An

Evaluation

of

Availability

Latency

in

Carrier-based

Vehicular

ad-hoc

Networks

Shahram

Ghandeharizadeh

Dept

of

Computer

Science

Univ

of

Southern

California

Los

Angeles,

CA

USA

shahram@usc.edu

Shyam

Kapadia

Dept

of

Computer

Science

Univ

of

Southern

California

Los

Angeles,

CA

USA

kapadia@usc.edu

Bhaskar

Krishnamachari

Dept

of

Computer

Science

Dept

of

Electrical

Engineering

Univ

of

Southern

California

Los

Angeles,

CA

USA

bkrishna@usc.edu

ABSTRACT

On-demand

delivery

of

audio

and

video

clips

in

peer-to-peer

vehicular

ad-hoc

networks

is

an

emerging

area

of

research.

Our

target

environment

uses

data

carriers,

termed

zebroids,

where

a

mobile

device

carries

a

data

item

on

behalf

of

a

server

to

a

client

thereby

minimizing

its

availability

latency.

In

this

study,

we

quantify

the

variation

in

availability

latency

with

zebroids

as

a

function

of

a

rich

set

of

parameters

such

as

car

density,

storage

per

device,

repository

size,

and

replacement

policies

employed

by

zebroids.

Using

analysis

and

extensive

simulations,

we

gain

novel

insights

into

the

design

of

carrier-based

systems.

Significant

improvements

in

latency

can

be

obtained

with

zebroids

at

the

cost

of

a

minimal

overhead.

These

improvements

occur

even

in

scenarios

with

lower

accuracy

in

the

predictions

of

the

car

routes.

Two

particularly

surprising

findings

are:

a

naive

random

replacement

policy

employed

by

the

zebroids

shows

competitive

performance,

and

latency

improvements

obtained

with

a

simplified

instantiation

of

zebroids

are

found

to

be

robust

to

changes

in

the

popularity

distribution

of

the

data

items.

Categories

and

Subject

Descriptors:

[Distributed

Systems]:

Client/Server

General

Terms:

Algorithms,

Performance,

Design,

Experimentation.

INTRODUCTION

Technological

advances

in

areas

of

storage

and

wireless

communications

have

now

made

it

feasible

to

envision

on-demand

delivery

of

data

items,

for

e.g.,

video

and

audio

clips,

in

vehicular

peer-topeer

networks.

In

prior

work,

Ghandeharizadeh

et

al.

introduce

the

concept

of

vehicles

equipped

with

a

Car-to-Car-Peer-toPeer

device,

termed

AutoMata,

for

in-vehicle

entertainment.

The

notable

features

of

an

AutoMata

include

a

mass

storage

device

offering

hundreds

of

gigabytes

(GB)

of

storage,

a

fast

processor,

and

several

types

of

networking

cards.

Even

with

today"s

GB

disk

drives,

a

repository

of

diverse

entertainment

content

may

exceed

the

storage

capacity

of

a

single

AutoMata.

Such

repositories

constitute

the

focus

of

this

study.

To

exchange

data,

we

assume

each

AutoMata

is

configured

with

two

types

of

networking

cards:

a

low-bandwidth

networking

card

with

a

long

radio-range

in

the

order

of

miles

that

enables

an

AutoMata

device

to

communicate

with

a

nearby

cellular

or

WiMax

station,

a

high-bandwidth

networking

card

with

a

limited

radio-range

in

the

order

of

hundreds

of

feet.

The

high

bandwidth

connection

supports

data

rates

in

the

order

of

tens

to

hundreds

of

Megabits

per

second

and

represents

the

ad-hoc

peer

to

peer

network

between

the

vehicles.

This

is

labelled

as

the

data

plane

and

is

employed

to

exchange

data

items

between

devices.

The

low-bandwidth

connection

serves

as

the

control

plane,

enabling

AutoMata

devices

to

exchange

meta-data

with

one

or

more

centralized

servers.

This

connection

offers

bandwidths

in

the

order

of

tens

to

hundreds

of

Kilobits

per

second.

The

centralized

servers,

termed

dispatchers,

compute

schedules

of

data

delivery

along

the

data

plane

using

the

provided

meta-data.

These

schedules

are

transmitted

to

the

participating

vehicles

using

the

control

plane.

The

technical

feasibility

of

such

a

two-tier

architecture

is

presented

in

with

preliminary

results

to

demonstrate

the

bandwidth

of

the

control

plane

is

sufficient

for

exchange

of

control

information

needed

for

realizing

such

an

application.

In

a

typical

scenario,

an

AutoMata

device

presents

a

passenger

with

a

list

of

data

showing

both

the

name

of

each

data

item

and

its

availability

latency.

The

latter,

denoted

as

δ,

is

defined

as

the

earliest

time

at

which

the

client

encounters

a

copy

of

its

requested

data

item.

A

data

item

is

available

immediately

when

it

resides

in

the

local

storage

of

the

AutoMata

device

serving

the

request.

Due

to

storage

constraints,

an

AutoMata

may

not

store

the

entire

repository.

In

this

case,

availability

latency

is

the

time

from

when

the

user

issues

a

request

until

when

the

AutoMata

encounters

another

car

containing

the

referenced

data

item.

(The

terms

car

and

AutoMata

are

used

interchangeably

in

this

study.)

The

availability

latency

for

an

item

is

a

function

of

the

current

location

of

the

client,

its

destination

and

travel

path,

the

mobility

model

of

the

AutoMata

equipped

vehicles,

the

number

of

replicas

constructed

for

the

different

data

items,

and

the

placement

of

data

item

replicas

across

the

vehicles.

A

method

to

improve

the

availability

latency

is

to

employ

data

carriers

which

transport

a

replica

of

the

requested

data

item

from

a

server

car

containing

it

to

a

client

that

requested

it.

These

data

carriers

are

termed

‘zebroids".

Selection

of

zebroids

is

facilitated

by

the

two-tiered

architecture.

The

control

plane

enables

centralized

information

gathering

at

a

dispatcher

present

at

a

Some

examples

of

control

Without

loss

of

generality,

the

term

data

item

might

be

either

traditional

media

such

as

text

or

continuous

media

such

as

an

audio

or

video

clip.

There

may

be

dispatchers

deployed

at

a

subset

of

the

base-stations

for

fault-tolerance

and

robustness.

Dispatchers

between

basestations

may

communicate

via

the

wired

infrastructure.

formation

are

currently

active

requests,

travel

path

of

the

clients

and

their

destinations,

and

paths

of

the

other

cars.

For

each

client

request,

the

dispatcher

may

choose

a

set

of

z

carriers

that

collaborate

to

transfer

a

data

item

from

a

server

to

a

client

(z-relay

zebroids).

Here,

z

is

the

number

of

zebroids

such

that

z

N,

where

N

is

the

total

number

of

cars.

When

z

there

are

no

carriers,

requiring

a

server

to

deliver

the

data

item

directly

to

the

client.

Otherwise,

the

chosen

relay

team

of

z

zebroids

hand

over

the

data

item

transitively

to

one

another

to

arrive

at

the

client,

thereby

reducing

availability

latency

(see

Section

for

details).

To

increase

robustness,

the

dispatcher

may

employ

multiple

relay

teams

of

z-carriers

for

every

request.

This

may

be

useful

in

scenarios

where

the

dispatcher

has

lower

prediction

accuracy

in

the

information

about

the

routes

of

the

cars.

Finally,

storage

constraints

may

require

a

zebroid

to

evict

existing

data

items

from

its

local

storage

to

accommodate

the

client

requested

item.

In

this

study,

we

quantify

the

following

main

factors

that

affect

availability

latency

in

the

presence

of

zebroids:

(i)

data

item

repository

size,

(ii)

car

density,

(iii)

storage

capacity

per

car,

(iv)

client

trip

duration,

(v)

replacement

scheme

employed

by

the

zebroids,

and

(vi)

accuracy

of

the

car

route

predictions.

For

a

significant

subset

of

these

factors,

we

address

some

key

questions

pertaining

to

use

of

zebroids

both

via

analysis

and

extensive

simulations.

Our

main

findings

are

as

follows.

A

naive

random

replacement

policy

employed

by

the

zebroids

shows

competitive

performance

in

terms

of

availability

latency.

With

such

a

policy,

substantial

improvements

in

latency

can

be

obtained

with

zebroids

at

a

minimal

replacement

overhead.

In

more

practical

scenarios,

where

the

dispatcher

has

inaccurate

information

about

the

car

routes,

zebroids

continue

to

provide

latency

improvements.

A

surprising

result

is

that

changes

in

popularity

of

the

data

items

do

not

impact

the

latency

gains

obtained

with

a

simple

instantiation

of

z-relay

zebroids

called

one-instantaneous

zebroids

(see

Section

This

study

suggests

a

number

of

interesting

directions

to

be

pursued

to

gain

better

understanding

of

design

of

carrier-based

systems

that

improve

availability

latency.

Related

Work:

Replication

in

mobile

ad-hoc

networks

has

been

a

widely

studied

topic

However,

of

these

studies

employ

zebroids

as

data

carriers

to

reduce

the

latency

of

the

client"s

requests.

Several

novel

and

important

studies

such

as

ZebraNet

DakNet

Data

Mules

Message

Ferries

and

Seek

and

Focus

have

analyzed

factors

impacting

intermittently

connected

networks

consisting

of

data

carriers

similar

in

spirit

to

zebroids.

Factors

considered

by

each

study

are

dictated

by

their

assumed

environment

and

target

application.

A

novel

characteristic

of

our

study

is

the

impact

on

availability

latency

for

a

given

database

repository

of

items.

A

detailed

description

of

related

works

can

be

obtained

in

The

rest

of

this

paper

is

organized

as

follows.

Section

provides

an

overview

of

the

terminology

along

with

the

factors

that

impact

availability

latency

in

the

presence

of

zebroids.

Section

describes

how

the

zebroids

may

be

employed.

Section

provides

details

of

the

analysis

methodology

employed

to

capture

the

performance

with

zebroids.

Section

describes

the

details

of

the

simulation

environment

used

for

evaluation.

Section

enlists

the

key

questions

examined

in

this

study

and

answers

them

via

analysis

and

simulations.

Finally,

Section

presents

brief

conclusions

and

future

research

directions.

OVERVIEW

AND

TERMINOLOGY

Table

summarizes

the

notation

of

the

parameters

used

in

the

paper.

Below

we

introduce

some

terminology

used

in

the

paper.

Assume

a

network

of

N

AutoMata-equipped

cars,

each

with

storage

capacity

of

α

bytes.

The

total

storage

capacity

of

the

system

is

ST

=N

·α.

There

are

T

data

items

in

the

database,

each

with

Database

Parameters

T

Number

of

data

items.

Si

Size

of

data

item

i

fi

Frequency

of

access

to

data

item

i.

Replication

Parameters

Ri

Normalized

frequency

of

access

to

data

item

i

ri

Number

of

replicas

for

data

item

i

n

Characterizes

a

particular

replication

scheme.

δi

Average

availability

latency

of

data

item

i

δagg

Aggregate

availability

latency,

δagg

T

δj

fj

AutoMata

System

Parameters

G

Number

of

cells

in

the

map

N

Number

of

AutoMata

devices

in

the

system.

α

Storage

capacity

per

AutoMata.

γ

Trip

duration

of

the

client

AutoMata.

ST

Total

storage

capacity

of

the

AutoMata

system,

ST

N

α.

Table

Terms

and

their

definitions

size

Si.

The

frequency

of

access

to

data

item

i

is

denoted

as

fi,

with

T

fj

Let

the

trip

duration

of

the

client

AutoMata

under

consideration

be

γ.

We

now

define

the

normalized

frequency

of

access

to

the

data

item

i,

denoted

by

Ri,

as:

Ri

(fi)n

T

n

The

exponent

n

characterizes

a

particular

replication

technique.

A

square-root

replication

scheme

is

realized

when

n

This

serves

as

the

base-line

for

comparison

with

the

case

when

zebroids

are

deployed.

Ri

is

normalized

to

a

value

between

and

The

number

of

replicas

for

data

item

i,

denoted

as

ri,

is:

ri

min

(N,

max

Ri·N·α

Si

This

captures

the

case

when

at

least

one

copy

of

every

data

item

must

be

present

in

the

ad-hoc

network

at

all

times.

In

cases

where

a

data

item

may

be

lost

from

the

ad-hoc

network,

this

equation

becomes

ri

min

(N,

max

Ri·N·α

Si

In

this

case,

a

request

for

the

lost

data

item

may

need

to

be

satisfied

by

fetching

the

item

from

a

remote

server.

The

availability

latency

for

a

data

item

i,

denoted

as

δi,

is

defined

as

the

earliest

time

at

which

a

client

AutoMata

will

find

the

first

replica

of

the

item

accessible

to

it.

If

this

condition

is

not

satisfied,

then

we

set

δi

to

γ.

This

indicates

that

data

item

i

was

not

available

to

the

client

during

its

journey.

Note

that

since

there

is

at

least

one

replica

in

the

system

for

every

data

item

i,

by

setting

γ

to

a

large

value

we

ensure

that

the

client"s

request

for

any

data

item

i

will

be

satisfied.

However,

in

most

practical

circumstances

γ

may

not

be

so

large

as

to

find

every

data

item.

We

are

interested

in

the

availability

latency

observed

across

all

data

items.

Hence,

we

augment

the

average

availability

latency

for

every

data

item

i

with

its

fi

to

obtain

the

following

weighted

availability

latency

(δagg)

metric:

δagg

T

δi

fi

Next,

we

present

our

solution

approach

describing

how

zebroids

are

selected.

SOLUTION

APPROACH

Zebroids

When

a

client

references

a

data

item

missing

from

its

local

storage,

the

dispatcher

identifies

all

cars

with

a

copy

of

the

data

item

as

servers.

Next,

the

dispatcher

obtains

the

future

routes

of

all

cars

for

a

finite

time

duration

equivalent

to

the

maximum

time

the

client

is

willing

to

wait

for

its

request

to

be

serviced.

Using

this

information,

the

dispatcher

schedules

the

quickest

delivery

path

from

any

of

the

servers

to

the

client

using

any

other

cars

as

intermediate

carriers.

Hence,

it

determines

the

optimal

set

of

forwarding

decisions

that

will

enable

the

data

item

to

be

delivered

to

the

client

in

the

minimum

amount

of

time.

Note

that

the

latency

along

the

quickest

delivery

path

that

employs

a

relay

team

of

z

zebroids

is

similar

to

that

obtained

with

epidemic

routing

under

the

assumptions

of

infinite

storage

and

no

interference.

A

simple

instantiation

of

z-relay

zebroids

occurs

when

z

and

the

client"s

request

triggers

a

transfer

of

a

copy

of

the

requested

data

item

from

a

server

to

a

zebroid

in

its

vicinity.

Such

a

zebroid

is

termed

one-instantaneous

zebroid.

In

some

cases,

the

dispatcher

might

have

inaccurate

information

about

the

routes

of

the

cars.

Hence,

a

zebroid

scheduled

on

the

basis

of

this

inaccurate

information

may

not

rendezvous

with

its

target

client.

To

minimize

the

likelihood

of

such

scenarios,

the

dispatcher

may

schedule

multiple

zebroids.

This

may

incur

additional

overhead

due

to

redundant

resource

utilization

to

obtain

the

same

latency

improvements.

The

time

required

to

transfer

a

data

item

from

a

server

to

a

zebroid

depends

on

its

size

and

the

available

link

bandwidth.

With

small

data

items,

it

is

reasonable

to

assume

that

this

transfer

time

is

small,

especially

in

the

presence

of

the

high

bandwidth

data

plane.

Large

data

items

may

be

divided

into

smaller

chunks

enabling

the

dispatcher

to

schedule

one

or

more

zebroids

to

deliver

each

chunk

to

a

client

in

a

timely

manner.

This

remains

a

future

research

direction.

Initially,

number

of

replicas

for

each

data

item

replicas

might

be

computed

using

Equation

This

scheme

computes

the

number

of

data

item

replicas

as

a

function

of

their

popularity.

It

is

static

because

number

of

replicas

in

the

system

do

not

change

and

no

replacements

are

performed.

Hence,

this

is

referred

to

as

the

‘nozebroids"

environment.

We

quantify

the

performance

of

the

various

replacement

policies

with

reference

to

this

base-line

that

does

not

employ

zebroids.

One

may

assume

a

cold

start

phase,

where

initially

only

one

or

few

copies

of

every

data

item

exist

in

the

system.

Many

storage

slots

of

the

cars

may

be

unoccupied.

When

the

cars

encounter

one

another

they

construct

new

replicas

of

some

selected

data

items

to

occupy

the

empty

slots.

The

selection

procedure

may

be

to

choose

the

data

items

uniformly

at

random.

New

replicas

are

created

as

long

as

a

car

has

a

certain

threshold

of

its

storage

unoccupied.

Eventually,

majority

of

the

storage

capacity

of

a

car

will

be

exhausted.

Carrier-based

Replacement

policies

The

replacement

policies

considered

in

this

paper

are

reactive

since

a

replacement

occurs

only

in

response

to

a

request

issued

for

a

certain

data

item.

When

the

local

storage

of

a

zebroid

is

completely

occupied,

it

needs

to

replace

one

of

its

existing

items

to

carry

the

client

requested

data

item.

For

this

purpose,

the

zebroid

must

select

an

appropriate

candidate

for

eviction.

This

decision

process

is

analogous

to

that

encountered

in

operating

system

paging

where

the

goal

is

to

maximize

the

cache

hit

ratio

to

prevent

disk

access

delay

The

carrier-based

replacement

policies

employed

in

our

study

are

Least

Recently

Used

(LRU),

Least

Frequently

Used

(LFU)

and

Random

(where

a

eviction

candidate

is

chosen

uniformly

at

random).

We

have

considered

local

and

global

variants

of

the

LRU/LFU

policies

which

determine

whether

local

or

global

knowledge

of

contents

of

the

cars

known

at

the

dispatcher

is

used

for

the

eviction

decision

at

a

zebroid

(see

for

more

details).

The

replacement

policies

incur

the

following

overheads.

First,

the

complexity

associated

with

the

implementation

of

a

policy.

Second,

the

bandwidth

used

to

transfer

a

copy

of

a

data

item

from

a

server

to

the

zebroid.

Third,

the

average

number

of

replacements

incurred

by

the

zebroids.

Note

that

in

the

no-zebroids

case

neither

overhead

is

incurred.

The

metrics

considered

in

this

study

are

aggregate

availability

latency,

δagg,

percentage

improvement

in

δagg

with

zebroids

as

compared

to

the

no-zebroids

case

and

average

number

of

replacements

incurred

per

client

request

which

is

an

indicator

of

the

overhead

incurred

by

zebroids.

Note

that

the

dispatchers

with

the

help

of

the

control

plane

may

ensure

that

no

data

item

is

lost

from

the

system.

In

other

words,

at

least

one

replica

of

every

data

item

is

maintained

in

the

ad-hoc

network

at

all

times.

In

such

cases,

even

though

a

car

may

meet

a

requesting

client

earlier

than

other

servers,

if

its

local

storage

contains

data

items

with

only

a

single

copy

in

the

system,

then

such

a

car

is

not

chosen

as

a

zebroid.

ANALYSIS

METHODOLOGY

Here,

we

present

the

analytical

evaluation

methodology

and

some

approximations

as

closed-form

equations

that

capture

the

improvements

in

availability

latency

that

can

be

obtained

with

both

oneinstantaneous

and

z-relay

zebroids.

First,

we

present

some

preliminaries

of

our

analysis

methodology.

Let

N

be

the

number

of

cars

in

the

network

performing

a

random

walk

on

a

G×

G

torus.

An

additional

car

serves

as

a

client

yielding

a

total

of

N

cars.

Such

a

mobility

model

has

been

used

widely

in

the

literature

chiefly

because

it

is

amenable

to

analysis

and

provides

a

baseline

against

which

performance

of

other

mobility

models

can

be

compared.

Moreover,

this

class

of

Markovian

mobility

models

has

been

used

to

model

the

movements

of

vehicles

We

assume

that

all

cars

start

from

the

stationary

distribution

and

perform

independent

random

walks.

Although

for

sparse

density

scenarios,

the

independence

assumption

does

hold,

it

is

no

longer

valid

when

N

approaches

G.

Let

the

size

of

data

item

repository

of

interest

be

T.

Also,

data

item

i

has

ri

replicas.

This

implies

ri

cars,

identified

as

servers,

have

a

copy

of

this

data

item

when

the

client

requests

item

i.

All

analysis

results

presented

in

this

section

are

obtained

assuming

that

the

client

is

willing

to

wait

as

long

as

it

takes

for

its

request

to

be

satisfied

(unbounded

trip

duration

γ

With

the

random

walk

mobility

model

on

a

there

is

a

guarantee

that

as

long

as

there

is

at

least

one

replica

of

the

requested

data

item

in

the

network,

the

client

will

eventually

encounter

this

replica

Extensions

to

the

analysis

that

also

consider

finite

trip

durations

can

be

obtained

in

Consider

a

scenario

where

no

zebroids

are

employed.

In

this

case,

the

expected

availability

latency

for

the

data

item

is

the

expected

meeting

time

of

the

random

walk

undertaken

by

the

client

with

any

of

the

random

walks

performed

by

the

servers.

Aldous

et

al.

show

that

the

the

meeting

time

of

two

random

walks

in

such

a

setting

can

be

modelled

as

an

exponential

distribution

with

the

mean

C

c

G

log

G,

where

the

constant

c

for

G

The

meeting

time,

or

equivalently

the

availability

latency

δi,

for

the

client

requesting

data

item

i

is

the

time

till

it

encounters

any

of

these

ri

replicas

for

the

first

time.

This

is

also

an

exponential

distribution

with

the

following

expected

value

(note

that

this

formulation

is

valid

only

for

sparse

cases

when

G

ri):

δi

cGlogG

ri

The

aggregate

availability

latency

without

employing

zebroids

is

then

this

expression

averaged

over

all

data

items,

weighted

by

their

frequency

of

access:

δagg(no

zeb)

T

fi

c

G

log

G

ri

T

fi

C

ri

One-instantaneous

zebroids

Recall

that

with

one-instantaneous

zebroids,

for

a

given

request,

a

new

replica

is

created

on

a

car

in

the

vicinity

of

the

server,

provided

this

car

meets

the

client

earlier

than

any

of

the

ri

servers.

Moreover,

this

replica

is

spawned

at

the

time

step

when

the

client

issues

the

request.

Let

Nc

i

be

the

expected

total

number

of

nodes

that

are

in

the

same

cell

as

any

of

the

ri

servers.

Then,

we

have

Nc

i

(N

ri)

G

)ri

In

the

analytical

model,

we

assume

that

Nc

i

new

replicas

are

created,

so

that

the

total

number

of

replicas

is

increased

to

ri

+Nc

i

The

availability

latency

is

reduced

since

the

client

is

more

likely

to

meet

a

replica

earlier.

The

aggregated

expected

availability

latency

in

the

case

of

one-instantaneous

zebroids

is

then

given

by,

δagg(zeb)

T

fi

c

G

log

G

ri

Nc

i

T

fi

C

ri

Nc

i

Note

that

in

obtaining

this

expression,

for

ease

of

analysis,

we

have

assumed

that

the

new

replicas

start

from

random

locations

in

the

torus

(not

necessarily

from

the

same

cell

as

the

original

ri

servers).

It

thus

treats

all

the

Nc

i

carriers

independently,

just

like

the

ri

original

servers.

As

we

shall

show

below

by

comparison

with

simulations,

this

approximation

provides

an

upper-bound

on

the

improvements

that

can

be

obtained

because

it

results

in

a

lower

expected

latency

at

the

client.

It

should

be

noted

that

the

procedure

listed

above

will

yield

a

similar

latency

to

that

employed

by

a

dispatcher

employing

oneinstantaneous

zebroids

(see

Section

Since

the

dispatcher

is

aware

of

all

future

car

movements

it

would

only

transfer

the

requested

data

item

on

a

single

zebroid,

if

it

determines

that

the

zebroid

will

meet

the

client

earlier

than

any

other

server.

This

selected

zebroid

is

included

in

the

Nc

i

new

replicas.

z-relay

zebroids

To

calculate

the

expected

availability

latency

with

z-relay

zebroids,

we

use

a

coloring

problem

analog

similar

to

an

approach

used

by

Spyropoulos

et

al.

Details

of

the

procedure

to

obtain

a

closed-form

expression

are

given

in

The

aggregate

availability

latency

(δagg)

with

z-relay

zebroids

is

given

by,

δagg(zeb)

T

[fi

C

N

N

ri

(N

log

N

ri

log

(N

ri))]

SIMULATION

METHODOLOGY

The

simulation

environment

considered

in

this

study

comprises

of

vehicles

such

as

cars

that

carry

a

fraction

of

the

data

item

repository.

A

prediction

accuracy

parameter

inherently

provides

a

certain

probabilistic

guarantee

on

the

confidence

of

the

car

route

predictions

known

at

the

dispatcher.

A

value

of

implies

that

the

exact

routes

of

all

cars

are

known

at

all

times.

A

value

for

this

parameter

indicates

that

the

routes

predicted

for

the

cars

will

match

the

actual

ones

with

probability

Note

that

this

probability

is

spread

across

the

car

routes

for

the

entire

trip

duration.

We

now

provide

the

preliminaries

of

the

simulation

study

and

then

describe

the

parameter

settings

used

in

our

experiments.

Similar

to

the

analysis

methodology,

the

map

used

is

a

torus.

A

Markov

mobility

model

representing

a

unbiased

random

walk

on

the

surface

of

the

torus

describes

the

movement

of

the

cars

across

this

torus.

Each

grid/cell

is

a

unique

state

of

this

Markov

chain.

In

each

time

slot,

every

car

makes

a

transition

from

a

cell

to

any

of

its

neighboring

cells.

The

transition

is

a

function

of

the

current

location

of

the

car

and

a

probability

transition

matrix

Q

[qij]

where

qij

is

the

probability

of

transition

from

state

i

to

state

j.

Only

AutoMata

equipped

cars

within

the

same

cell

may

communicate

with

each

other.

The

parameters

γ,

δ

have

been

discretized

and

expressed

in

terms

of

the

number

of

time

slots.

An

AutoMata

device

does

not

maintain

more

than

one

replica

of

a

data

item.

This

is

because

additional

replicas

occupy

storage

without

providing

benefits.

Either

one-instantaneous

or

z-relay

zebroids

may

be

employed

per

client

request

for

latency

improvement.

Unless

otherwise

mentioned,

the

prediction

accuracy

parameter

is

assumed

to

be

This

is

because

this

study

aims

to

quantify

the

effect

of

a

large

number

of

parameters

individually

on

availability

latency.

Here,

we

set

the

size

of

every

data

item,

Si,

to

be

α

represents

the

number

of

storage

slots

per

AutoMata.

Each

storage

slot

stores

one

data

item.

γ

represents

the

duration

of

the

client"s

journey

in

terms

of

the

number

of

time

slots.

Hence

the

possible

values

of

availability

latency

are

between

and

γ.

δ

is

defined

as

the

number

of

time

slots

after

which

a

client

AutoMata

device

will

encounter

a

replica

of

the

data

item

for

the

first

time.

If

a

replica

for

the

data

item

requested

was

encountered

by

the

client

in

the

first

cell

then

we

set

δ

If

δ

γ

then

we

set

δ

γ

indicating

that

no

copy

of

the

requested

data

item

was

encountered

by

the

client

during

its

entire

journey.

In

all

our

simulations,

for

illustration

we

consider

a

with

γ

set

to

Our

experiments

indicate

that

the

trends

in

the

results

scale

to

maps

of

larger

size.

We

simulated

a

skewed

distribution

of

access

to

the

T

data

items

that

obeys

Zipf"s

law

with

a

mean

of

This

distribution

is

shown

to

correspond

to

sale

of

movie

theater

tickets

in

the

United

States

We

employ

a

replication

scheme

that

allocates

replicas

for

a

data

item

as

a

function

of

the

square-root

of

the

frequency

of

access

of

that

item.

The

square-root

replication

scheme

is

shown

to

have

competitive

latency

performance

over

a

large

parameter

space

The

data

item

replicas

are

distributed

uniformly

across

the

AutoMata

devices.

This

serves

as

the

base-line

no-zebroids

case.

The

square-root

scheme

also

provides

the

initial

replica

distribution

when

zebroids

are

employed.

Note

that

the

replacements

performed

by

the

zebroids

will

cause

changes

to

the

data

item

replica

distribution.

Requests

generated

as

per

the

Zipf

distribution

are

issued

one

at

a

time.

The

client

car

that

issues

the

request

is

chosen

in

a

round-robin

manner.

After

a

maximum

period

of

γ,

the

latency

encountered

by

this

request

is

recorded.

In

all

the

simulation

results,

each

point

is

an

average

of

requests.

Moreover,

the

confidence

intervals

determined

for

the

results

are

quite

tight

for

the

metrics

of

latency

and

replacement

overhead.

Hence,

we

only

present

them

for

the

metric

that

captures

the

percentage

improvement

in

latency

with

respect

to

the

no-zebroids

case.

RESULTS

In

this

section,

we

describe

our

evaluation

results

where

the

following

key

questions

are

addressed.

With

a

wide

choice

of

replacement

schemes

available

for

a

zebroid,

what

is

their

effect

on

availability

latency?

A

more

central

question

is:

Do

zebroids

provide

Number

of

cars

Aggregate

availability

latency

(δ

agg

random

Figure

Figure

shows

the

availability

latency

when

employing

one-instantaneous

zebroids

as

a

function

of

(N,α)

values,

when

the

total

storage

in

the

system

is

kept

fixed,

ST

significant

improvements

in

availability

latency?

What

is

the

associated

overhead

incurred

in

employing

these

zebroids?

What

happens

to

these

improvements

in

scenarios

where

a

dispatcher

may

have

imperfect

information

about

the

car

routes?

What

inherent

trade-offs

exist

between

car

density

and

storage

per

car

with

regards

to

their

combined

as

well

as

individual

effect

on

availability

latency

in

the

presence

of

zebroids?

We

present

both

simple

analysis

and

detailed

simulations

to

provide

answers

to

these

questions

as

well

as

gain

insights

into

design

of

carrier-based

systems.

How

does

a

replacement

scheme

employed

by

a

zebroid

impact

availability

latency?

For

illustration,

we

present

‘scale-up"

experiments

where

oneinstantaneous

zebroids

are

employed

(see

Figure

By

scale-up,

we

mean

that

α

and

N

are

changed

proportionally

to

keep

the

total

system

storage,

ST

constant.

Here,

T

and

ST

We

choose

the

following

values

of

(N,α)

The

figure

indicates

that

a

random

replacement

scheme

shows

competitive

performance.

This

is

because

of

several

reasons.

Recall

that

the

initial

replica

distribution

is

set

as

per

the

squareroot

replication

scheme.

The

random

replacement

scheme

does

not

alter

this

distribution

since

it

makes

replacements

blind

to

the

popularity

of

a

data

item.

However,

the

replacements

cause

dynamic

data

re-organization

so

as

to

better

serve

the

currently

active

request.

Moreover,

the

mobility

pattern

of

the

cars

is

random,

hence,

the

locations

from

which

the

requests

are

issued

by

clients

are

also

random

and

not

known

a

priori

at

the

dispatcher.

These

findings

are

significant

because

a

random

replacement

policy

can

be

implemented

in

a

simple

decentralized

manner.

The

lru-global

and

lfu-global

schemes

provide

a

latency

performance

that

is

worse

than

random.

This

is

because

these

policies

rapidly

develop

a

preference

for

the

more

popular

data

items

thereby

creating

a

larger

number

of

replicas

for

them.

During

eviction,

the

more

popular

data

items

are

almost

never

selected

as

a

replacement

candidate.

Consequently,

there

are

fewer

replicas

for

the

less

popular

items.

Hence,

the

initial

distribution

of

the

data

item

replicas

changes

from

square-root

to

that

resembling

linear

replication.

The

higher

number

of

replicas

for

the

popular

data

items

provide

marginal

additional

benefits,

while

the

lower

number

of

replicas

for

the

other

data

items

hurts

the

latency

performance

of

these

global

policies.

The

lfu-local

and

lru-local

schemes

have

similar

performance

to

random

since

they

do

not

have

enough

history

of

local

data

item

requests.

We

speculate

that

the

performance

of

these

local

policies

will

approach

that

of

their

global

variants

for

a

large

enough

history

of

data

item

requests.

On

account

of

the

competitive

performance

shown

by

a

random

policy,

for

the

remainder

of

the

paper,

we

present

the

performance

of

zebroids

that

employ

a

random

replacement

policy.

Do

zebroids

provide

significant

improvements

in

availability

latency?

We

find

that

in

many

scenarios

employing

zebroids

provides

substantial

improvements

in

availability

latency.

Analysis

We

first

consider

the

case

of

one-instantaneous

zebroids.

Figure

shows

the

variation

in

δagg

as

a

function

of

N

for

T

and

α

with

a

torus

using

Equation

Both

the

x

and

y

axes

are

drawn

to

a

log-scale.

Figure

show

the

improvement

in

δagg

obtained

with

one-instantaneous

zebroids.

In

this

case,

only

the

x-axis

is

drawn

to

a

log-scale.

For

illustration,

we

assume

that

the

T

data

items

are

requested

uniformly.

Initially,

when

the

network

is

sparse

the

analytical

approximation

for

improvements

in

latency

with

zebroids,

obtained

from

Equations

and

closely

matches

the

simulation

results.

However,

as

N

increases,

the

sparseness

assumption

for

which

the

analysis

is

valid,

namely

N

G,

is

no

longer

true.

Hence,

the

two

curves

rapidly

diverge.

The

point

at

which

the

two

curves

move

away

from

each

other

corresponds

to

a

value

of

δagg

Moreover,

as

mentioned

earlier,

the

analysis

provides

an

upper

bound

on

the

latency

improvements,

as

it

treats

the

newly

created

replicas

given

by

Nc

i

independently.

However,

these

Nc

i

replicas

start

from

the

same

cell

as

one

of

the

server

replicas

ri.

Finally,

the

analysis

captures

a

oneshot

scenario

where

given

an

initial

data

item

replica

distribution,

the

availability

latency

is

computed.

The

new

replicas

created

do

not

affect

future

requests

from

the

client.

On

account

of

space

limitations,

here,

we

summarize

the

observations

in

the

case

when

z-relay

zebroids

are

employed.

The

interested

reader

can

obtain

further

details

in

Similar

observations,

like

the

one-instantaneous

zebroid

case,

apply

since

the

simulation

and

analysis

curves

again

start

diverging

when

the

analysis

assumptions

are

no

longer

valid.

However,

the

key

observation

here

is

that

the

latency

improvement

with

z-relay

zebroids

is

significantly

better

than

the

one-instantaneous

zebroids

case,

especially

for

lower

storage

scenarios.

This

is

because

in

sparse

scenarios,

the

transitive

hand-offs

between

the

zebroids

creates

higher

number

of

replicas

for

the

requested

data

item,

yielding

lower

availability

latency.

Moreover,

it

is

also

seen

that

the

simulation

validation

curve

for

the

improvements

in

δagg

with

z-relay

zebroids

approaches

that

of

the

one-instantaneous

zebroid

case

for

higher

storage

(higher

N

values).

This

is

because

one-instantaneous

zebroids

are

a

special

case

of

z-relay

zebroids.

Simulation

We

conduct

simulations

to

examine

the

entire

storage

spectrum

obtained

by

changing

car

density

N

or

storage

per

car

α

to

also

capture

scenarios

where

the

sparseness

assumptions

for

which

the

analysis

is

valid

do

not

hold.

We

separate

the

effect

of

N

and

α

by

capturing

the

variation

of

N

while

keeping

α

constant

(case

and

vice-versa

(case

both

with

z-relay

and

one-instantaneous

zebroids.

Here,

we

set

the

repository

size

as

T

Figure

captures

case

mentioned

above.

Similar

trends

are

observed

with

case

a

complete

description

of

those

results

are

available

in

With

Figure

keeping

α

constant,

initially

increasing

car

density

has

higher

latency

benefits

because

increasing

N

introduces

more

zebroids

in

the

system.

As

N

is

further

increased,

ω

reduces

because

the

total

storage

in

the

system

goes

up.

Consequently,

the

number

of

replicas

per

data

item

goes

up

thereby

increasing

the

number

of

servers.

Hence,

the

replacement

policy

cannot

find

a

zebroid

as

often

to

transport

the

requested

data

item

to

the

client

earlier

than

any

of

the

servers.

On

the

other

hand,

the

increased

number

of

servers

benefits

the

no-zebroids

case

in

bringing

δagg

down.

The

net

effect

results

in

reduction

in

ω

for

larger

values

of

N.

−1

Number

of

cars

no−zebroidsanal

no−zebroids

sim

one−instantaneous

anal

one−instantaneoussim

Aggregate

Availability

latency

(δagg

δagg

Number

of

cars

Improvement

in

δagg

wrt

no−zebroids

(ω)

analytical

upper−bound

simulation

ω

Figure

Figure

shows

the

latency

performance

with

oneinstantaneous

zebroids

via

simulations

along

with

the

analytical

approximation

for

a

torus

with

T

The

trends

mentioned

above

are

similar

to

that

obtained

from

the

analysis.

However,

somewhat

counter-intuitively

with

relatively

higher

system

storage,

z-relay

zebroids

provide

slightly

lower

improvements

in

latency

as

compared

to

one-instantaneous

zebroids.

We

speculate

that

this

is

due

to

the

different

data

item

replica

distributions

enforced

by

them.

Note

that

replacements

performed

by

the

zebroids

cause

fluctuations

in

these

replica

distributions

which

may

effect

future

client

requests.

We

are

currently

exploring

suitable

choices

of

parameters

that

can

capture

these

changing

replica

distributions.

What

is

the

overhead

incurred

with

improvements

in

latency

with

zebroids?

We

find

that

the

improvements

in

latency

with

zebroids

are

obtained

at

a

minimal

replacement

overhead

per

client

request).

Analysis

With

one-instantaneous

zebroids,

for

each

client

request

a

maximum

of

one

zebroid

is

employed

for

latency

improvement.

Hence,

the

replacement

overhead

per

client

request

can

amount

to

a

maximum

of

one.

Recall

that

to

calculate

the

latency

with

one-instantaneous

Number

of

cars

Aggregate

availability

latency

(δagg

no−zebroids

one−instantaneous

z−relays

Number

of

cars

Improvement

in

δagg

wrt

no−zebroids

(ω)

one−instantaneous

z−relays

Figure

Figure

depicts

the

latency

performance

with

both

one-instantaneous

and

z-relay

zebroids

as

a

function

of

the

car

density

when

α

and

T

zebroids,

Nc

i

new

replicas

are

created

in

the

same

cell

as

the

servers.

Now

a

replacement

is

only

incurred

if

one

of

these

Nc

i

newly

created

replicas

meets

the

client

earlier

than

any

of

the

ri

servers.

Let

Xri

and

XNc

i

respectively

be

random

variables

that

capture

the

minimum

time

till

any

of

the

ri

and

Nc

i

replicas

meet

the

client.

Since

Xri

and

XNc

i

are

assumed

to

be

independent,

by

the

property

of

exponentially

distributed

random

variables

we

have,

Overhead/request

P(XNc

i

Xri

P(Xri

XNc

i

Overhead/request

ri

C

ri

C

Nc

i

C

ri

ri

Nc

i

Recall

that

the

number

of

replicas

for

data

item

i,

ri,

is

a

function

of

the

total

storage

in

the

system

i.e.,

ri

k·N

·α

where

k

satisfies

the

constraint

ri

N.

Using

this

along

with

Equation

we

get

Overhead/request

G

G

N

k

α)

Now

if

we

keep

the

total

system

storage

N

α

constant

since

G

and

T

are

also

constant,

increasing

N

increases

the

replacement

overhead.

However,

if

N

·α

is

constant

then

increasing

N

causes

α

Number

of

cars

one−instantaneous

zebroids

Average

number

of

replacements

per

request

Figure

Figure

captures

replacement

overhead

when

employing

one-instantaneous

zebroids

as

a

function

of

(N,α)

values,

when

the

total

storage

in

the

system

is

kept

fixed,

ST

to

go

down.

This

implies

that

a

higher

replacement

overhead

is

incurred

for

higher

N

and

lower

α

values.

Moreover,

when

ri

N,

this

means

that

every

car

has

a

replica

of

data

item

i.

Hence,

no

zebroids

are

employed

when

this

item

is

requested,

yielding

an

overhead/request

for

this

item

as

zero.

Next,

we

present

simulation

results

that

validate

our

analysis

hypothesis

for

the

overhead

associated

with

deployment

of

one-instantaneous

zebroids.

Simulation

Figure

shows

the

replacement

overhead

with

one-instantaneous

zebroids

when

(N,α)

are

varied

while

keeping

the

total

system

storage

constant.

The

trends

shown

by

the

simulation

are

in

agreement

with

those

predicted

by

the

analysis

above.

However,

the

total

system

storage

can

be

changed

either

by

varying

car

density

(N)

or

storage

per

car

(α).

On

account

of

similar

trends,

here

we

present

the

case

when

α

is

kept

constant

and

N

is

varied

(Figure

We

refer

the

reader

to

for

the

case

when

α

is

varied

and

N

is

held

constant.

We

present

an

intuitive

argument

for

the

behavior

of

the

perrequest

replacement

overhead

curves.

When

the

storage

is

extremely

scarce

so

that

only

one

replica

per

data

item

exists

in

the

AutoMata

network,

the

number

of

replacements

performed

by

the

zebroids

is

zero

since

any

replacement

will

cause

a

data

item

to

be

lost

from

the

system.

The

dispatcher

ensures

that

no

data

item

is

lost

from

the

system.

At

the

other

end

of

the

spectrum,

if

storage

becomes

so

abundant

that

α

T

then

the

entire

data

item

repository

can

be

replicated

on

every

car.

The

number

of

replacements

is

again

zero

since

each

request

can

be

satisfied

locally.

A

similar

scenario

occurs

if

N

is

increased

to

such

a

large

value

that

another

car

with

the

requested

data

item

is

always

available

in

the

vicinity

of

the

client.

However,

there

is

a

storage

spectrum

in

the

middle

where

replacements

by

the

scheduled

zebroids

result

in

improvements

in

δagg

(see

Figure

Moreover,

we

observe

that

for

sparse

storage

scenarios,

the

higher

improvements

with

z-relay

zebroids

are

obtained

at

the

cost

of

a

higher

replacement

overhead

when

compared

to

the

one-instantaneous

zebroids

case.

This

is

because

in

the

former

case,

each

of

these

z

zebroids

selected

along

the

lowest

latency

path

to

the

client

needs

to

perform

a

replacement.

However,

the

replacement

overhead

is

still

less

than

indicating

that

on

an

average

less

than

one

replacement

per

client

request

is

needed

even

when

z-relay

zebroids

are

employed.

Number

of

cars

z−relays

one−instantaneous

Average

number

of

replacements

per

request

Figure

Figure

shows

the

replacement

overhead

with

zebroids

for

the

cases

when

N

is

varied

keeping

α

Prediction

percentage

no−zebroids

one−instantaneous

z−relays

no−zebroids

one−instantaneous

z−relays

Aggregate

Availability

Latency

(δagg

Figure

Figure

shows

δagg

for

different

car

densities

as

a

function

of

the

prediction

accuracy

metric

with

α

and

T

What

happens

to

the

availability

latency

with

zebroids

in

scenarios

with

inaccuracies

in

the

car

route

predictions?

We

find

that

zebroids

continue

to

provide

improvements

in

availability

latency

even

with

lower

accuracy

in

the

car

route

predictions.

We

use

a

single

parameter

p

to

quantify

the

accuracy

of

the

car

route

predictions.

Analysis

Since

p

represents

the

probability

that

a

car

route

predicted

by

the

dispatcher

matches

the

actual

one,

hence,

the

latency

with

zebroids

can

be

approximated

by,

δerr

agg

p

δagg(zeb)

p)

δagg(no

zeb)

δerr

agg

p

δagg(zeb)

p)

C

ri

Expressions

for

δagg(zeb)

can

be

obtained

from

Equations

(one-instantaneous)

or

(z-relay

zebroids).

Simulation

Figure

shows

the

variation

in

δagg

as

a

function

of

this

route

prediction

accuracy

metric.

We

observe

a

smooth

reduction

in

the

improvement

in

δagg

as

the

prediction

accuracy

metric

reduces.

For

zebroids

that

are

scheduled

but

fail

to

rendezvous

with

the

client

due

to

the

prediction

error,

we

tag

any

such

replacements

made

by

the

zebroids

as

failed.

It

is

seen

that

failed

replacements

gradually

increase

as

the

prediction

accuracy

reduces.

Under

what

conditions

are

the

improvements

in

availability

latency

with

zebroids

maximized?

Surprisingly,

we

find

that

the

improvements

in

latency

obtained

with

one-instantaneous

zebroids

are

independent

of

the

input

distribution

of

the

popularity

of

the

data

items.

Analysis

The

fractional

difference

(labelled

ω)

in

the

latency

between

the

no-zebroids

and

one-instantaneous

zebroids

is

obtained

from

equations

and

as

ω

T

fi·C

ri

T

fi·C

G

)ri

T

fi·C

ri

Here

C

c·G·log

G.

This

captures

the

fractional

improvement

in

the

availability

latency

obtained

by

employing

one-instantaneous

zebroids.

Let

α

making

the

total

storage

in

the

system

ST

N.

Assuming

the

initial

replica

distribution

is

as

per

the

squareroot

replication

scheme,

we

have,

ri

fi·N

T

fj

Hence,

we

get

fi

i

where

K

T

fj.

Using

this,

along

with

the

approximation

x)n

n

x

for

small

x,

we

simplify

the

above

equation

to

get,

ω

T

ri

N−ri

G

T

ri

In

order

to

determine

when

the

gains

with

one-instantaneous

zebroids

are

maximized,

we

can

frame

an

optimization

problem

as

follows:

Maximize

ω,

subject

to

T

ri

ST

THEOREM

With

a

square-root

replication

scheme,

improvements

obtained

with

one-instantaneous

zebroids

are

independent

of

the

input

popularity

distribution

of

the

data

items.

(See

for

proof)

Simulation

We

perform

simulations

with

two

different

frequency

distribution

of

data

items:

Uniform

and

Zipfian

(with

mean=

Similar

latency

improvements

with

one-instantaneous

zebroids

are

obtained

in

both

cases.

This

result

has

important

implications.

In

cases

with

biased

popularity

toward

certain

data

items,

the

aggregate

improvements

in

latency

across

all

data

item

requests

still

remain

the

same.

Even

in

scenarios

where

the

frequency

of

access

to

the

data

items

changes

dynamically,

zebroids

will

continue

to

provide

similar

latency

improvements.

CONCLUSIONS

AND

FUTURE

RESEARCH

DIRECTIONS

In

this

study,

we

examined

the

improvements

in

latency

that

can

be

obtained

in

the

presence

of

carriers

that

deliver

a

data

item

from

a

server

to

a

client.

We

quantified

the

variation

in

availability

latency

as

a

function

of

a

rich

set

of

parameters

such

as

car

density,

storage

per

car,

title

database

size,

and

replacement

policies

employed

by

zebroids.

Below

we

summarize

some

key

future

research

directions

we

intend

to

pursue.

To

better

reflect

reality

we

would

like

to

validate

the

observations

obtained

from

this

study

with

some

real

world

simulation

traces

of

vehicular

movements

(for

example

using

CORSIM

This

will

also

serve

as

a

validation

for

the

utility

of

the

Markov

mobility

model

used

in

this

study.

We

are

currently

analyzing

the

performance

of

zebroids

on

a

real

world

data

set

comprising

of

an

ad-hoc

network

of

buses

moving

around

a

small

neighborhood

in

Amherst

Zebroids

may

also

be

used

for

delivery

of

data

items

that

carry

delay

sensitive

information

with

a

certain

expiry.

Extensions

to

zebroids

that

satisfy

such

application

requirements

presents

an

interesting

future

research

direction.

ACKNOWLEDGMENTS

This

research

was

supported

in

part

by

an

Annenberg

fellowship

and

NSF

grants

numbered

(NeTS

NOSS),

(CAREER),

and

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for

Content

Availabilty

in

Vehicular

ad-hoc

Networks.

In

VANET,

New

York,

NY,

USA,

ACM

Press.

S.

Ghandeharizadeh,

S.

Kapadia,

and

B.

Krishnamachari.

Comparison

of

Replication

Strategies

for

Content

Availability

in

networks.

In

MDM,

May

S.

Ghandeharizadeh,

S.

Kapadia,

and

B.

Krishnamachari.

An

Evaluation

of

Availability

Latency

in

Carrier-based

Vehicular

ad-hoc

Networks.

Technical

report,

Department

of

Computer

Science,

University

of

Southern

S.

Ghandeharizadeh

and

B.

Krishnamachari.

A

peer-to-peer

network

for

on-demand

automobile

information

services.

In

Globe.

IEEE,

T.

Hara.

Effective

Replica

Allocation

in

ad-hoc

Networks

for

Improving

Data

Accessibility.

In

IEEE

Infocom,

H.

Hayashi,

T.

Hara,

and

S.

Nishio.

A

Replica

Allocation

Method

Adapting

to

Topology

Changes

in

ad-hoc

Networks.

In

DEXA,

P.

Juang,

H.

Oki,

Y.

Wang,

M.

Martonosi,

L.

Peh,

and

D.

Rubenstein.

Energy-efficient

computing

for

wildlife

tracking:

design

tradeoffs

and

early

experiences

with

ZebraNet.

SIGARCH

Comput.

Archit.

News,

A.

Pentland,

R.

Fletcher,

and

A.

Hasson.

DakNet:

Rethinking

Connectivity

in

Developing

Nations.

Computer,

F.

Sailhan

and

V.

Issarny.

Cooperative

Caching

in

ad-hoc

Networks.

In

MDM,

R.

Shah,

S.

Roy,

S.

Jain,

and

W.

Brunette.

Data

mules:

Modeling

and

analysis

of

a

three-tier

architecture

for

sparse

sensor

networks.

Elsevier

ad-hoc

Networks

Journal,

September

T.

Spyropoulos,

K.

Psounis,

and

C.

Raghavendra.

Single-Copy

Routing

in

Intermittently

Connected

Mobile

Networks.

In

SECON,

April

A.

Tanenbaum.

Modern

Operating

Systems,

Edition,

Chapter

Section

Prentice

Hall,

A.

Vahdat

and

D.

Becker.

Epidemic

routing

for

partially-connected

ad-hoc

networks.

Technical

report,

Department

of

Computer

Science,

Duke

University,

W.

Zhao,

M.

Ammar,

and

E.

Zegura.

A

message

ferrying

approach

for

data

delivery

in

sparse

mobile

ad-hoc

networks.

In

MobiHoc,

pages

New

York,

NY,

USA,

ACM

Press.

M.

Zonoozi

and

P.

Dassanayake.

User

Mobility

Modeling

and

Characterization

of

Mobility

Pattern.

IEEE

Journal

on

Selected

Areas

in

Communications,

September

O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O B I B I I B I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O 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audio and video clip
peer-to-peer vehicular ad-hoc network
datum carrier
termed zebroid
naive random replacement policy
simplified instantiation of zebroid
zebroid simplified instantiation
vehicular network
automaton
markov model

mobile device
availability latency
car density
storage per device
repository size
replacement policy
zebroid
mobility
latency