc. The length of a path is the sum of the lengths of the arcs that comprise the path.

Problem Definition

Shortest Path Problem is a problem that finds, for any two given nodes i and j, a path with the shortest path length.

Bellman – Ford Algorithm

At each step, calculate the shortest path using h or less arcs.

At the end of the first step, we have the shortest paths using one arcs.

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Routing in ARPANET

Original version (1969)

Length of each link depends on the number of packets waiting in the link queue.

Nodes exchange information on the shortest distance every 625 msec.

Bellman-Ford algorithm is used for shortest paths.

Prone to oscillation.

Modified version (1979)

Length of each link is proportional to the average delay.

Link length is updated every 10 seconds.

Nodes exchange information on the length of their outgoing links every 60 seconds.

Shortest path is calculated by Dijkstra’s algorithm.

Prone to oscillation.

Optimal Routing

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In optimal routing, there is a positive flow only on those paths with minimum first derivative length (MFDL).

A path flow vector x is strictly sub optimal if there is a positive flow on a non NFDL path.

Given a sub optimal path flow vector, we can improve the routing by shifting flows from non MFDL paths to MFDL paths.

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Topological Design

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Locations of terminal are known.

Traffic level between each OD pair is known.

Selection

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Topology of local access network

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Satisfy the average delay per packet constraint for a given routing scheme.

Satisfy the reliability constraint with respect to node and link failures.

Minimize cost.

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