multi path performance 01

8/3/2019 Multi Path Performance 01

1/31

19.05.2005c nom etsKommunikationsnetze

Universitt Bremen

Theory Seminar

An Analytic Modeling to determine thePerformance of Multi-path Routing (forOn-Demands Protocols in Mobile Ad Hoc

Networks)

Koojana KuladinithiComNets, Universitt Bremen, Otto-Hahn-Allee NW1

28359 Bremen, Germany


2/31


Universitt Bremen

Theory Seminar

Motivation

Mobile Ad hoc NETwork (MANET) MANET : On-demand depends onflooding (i.e. each node should b/c) to discover routesFlooding (route discovery) takes

more BW

How to reduce the frequency offlooding?Use of multi-path routes: Keep

more than one route to the D

Analytical Modeling to determinethe relative frequency of floods

Wireless Connectivity (802.11x,802.15x, etc)

Two types of MANET

Reactive (On-Demand) Routingoverhead is Less

Proactive (Table Driven) Routing overhead is more


3/31


Universitt Bremen

Theory Seminar

Reference

Performance of Multi-path Routing for On-DemandProtocols in Mobile Ad Hoc Networks

ASIS NASIPURI and ROBERT CASTAEDA Department of Electrical and Computer Engineering, University of North

Carolina, Charlotte, NC 28223-0001, USA SAMIR R. DAS

Department of Electrical & Computer Engineering and Computer Science,University of Cincinnati, Cincinnati, OH 45221-0030, USA

[Published in Mobile Networks and Applications 6, 339349, 2001 KluwerAcademic Publishers. Manufactured in The Netherlands]


4/31


Universitt Bremen

Theory Seminar

Overview

Overview to DSR (Dynamic Source Routing)How to find multiple paths ? Two ways of keeping

multiple paths (Protocol 1 & Protocol 2)Analytical Model : Time between Route Discoveries

for Protocol 1for Protocol 2

Analysis of Numerical ResultsAnalysis of Simulation ResultsConclusion


5/31


6/31


Universitt Bremen

Theory Seminar

DSR Dynamic Source Routing, Cont.

Route is included in eachDATA packet as sourcerouteIf node 5 is not reachable,node 2 can notice and sendRERR to S

S2

5 D

1

3

4

6

7

DATA[5,D]

DATA[D]

DATA[2,5,D]

Routing Cache of S for D

P1 S, 2, 5, D (3 hops)

P2 S, 3, 4, 6, D (4 hops)


7/31


Universitt Bremen

Theory Seminar

Protocol 1 :

S D

n1

n2

n3 n

4nk+1

P2

P3

P4

L1

L2

L3

LkL

4

P1

PN

N number of disjoint routes

P1 Primary Route

P2 PN-1 - Alternate routes

Source maintains alternate routes to the D, except the Primaryroute


8/31


Universitt Bremen

Theory Seminar

Protocol 2 :

S D

n1

n2

n3 n

4nk+1

P1

P2

P3

P4

L1

L2

L3

LkL

4

If L3 breaks in the primary route (Primary route has been broken), n3 will change therouting path to P3

Each intermediate node in the primary path maintains an alternateroute to the D


9/31


Universitt Bremen

Theory Seminar

Analytical Modeling

To show the performance improvements in using multi-path routingMeasuring the Frequency of Route Discoveries

To find Interval between Route Discoveries (T ) for bothprotocols?

By representing the lifetime of a Link between two neighboringnodes by an Exponential Random Variable


10/31


Universitt Bremen

Theory Seminar

Distribution of Life time of a route

LiX

iL

L1 L2 L3 LkL4

ith link in a route, i = 1,2.k

Lifetime of ith route

iid exponential random variable with meanLiX

P

Lifetime of a route P, consisting of k wireless links is

LkLLP XXXX ,......,,min 21!

PX

PX is also exponentially distributed random variable with mean kl/

l

Handout Section 1 (P 1)

We assume that

k is equal to number of Links/hops in the route


11/31


Universitt Bremen

Theory Seminar

Modeling of Protocol 1

Lifetime of a Pi route, i=1,2, N

N = 3 ->

S DL1

L2

L3

Lk

L4P1

PN N number of disjoint routes

P1 Primary Route

P2 .PN-1 Alternate routes

PNPP

XXXT ,......,,max21

!

T

PNPP XXX ,......,, 21

Time interval between two route discoveries (i.e, after T, nextroute discovery should be started)

1PX 2PX 3PX


12/31


Universitt Bremen

Theory Seminar

Modeling of Protocol 1, Cont..

PNPP XXXT ,......,,max 21!

Frequency of Route Discoveries ~ time between successiveroute discoveries (T)

How to find the Expected value of T?

What is the pdf of T, )(tfT

where mean

!

)1)......(1)(1()( 3211

tttt

TNeeeetf

PPPPP

)1)......(1)(1( 3122

tttt Neeee PPPPP

)1()1)......(1)(1(..... 121 p

Aeqneeeetttt

NNN PPPPP

lkii /!P


13/31


Universitt Bremen

Theory Seminar


Proof of Eqn A-1;

where

Where i = 1,2, . N

PNPP XXXT ,......,,max 21!

,21 ,......,, PNPP XXX are N number of iid random variables with pdf of

t

iXi

iPetf

PP

!)(

Therefore cdf of T,

are independent

PiX

? AtTPtFT e!)(

? AtXXXPtFPNPPT

e! ,......,max)(21

? AtXtXtXPtFPNPPT

eee! .......)(21

++

)2()()(1

p!

!AeqntFtF

N

i

XTPi

t

Xi

PietF

P!1)(

1PX

Handout Section 2.1


14/31


Universitt Bremen

Theory Seminar


PNPP XXXT ,......,,max 21! tX iPi etFP! 1)(

By differentiating eqn. (A-2), w.r.t. t, you will get pdf of T as shown in eqn (A-1)

! )1)......(1)(1()( 3211

tttt

TNeeeetf PPPPP

)1)......(1)(1( 3122

tttt Neeee PPPPP

)1()1)......(1)(1(..... 121 p

Aeqneeeetttt

NNN PPPPP

)2()()(1

p!! AeqntFtFN

i

XT Pi

Handout Section 2.2 (p2)

)1()1()(1 1

p

!

! {!

AEqneetf

N

i

N

ikk

tt

iTki PPP

t

iXi

iPetf

PP

!)(

Cdf of T

How to find pdf of T?

N routes Pdf of Xp

Pdf of T

Cdf of Xp


15/31


Universitt Bremen

Theory Seminar


How to find E[T] from pdf of T [eqn (A-1)] ?When N = 2, what is the expected value of T ?

4&3,2 21 !!! kkN l/31 !P l/42 !P ? A _ a _ a lllTE 44.0)84/37()7(12/12169 !!!

3,11!! kN ? A llTE 33.03/ !!

l/31!P


l Mean Value of a life time of a link


16/31


Universitt Bremen

Theory Seminar


Special case -> k1 = k2=-----= kN = k, where


S DL1

L2

L3

LkL4P1

PN

lk/!P


17/31


Universitt Bremen

Theory Seminar

Numerical Results of Protocol 1

Length of the Primary route is k

S DL1

L2

L3

LkL4P1

PN

Case A is best case in multi-path routing (All routes have the shortest path), but this isan exceptional case

Mean lifetime of a single link (l) is assumed to be 5

Length of each route is sameLength increases by one hop each

Length increases by two hops each


18/31


Universitt Bremen

Theory Seminar


E(T) (Interval between route discoveries) of single Path (N=1) vs Multiple Paths (N=2),while varying the length of the primary route

E(T) is less in single pathcase

E(T) decreases with the

increase of the kRelative advantage of multi-path routing is less with theincrease of k

Case A is better than Case B& C


19/31


Universitt Bremen

Theory Seminar


E(T) (Interval between route discoveries) vs Number of routes (N) maintained forfixed number (k= 3 & 6) of primary length

E(T) - is higher with theincrease of alternate routes

After N > 3, incrementalimprovements is less exceptfor Case A

Case A is an exceptional case

Usually one/two alternate routes will be sufficient


20/31


Universitt Bremen

Theory Seminar

Modeling of Protocol 2

- Event that the link Li fails- Event that the link Pi fails

Each intermediate node in the primary path maintains an alternate route to the D

-When the event E is true, you have to start the next route discovery- Event E is expressed in following logical expression,

)1(...........))((())(()( 123213

12121

1 p! BeqnPPPLLLPPLLPLE

S D

P1

P2

P3

P4

L1

L2

L3

LkL4

n2

iL

iP


21/31


Universitt Bremen

Theory Seminar

Modeling of Protocol 2, Cont.

)1(...........))((())(()( 123213

12121

1 p! BeqnPPPLLLPPLLPLE

)2()........(...........)()()( 111233

1221

1 p! BeqnPPPLPPPLPPLPLE kkk

)),........,,max(),.......,,,max(),,min(max(1112211 PPkPkLkPPLPL XXXXXXXXXT !

S D

P1

P2

P3

P4

L1

L2

L3

LkL4

n2

),........,,max(11 PPiPiLi XXXX iZ

),max(11 PL XX ),,max(

122 PPL XXX


22/31


Universitt Bremen

Theory Seminar

Modeling of Protocol 2, Cont.

PNPP XXXT ,......,,max 21! )1()1()(1 1

p

!

! {!

AEqneetf

N

i

N

ikk

tt

iTki PPP

),........,,max(11 PPiPiLi

XXXXZi

!How to find pdf of Zi ?

From (Eqn A-1) from the first protocol

),........,,max(11 PPiPiLi XXXXZi !

For Zi ?



23/31


Universitt Bremen

Theory Seminar

Modeling of Protocol 2, Cont.)),........,,max(),.......,,,max(),,min(max(

1112211 PPkPkLkPPLPL XXXXXXXXXT !

Pdf of T ?

),........,,max(11 PPiPiLi XXXX iZ

),........,,min(321 kZZZZT !



24/31


Universitt Bremen

Theory Seminar


Length of the Primary route is k, Alternate routes of Pi, i=1,2,k

Case A is best case in multi-path routing (All routes have the shortest path), but this isan exceptional case

Mean lifetime of a single link (l) is assumed to be 5

Only one alternate route was maintained except the primary path

Length of the Primary route for I to D & Pk is same

Length increases by one hop each

Length increases by two hops each

S D

P1

P2

P3

P4

L1

L2

L3

LkL4

n2


25/31


Universitt Bremen

Theory Seminar

Numerical Results of Protocol 2, Cont.

Protocol 2 Protocol 1


26/31


Universitt Bremen

Theory Seminar

Protocol 1 Vs Protocol 2

S D

P1

P2

P3

P4

L1

L2

L3

LkL4

n2

S DL1

L2

L3

LkL4P1

PN

Protocol 2 is practically true forsparse networks


27/31


Universitt Bremen

Theory Seminar

Performance Evaluation via Simulation

Modeling uses idealized assumptions such as iidexponential link lifetimes

Independent? Breakage of existing route &alternate routes are correlated (e.g, if D moves, all

routes will be broken)It does not model

the routing load (e.g. number of controlled packetthat are transmitted)

End to end delay (longer the alternate route,more delay)

More realistic results


28/31


Universitt Bremen

Theory Seminar

Simulation Results

Event Driven Packet-level routing simulator (MaRS)Uni-directional data flow between a pair of sourceand sink nodes (a conversation)

Protocol 2 with only one alternate route

Parameters evaluated in 60 nodes network

Fraction of packets dropped

End-to-end delay

Number of route discoveries

Routing load


29/31


Universitt Bremen

Theory Seminar

Simulation Results

When having Multi-Path routes,

Less route discovery

Less Packet losses (Pkts lost during aRD is saved)

End-to-End delay is higher (alternateroute is longer)


30/31


Universitt Bremen

Theory Seminar

Conclusion

For DSR, two techniques to enable multi-pathrouting has been discussed

Provided an analytical model to evaluate theperformance of multi-path routing (based on simpleassumptions on the lifetime of a link)

Performance of Multi-pathReduce the frequency of route discoveries

Longer alternate paths are less advantages (tends to break tooearly)

better than single path (tradeoff between a routing load and end-to-end delay)

Performance advantage of using more than one or two alternateroutes is usually minimum


31/31


Universitt Bremen

Theory Seminar

Further Outlook

Use of alternate route might not always be better

How to apply this for AODV? No Routing Cache, In

AODV route lifetime will be maintained

multi path performance 01

Documents