Vehicular Connectivity Models

Simulation in Vehicular Ad-hoc NetworksMethodology

Simulation Results

Vehicular Connectivity ModelsFrom Single-Hop Links to Large-Scale Behavior

Rui Meireles Michel Ferreira João Barros{[email protected] [email protected] [email protected]}

Instituto de Telecomunicações & University of Porto, Portugal

June 23rd 2009

Rui Meireles, Michel Ferreira, João Barros Vehicular Connectivity Models


Simulation Results

Outline

1 Simulation in Vehicular Ad-hoc Networks

2 Methodology

3 Simulation Results



Simulation Results

Outline


2 Methodology




Simulation Results

VANETs: a Case For Simulation

Testbed challenges

Large number of nodes;

Hardware cost and availability;

Time and effort required.

Simulation allows

Faster development and testing of protocols and applications;

Large cost savings;

Larger scale possible.



Simulation Results

Project Context

Major concern of VANET simulations: accuracy

Of vehicle movement: mobility models;

Of communications: connectivity models.

Project goals

Characterize:

Large scale connectivity The impact of using different one-hop link models,

from unit-disks to shadow fading, assuming a perfect MAC.

Fundamental trade-offs Between link model computational complexity and

simulation accuracy.



Simulation Results

State of the Art in VANET Simulation

Popular simulators

TraNS Real map support, uses ns2 for communications.

GrooveSim Developed at CMU, supports augmented-reality simulations.

NCTUns User-drawn maps, radio obstacle support.

Divert [1] Developed by Prof. Luís Damas at DCC-FCUP. Real maps, photorealisticinterface, large scale simulation. No integrated communication.



Simulation Results

Outline


2 Methodology




Simulation Results

Connectivity Metrics

Node degree

Extended to a time interval because old information can still be useful:

d(ui)[0...t] = |⋃t

j=0 N (ui)j |

Transitive closure because communication through intermediate nodes is

also useful:

{ui ,uj , t ′} ∈L ′∗↔

{uj ∈N (ui)t ′

∃uk ∈U ,{ui ,uk , t ′} ∈L ′∧{uk ,uj , t ′′} ∈L ′∗∧ t ′′ < t ′

Connection duration

Measures connection stability: ∀c ∈ C[0...t],c(tdis)− c(tconn)



Simulation Results

Communication Models: Disk Models (distance based)

Unit disk

All nodes within distance d are

reachable with 100% probability:

All other nodes are unreachable.

0% Link Probability

Non-trivial Link Probability

100% Link Probability

P

0% Link Probability

100% Link Probability

Quasi-unit disk [4]

Nodes within distance d ′ < d are

reachable with 100% probability;

Nodes within distance d ′ ≤ x ≤ d

have non-trivial link probabilities;

All other nodes are unreachable.



Simulation Results

Communication Models: Shadow Fading [2]

Attenuation is the sum of two components

A β1 component proportional to the distance between the nodes;

A β2 probabilistic fading component following a (0,σ 2) normal

distribution.

Link probability

P(β (u,v)≤ βth|s(u,v)) =1

2− 1

2erf(

10α√2σ

logs(u,v)

10βth

α10dB mdB)

Parameters [3]

α — path loss exponent, usually between 1.8 and 4;

σ — noise standard deviation, usually between 4 and 8 dB;

βth — acceptable attenuation, usually above 90 dB.



Simulation Results

Link Probability: Disk-Based vs Shadow Fading

0 50 100 150

0.0

0.2

0.4

0.6

0.8

1.0

Distance (m)

Link

pro

babi

lity

150m unit disk75m unit diskQuasi−unit disk w/ linear fadingQuasi−unit disk w/ exponential fadingQuasi−unit disk w/ constant fading

Figure: Unit and quasi-unit disk models

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Distance (m)

Link

pro

babi

lity

α=1.9, σ=8dB, β=110dBα=2.9, σ=8dB, β=110dBα=1.9, σ=6dB, β=110dBα=1.9, σ=8dB, β=90dB

Figure: Shadow fading models



Simulation Results

Simulation Design

Overall design

Real map of Porto, 965 Km of roads;

300s simulations to study transient behavior;

≈ 500 wireless-equipped vehicles.

Link computation speedup

Naïve algorithm: O(n2), discretized map: O(n)

y

1.0 (4,4) (4,2)

x

Link probability Cell list

0.75 (3,3) (4,5) (5,3) (3,3)

... ... ... ... ...

... ...

Unit Disk Quasi-Unit Disk Shadow fadingr = 50m d = 50m, r = 150m, constant fading α = 1.9,σ = 8,βth = 110dBr = 100m d = 50m, r = 150m, linear fading α = 1.9,σ = 6,βth = 110dBr = 150m d = 50m, r = 150m, exponential fading α = 2.9,σ = 8,βth = 110dB

α = 1.9,σ = 8,βth = 90dB

Table: Fading models variations usedRui Meireles, Michel Ferreira, João Barros Vehicular Connectivity Models


Simulation Results

Outline


2 Methodology




Simulation Results

Cumulative Average Node Degree

0 50 100 150 200 250 300

510

1520

25

Time (s)

Ave

rage

nod

e de

gree

unit−disk (150m)unit−disk (50m)unit−disk (100m)exp−fad q−unit disk (50−150m)lin−fad q−unit disk (50−150m)const−fad q−unit disk (50−150m)


0 50 100 150 200 250 3000

510

1520

Time (s)A

vera

ge n

ode

degr

ee



Linear growth. Equivalences: 100m disk≈ α = 1.9,σ = 8,βth = 110dB,

50m disk≈ α = 2.9,σ = 8,βth = 110dB.Rui Meireles, Michel Ferreira, João Barros Vehicular Connectivity Models


Simulation Results

Cumulative Average Node Degree Transitive Closure

0 50 100 150 200 250 300

010

020

030

040

0

Time (s)

Ave

rage

nod

e de

gree



0 50 100 150 200 250 3000

100

200

300

400

Time (s)A

vera

ge n

ode

degr

ee



Transitive-closure increases node degree by an order of magnitude,

approaches saturation. Equivalences remain the same.



Simulation Results

Link Duration

0 5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

Connection duration (s)

Fre

quen

cy



0 5 10 15 200.

00.

10.

20.

30.

40.

5Connection duration (s)

Fre

quen

cy



Resembles an inverse exponential distribution. Unit-disk models allow for

longer connections.



Simulation Results

Conclusions

Node degree

a) Connectivity heavily affected by the choice of parameters;

b) An appropriate disk-based model can replace a shadow fading model.

Link duration

Unit-disk models allow for longer connections than either quasi-unit disks or

shadow fading: serious implications for topology-based routing protocols.



Simulation Results

References

DIVERT—Development of Inter-VEhicular Reliable Telematics, 2008.

http://divert.ncc.up.pt.

Christian Bettstetter and Christian Hartmann.

Connectivity of wireless multihop networks in a shadow fading environment.

Wirel. Netw., 11(5):571–579, 2005.

David Kotz, Calvin Newport, Robert S. Gray, Jason Liu, Yougu Yuan, and Chip Elliott.

Experimental evaluation of wireless simulation assumptions.

In MSWiM ’04: Proceedings of the 7th ACM international symposium on Modeling,analysis and simulation of wireless and mobile systems, pages 78–82, New York, NY,USA, 2004. ACM.

Fabian Kuhn and Aaron Zollinger.

Ad-hoc networks beyond unit disk graphs.

In DIALM-POMC ’03: Proceedings of the 2003 joint workshop on Foundations of mobilecomputing, pages 69–78, New York, NY, USA, 2003. ACM.


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Vehicular Connectivity Models