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# Data Communication and Networks - PowerPoint PPT Presentation

Data Communication and Networks. Lecture 7 Networks: Part 2 Routing Algorithms October 27, 2005. Some Perspective on Routing …. When we wish to take a long trip by car, we consult a road map. The road map shows the possible routes to our destination.

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### Data Communication and Networks

Lecture 7

Networks: Part 2

Routing Algorithms

October 27, 2005

• When we wish to take a long trip by car, we consult a road map.

• The road map shows the possible routes to our destination.

• It might show us the shortest distance, but, it can’t always tell us what we really want to know:

• What is the fastest route!

• Why is this not always obvious?

• Question: What’s the difference between you and network packet?

• We adapt to traffic conditions as we go.

• Packets depend on routers to choose how they get their destination.

• Routers have maps just like we do. These are called routing tables.

• What we want to know is:

• How to these tables get constructed/updated?

• How are routes chosen using these tables?

Routing in Circuit Switched Network

• Many connections will need paths through more than one switch

• Need to find a route

• Efficiency

• Resilience

• Public telephone switches are a tree structure

• Static routing uses the same approach all the time

• Dynamic routing allows for changes in routing depending on traffic

• Uses a peer structure for nodes

• Possible routes between end offices predefined

• Originating switch selects appropriate route

• Routes listed in preference order

• Different sets of routes may be used at different times

AlternateRoutingDiagram

Routing in Packet Switched Network

• Complex, crucial aspect of packet switched networks

• Characteristics required

• Correctness

• Simplicity

• Robustness

• Stability

• Fairness

• Optimality

• Efficiency

• Used for selection of route

• Minimum hop

• Least cost

• See Stallings chapter 12 for routing algorithms

• Routing decisions usually based on knowledge of network (not always)

• Distributed routing

• Nodes use local knowledge

• May collect info from adjacent nodes

• May collect info from all nodes on a potential route

• Central routing

• Collect info from all nodes

• Update timing

• When is network info held by nodes updated

• Fixed - never updated

• Fixed

• Flooding

• Random

• Single permanent route for each source to destination pair

• Determine routes using a least cost algorithm (Chapter 12)

• Route fixed, at least until a change in network topology

• No network info required

• Packet sent by node to every neighbor

• Eventually a number of copies will arrive at destination

• Each packet is uniquely numbered so duplicates can be discarded

• Nodes can remember packets already forwarded to keep network load in bounds

• Can include a hop count in packets

Flooding Example

• All possible routes are tried

• Very robust

• At least one packet will have taken minimum hop count route

• Can be used to set up virtual circuit

• All nodes are visited

• Useful to distribute information (e.g. 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

• No network info needed

• Route is typically not least cost nor minimum hop

• Used by almost all packet switching networks

• Routing decisions change as conditions on the network change

• Failure

• Congestion

• Decisions more complex

• Reacting too quickly can cause oscillation

• Reacting too slowly to be relevant

• Improved performance

• Aid congestion control (See chapter 13)

• Complex system

• May not realize theoretical benefits

• Basis for routing decisions

• Can minimize hop with each link cost 1

• Can have link value inversely proportional to capacity

• Given network of nodes connected by bi-directional links

• Each link has a cost in each direction

• Define cost of path between two nodes as sum of costs of links traversed

• For each pair of nodes, find a path with the least cost

• Link costs in different directions may be different

• E.g. length of packet queue

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Graph abstraction

Graph: G = (N,E)

N = set of routers = { u, v, w, x, y, z }

E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }

Remark: Graph abstraction is useful in other network contexts

Example: P2P, where N is set of peers and E is set of TCP connections

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Graph abstraction: costs

• c(x,x’) = cost of link (x,x’)

• - e.g., c(w,z) = 5

• cost could always be 1, or

• inversely related to bandwidth,

• or inversely related to

• congestion

Cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)

Question: What’s the least-cost path between u and z ?

Routing algorithm: algorithm that finds least-cost path

net topology, link costs known to all nodes

all nodes have same info

computes least cost paths from one node (‘source”) to all other nodes

gives forwarding table for that node

iterative: after k iterations, know least cost path to k dest.’s

Notation:

c(x,y): link cost from node x to y; = ∞ if not direct neighbors

D(v): current value of cost of path from source to dest. v

p(v): predecessor node along path from source to v

N': set of nodes whose least cost path definitively known

1 Initialization:

2 N' = {u}

3 for all nodes v

4 if v adjacent to u

5 then D(v) = c(u,v)

6 else D(v) = ∞

7

8 Loop

9 find w not in N' such that D(w) is a minimum

11 update D(v) for all v adjacent to w and not in N' :

12 D(v) = min( D(v), D(w) + c(w,v) )

13 /* new cost to v is either old cost to v or known

14 shortest path cost to w plus cost from w to v */

15 until all nodes in N'

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Dijkstra’s algorithm: example

D(v),p(v)

2,u

2,u

2,u

D(x),p(x)

1,u

D(w),p(w)

5,u

4,x

3,y

3,y

D(y),p(y)

2,x

Step

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N'

u

ux

uxy

uxyv

uxyvw

uxyvwz

D(z),p(z)

4,y

4,y

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Algorithm complexity: n nodes

each iteration: need to check all nodes, w, not in N

n(n+1)/2 comparisons: O(n2)

more efficient implementations possible: O(nlog(n))

Oscillations possible:

e.g., link cost = amount of carried traffic

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… recompute

… recompute

routing

… recompute

initially

Dijkstra’s algorithm, discussion

Bellman-Ford Equation (dynamic programming)

Define

dx(y) := cost of least-cost path from x to y

Then

dx(y) = min {c(x,v) + dv(y) }

where min is taken over all neighbors of x

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Bellman-Ford example (2)

Clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3

B-F equation says:

du(z) = min { c(u,v) + dv(z),

c(u,x) + dx(z),

c(u,w) + dw(z) }

= min {2 + 5,

1 + 3,

5 + 3} = 4

Node that achieves minimum is next

hop in shortest path ➜ forwarding table

• Dx(y) = estimate of least cost from x to y

• Distance vector: Dx = [Dx(y): y є N ]

• Node x knows cost to each neighbor v: c(x,v)

• Node x maintains Dx = [Dx(y): y є N ]

• Node x also maintains its neighbors’ distance vectors

• For each neighbor v, x maintains Dv = [Dv(y): y є N ]

Basic idea:

• Each node periodically sends its own distance vector estimate to neighbors

• When node a node x receives new DV estimate from neighbor, it updates its own DV using B-F equation:

Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N

• Under minor, natural conditions, the estimate Dx(y) converge the actual least cost dx(y)

Iterative, asynchronous: each local iteration caused by:

DV update message from neighbor

Distributed:

each node notifies neighbors only when its DV changes

neighbors then notify their neighbors if necessary

wait for (change in local link cost of msg from neighbor)

recompute estimates

if DV to any dest has changed, notify neighbors

Distance Vector Algorithm (5)

Each node:

x y z

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0 2 7

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y

Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)}

= min{2+1 , 7+0} = 3

Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2

node x table

cost to

cost to

x y z

x y z

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0 2 3

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from

2 0 1

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node y table

cost to

cost to

cost to

x y z

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x y z

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node z table

cost to

cost to

cost to

x y z

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∞ ∞ ∞

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time

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• node detects local link cost change

• updates routing info, recalculates distance vector

• if DV changes, notify neighbors

and informs its neighbors.

At time t1, z receives the update from y and updates its table.

It computes a new least cost to x and sends its neighbors its DV.

At time t2, y receives z’s update and updates its distance table.

y’s least costs do not change and hence y does not send any

message to z.

“good

news

travels

fast”

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• good news travels fast

• bad news travels slow - “count to infinity” problem!

• 44 iterations before algorithm stabilizes: see text

Poissoned reverse:

• If Z routes through Y to get to X :

• Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)

• will this completely solve count to infinity problem?

LS: with n nodes, E links, O(nE) msgs sent

DV: exchange between neighbors only

convergence time varies

Speed of Convergence

LS: O(n2) algorithm requires O(nE) msgs

may have oscillations

DV: convergence time varies

may be routing loops

count-to-infinity problem

Robustness: what happens if router malfunctions?

LS: