university of southern california paths: analysis of path duration statistics and their impact on...

UNIVERSITY OFSOUTHERN CALIFORNIA

PATHS: Analysis of PATH Duration Statistics and their Impact on Reactive

MANET Routing Protocols

Narayanan Sadagopan*, Fan Bai+,

Bhaskar Krishnamachari*+, Ahmed Helmy+

* Computer Science Department

+ Electrical Engineering Department

University of Southern California


Outline• Introduction and Motivation• Background on Mobility Models• Link/Path Duration Metrics• Results & Observations

– Distributions at low and high mobility

– Is it exponential?!

• Models: Path Duration, Throughput & Overhead• Conclusions and Future Work


Introduction and Motivation

• Mobility affects performance of MANET protocols significantly [IMPORTANT ‘Infocom BSH03’]

• Mobility affects connectivity, and in turn protocol mechanisms and performance

• In this study: – Closer look at the mobility effects on connectivity metrics

(statistics of link duration (LD) and path duration (PD))

– Develop approximate expressions for LD & PD distributions (Is it really exponential? When is it exponential?)

– Develop first order models for Tput & Overhead as f(PD)

Mobility Connectivity

Protocol MechanismsPerformance(Throughput,

Overhead)


Mobility Models

• Used the IMPORTANT framework and tools[BSH’03]• Rich set of mobility models that exhibit various spatial

correlation and relative velocities• Four main models:

– Random Waypoint (RW) [CMU Monarch, BMJHJ’98]

– Reference Point Group Mobility (RPGM) [UCLA, HGPC’99]

– Freeway (FW)

– Manhattan (MH)


max

max())()(

()|)(||)(|

ADRrandomttVSDRrandomtVtV

referencenode

referencenode

Mobility Models (contd.)• Random Waypoint Model (RWP)

– A node picks random destination & random velocity [0, Vmax]

– After reaching the destination, it stops for the “pause time”.

– This procedure is repeated until simulation ends

• Reference Point Group Mobility (RPGM)– A group’s general movement is determined by a logical reference point

– Each node in a group follows the reference point with small deviation:

– Angle Deviation Ratio(ADR) and Speed Deviation Ratio(SDR). • In our study ADR=SDR=0.1

– Two scenarios: Single Group (SG) and Multiple Group (MG)


Map for FW

Map for MH

Mobility Models (contd.)• Freeway Model (FW)

– A node is restricted to its lane on the freeway

– Velocity of a node is temporally dependent on its previous velocity

– If two mobile nodes on the same freeway lane are within the Safety Distance (SD), the velocity of the following node cannot exceed the velocity of preceding node

• Manhattan Model (MH)– Similar to Freeway model

– Allows nodes to make turns at intersections


Connectivity Metrics

• Link Duration (LD): – For nodes i,j, the duration of link i-j is the longest interval

in which i & j are directly connected

– LD(i,j,t1)=t2-t1

• iff t, t1 t t2, > 0 : X(i,j,t)=1,X(i,j,t1-)=0, X(i,j,t2+)=0

• Path Duration (PD):– Duration of path P={n1,n2,…,nk} is the longest interval in

which all k-1 links exist


Simulation Scenarios in NS-2• Path duration computed for the shortest path (at graph

level) until it breaks.Validated later via protocol paths.• Mobility Models (IMPORTANT tool)

– Vmax = 1,5,10,20,30,40,50,60 m/s,

– RPGM: 4 groups (called RPGM4)

– Speed/Angle Deviation Ratio=0.1

• 40 nodes, in 1000mx1000m area• Radio range (R)=50,100,150,200,250m• Simulation time 900sec


Link Duration (LD) PDFs

• At low speeds (Vmax < 10m/s) link duration has multi-modal distribution for FW and RPGM4– In FW due to geographic restriction of the map

• Nodes moving in same direction have high link duration

• Nodes moving in opposite directions have low link duration

– In RPGM4 due to correlated node movement• Nodes in same group have high link duration

• Nodes in different groups have low link duration

• At higher speeds (Vmax > 10m/s) link duration does not exhibit multi-modal distribution


FW modelVmax=5m/s R=250m

Nodes moving in opposite directions

Nodes moving inthe same direction/lane

Multi-modal Distribution of Link Duration for Freeway model at low speeds


RPGM w/ 4 groups Vmax=5m/s

R=250m

Nodes in the same group

Nodes in different groups

Multi-modal Distribution of Link Duration for RPGM4 model at low speeds


Vmax=30m/sR=250m

RPGM (4 groups)RW

FW


Path Duration (PD) PDFs

• At low speeds (Vmax < 10m/s) and for short paths (h2) path duration has multi-modal for FW and RPGM4

• At higher speeds (Vmax > 10m/s) and longer path length (h2) path duration can be reasonably approximated using exponential distribution for RW, FW, MH, RPGM4.


FWVmax=5m/sh=1 hop R=250m

Nodes moving in opposite directions

Nodes moving inthe same direction

Multi-modal Distribution of Path Duration for Freeway model at low speeds, low hops


RPGM4Vmax=5m/sh=2 hops R=250m Nodes in the same group

Nodes in different groups

Multi-modal Distribution of Path Duration for RPGM4 model at low speeds, low hops


100

Vmax=30m/sR=250m

RPGM4RW

FW

h=2 h=4

h=4


Exponential Model for Path Duration (PD)

• Let path be the parameter for the exponential PD distribution: PD PDF f(x)= path e- path x

– As path increases average PD decreases (and vice versa)

• Intuitive qualitative analysis:– PD=f(V,h,R); V is relative velocity, h is path hops & R is radio range

– As V increases, average PD decreases, i.e., path increases

– As h increases, average PD decreases, i.e., path increases

– As R increases, average PD increases, i.e., path decreases


But, PD PDF f(x)= path e- path x

Exponential Model for PD


FWh=4

0

0.05

0.1

0 10 20 30 40 50

Path Duration (sec)

Prob

abili

ty

Exponential

PDRWh=2

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50

Path Duration (sec)

Pro

babi

lity

Exponential

PD

RGPM4h=4

- Correlation: 94.1-99.8%

Vmax=30m/s

R=250m

0

0.1

0.2

0.3

0.4

0.5

0 10 20

Path Duration (sec)

Prob

abili

ty

Exponential

PD FWh=4


0

0.1

0.20.3

0.4

0.5

0.6

0.70.8

0.9

1

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Cumulative Distribution Function (CDF)

Pro

ba

bil

ity

Exponential

PDD= 0.048

00.10.20.30.40.50.60.70.80.9

1

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54

Cumulative Distrbution Function (CDF)

Pro

ba

bil

ity

Exponential

PDD= 0.0477

0

0.1

0.20.3

0.4

0.5

0.6

0.70.8

0.9

1

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

Cumulative Distribution Function (CDF)

Pro

ba

bil

ity

Exponential

PD

D= 0.093

Vmax=30m/s

R=250m - Goodness-of-fit Test

RGPM4h=4

FWh=4

RWh=2

K-S testRW 0.04-0.065FW 0.045-0.085RPGM 0.09-0.12


Effect of Path Duration (PD) on Performance (in-progress): Case Study for DSR

• PD observed to have significant effect on performance• (I) Throughput: First order model

– T: simulation time, D: data transferred, Tflow: data transfer time, Trepair: total path repair time, trepair: av. path repair time, f: path break frequency

T

DThroughput

TPD

tTTftTTTT repairflowrepairflowrepairflow .1

... )1(

PD

t

TT

repair

flow

)1

(PD

Throughput

ratePD

t

T

D

PD

tThroughput repair

flow

repair ).1()1(


• (II) Overhead: First order model– Number of DSR route requests=– p: non-propagating cache hit ratio, N: number of nodes

• Evaluation through NS-2 simulations for DSR

– RPGM exhibits low , due to relatively low path changes/route requests

Effect of PD on Performance (contd.)

PD

T

PDOverhead

1

Random Waypoint (RW) Freeway (FW) Manhattan (MH)Throughput -0.9165 -0.9597 -0.9132Overhead 0.9753 0.9812 0.9978

Pearson coefficient of correlation () with PD

1


Conclusions• Detailed statistical analysis of link and path duration for

multiple mobility models (RW,FW,MH,RPGM4):– Link Duration: multi-modal FW and RPGM4 at low speeds– Path Duration PDF:

• Multi-modal FW and RPGM4 at low speeds and hop count• Exponential-like at high speeds & med/high hop count for all models

• Developed parametrized exponential model for PD PDF, as function of relative velocity V, hop count h and radio range R

• Proposed simple analytical models for throughput & overhead that show strong correlation with reciprocal of average PD


Future Work

• Apply path duration analysis to various ad hoc protocols• Attempt to explain: Why does path duration distribution

become exponential?• Analyze convergence time and cache performance to

account for varying performance between different protocols. Use it to extend first order models.

• Analysis of effects of mobility on protocol mechanisms• Extend and release the IMPORTANT mobility tool:

– URL: http://nile.usc.edu/important


Backup/Extra Slides


Rel vel. (V) prop to max vel (Vmax)


D: total data transferred during simulationT: simulation timeTflow: data transfer timeTrepair: total time spent in repairing paths trepair: time to repair path each timePD: average path durationf: frequency of path breakage,r: is constant data rate=D/Tflow

N: number of of nodes


• Number of path repairs=T/(PD+trepair)

ratetPD

PD

T

D

tPD

tThroughput

repairflowrepair

repair ).()1(


• Expression for cache hit ratio (Hit): [FW model]

Hit=


Non-propagating Cache Hit Ratio in DSR (independent of velocity!)

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