dual seminar

7/30/2019 DUAL Seminar

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The Diffusing Update Algorithm

Presented by

Anil K.C (Roll: 12)

Central Department of Computer Science andInformation Technology, T.U.


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Objective

To present a routing algorithm that is loop free

To illustrate the underlying principle of

popular routing protocol, the EIGRP

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Overview

Routing loops

Sufficient conditions for loop avoidance

Diffusing Update Algorithm (DUAL) Example

Conclusion

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Routing Loops

Fundamental routing algorithms

Distance vector routing (Distributed Bellman ford

algorithm)[3]

Link state routing (Dijkstras algorithm)[4]

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Loop formation in distance vector

routing

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Fig 1: Two-node instability [5]


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Solutions to these instability

Two node instability

Defining Infinity

Split Horizon

Split Horizon and Poison Reverse

Three node instability

Stability cannot be guaranteed

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Loop formation in link state routing

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Fig 3: Microloop Example

due to the timingdifferences, B

calculates and

installs its new

best path through

A before A has a

chance to switchfrom B to E, a

microloop will

form between A

and B for the

duration of time

required for A to

complete

its routing table

update.


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How can routing loops be avoided at

all ?

By properly choosing the successor after achange in link cost or link failure has beendetected

Sufficient Conditions for Loop freedom(Feasibility Conditions, FC)

Distance Increase Condition (DIC) Current Successor Condition (CSC)

Source Node Condition (SNC)

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G = (V, E): Network Model and

Notation G: a connected network of arbitrary topology

E:The set of links in G

N: The set of nodes in G

j: The identifier of destination nodej N

(i,x): The link in Ebetween nodes iandx sij(t): The successor (or next hop) in the path to nodejcurrently

chosen by node iat time t

lik(t): The cost of the link from node ito neighbor node kas knownby node iat time t; the cost of a nonexistent link or a failed link isconsidered to be infinity

Vi(t): The set of destination nodes node iknows at time t Ni(t): Theset of nodes connected through a link with node iat time

tmore formally, Ni(t) = {x| (i,x), lix(t)< }; a node in that set is

said to be a neighbor of node i.

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Contd.

Dij(t): Thecurrent distance from node ito nodejas known by node iattime t

Dijk(t): Thedistance from node kto nodejas known by node iat time t

D*ij(t): The smallest value assigned to Dijup to time t

D*ijk(t): The smallest value ofDkjknown by node iup to time t

RDij(t): The distance from node ito nodejthat node ican report to itsneighbors at time t(and which need not equal Di

j

(t))

FDij(t): The distance value used by node ito evaluate whether a feasibilitycondition is satisfied at time t; depending on the condition used, it can beequal to either D*ij(t) or D*

ijk(t).

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Source Node Condition (SNC)

If at time tnode ineeds to change its currentsuccessor, it can choose as its new successor anyneighbor q Ni(t) for which

Dijq(t) + liq(t) = Min{D

ijx(t) + l

ix(t) | x Ni(t)}

andDijq(t) FD

ij(t), where FD

ij(t) = D

*ij(t).

If no such neighbor exists, then node imust maintainits old successor if it has any.

The variable FDij(t) is called thefeasible distance ofnode ifor destinationj.

Feasibility Condition, FC.

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Contd

DIC, CSC and SNC ensures loop freedom at everyinstant,

But none of them guarantees shortest path

Routing algorithms has to be derived based onthese FCs to achieve both Loop Freedom at every instant

Shortest paths for each destination

Goal: For each destination, successor entries ofthe routing table should define another graphthat is a dag or ASG.

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The DUAL

Uses the concept of Diffusing Computations[2] The diffusing computation started by a node grows by

sending queries and shrinks by receiving replies along anacyclic graph rooted at the source of the computation.

Input Events for a node Reply

Query

Update

Computation Types: Depends whether FC issatisfied

Local

Diffusing

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DUAL Contd.

States of a node on a macro level

Active by commencing a DC

Passive after termination of DC

States of a node on a micro level is specifiedby

Reply status flag: rijkto remember whethernode khas sent a reply to node i's query

(0 or 1)

Query origin flag: oij(0, 1, 2, 3)

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States in DUAL

15Fig 4: Active and Passive States in DUAL [1]


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Example

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Fig 5: Example ofDUALs operation [1]

The label of

parentheses

assigned to

each node

[Dxj, FDxj, O

xj]


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Conclusion

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The DUAL is basically a concept that can be

adapted by either of distance vector routing

algorithms or the link state ones. That is, either

of two well-known algorithms can be used ateach node to compute shortest paths once

topology information is gathered and updated

using DUAL.


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References

1. J. J. Garcia-Luna-Aceves, "Loop free routing using diffusingcomputations", IEEE/ACM Transactions on Networking ,Vol 1, No. 1, February 1993.

2. E. W. Dijkstra and C. S. Scholten. Termination detectionfor diffusing computations, Inform Process. Lett., vol. 11,no. 1, pp. 1-4, Aug. 1980

3. C. Hedrick, Routing information protocol, RFC 1058,Netw. Inform. Cent., SRI Int., Menlo Park. CA, June 1988.

4. R. Coltun, OSPF: An internet routing protocol,

ConneXions, vol. 3, no. 8, pp. 19-25, Aug. 19895. A. F. Behrouz,Data Communications and Networking,

fourth edition, pp. 663-665, 2006

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