Scaling Properties of Delay Tolerant Networks with Correlated Motion Patterns Uichin Lee, Bell Labs/Alcatel-Lucent Soon Y. Oh, Mario Gerla (UCLA) Kang-Won

Scaling Properties of Delay Tolerant Networks with Correlated Motion Patterns

Uichin Lee, Bell Labs/Alcatel-Lucent

Soon Y. Oh, Mario Gerla (UCLA)Kang-Won Lee (IBM T.J. Watson Research)

2 | CHANTS’09 | Sept. 2009 Alcatel-Lucent

Key DTN Metric: Pair-wise Inter-contact Time

Key metric for measuring end-to-end delay

Pair-wise inter-contact time: interval between two contact points

Inter-contact distribution: Exponential : bounded delay, but not realistic? Power-law : may cause infinite delay, but more realistic?

T1T2 T3

Contact points between two nodes: i and j

Tic(n): pair-wise inter-contact time

time

Tic(1)

T1

Tic(2)

T2

Tic(3)

T3


Two-phase Inter-contact Time

Two-phase distribution: power-law head and exponential tail

Levy walk based mobility Lee et al. Infocom’08/09

Inte

r-con

tact

tim

e C

CD

FTime (min)

Power LawHead

ExponentialTail

Power LawHead

Inte

r-con

tact

tim

e C

CD

FIn

ter-

con

tact

tim

e C

CD

F

ExponentialTail

ExponentialTail

Karagiannis et al., MobiCom’07• Association times w/ AP (UCSD) or cell tower (MIT cell)• Direct contact traces: Infocom, cambridge (imotes), MIT-bt

Power LawHead

Log-log plot

Log-log plot

Time (days)

Time (days)

Log-log plot


Two-phase Inter-contact Time

Why two-phase distribution? One possible cause: Flight distance of each random trip (within a finite area) [Cai08] The shorter the flight distance, the higher the motion

correlation in local area, resulting heavier power-law head Power-law head while in local area vs. exponential tail for future

encounters

Examples of motion correlation: Manhattan sightseers: In Time Square, sightseers tend to bump

into each other; and then depart for other sights Levy flight of human walks [Rhee08]: short flights + occasional long

flights Vehicular mobility: constrained by road traffic (+traffic jam)

High correlation among vehicles in close proximity After leaving locality, vehicles meet like “ships in the night”

*Cai08: Han Cai and Do Young Eun, Toward Stochastic Anatomy of Inter-meeting Time Distribution under General Mobility Models, MobiHoc’08*Rhee08: Injong Rhee, Minsu Shin, Seongik Hong, Kyunghan Lee and Song Chong, On the Levy-walk Nature of Human Mobility, INFOCOM’08

Goal: understanding impacts of correlated motion patterns on throughput/delay/buffer

scaling properties

Frequent encounters in local area

Local area


DTN Model: Inter-contact rate + flight distance

Inter-contact rate: λ ~ speed (v)*radio range (r) [Groenevelt, Perf’05]

Random waypoint/direction (exp inter-contact time)

Flight distance (motion correlation):

Ranging from radio radius Ω(r) to network width O(1)

Invariance property: avg inter-contact time does not depend on the degree of correlation in the mobility patterns [Cai and Eun, Mobihoc’08]

1

1

flight distance = Θ(1)

Random directionRandom walk

1

1

flight distance = Θ(r)

radio range=Θ(r)radio range=Θ(r)

Varyingflight

distance


2-Hop Relay: DTN Routing

Each source has a random destination (n source-destination pairs)

2-hop relay protocol:

1. Source sends a packet to a relay node

2. Relay node delivers a packet to the corresponding receiver

2-hop Relay by Grossglauser and Tse

Source

Relay

Destination

Source to Relay

Relay to Dest


2-Hop Relay: Throughput Analysis

Intuition: avg throughput is determined by aggregate meeting rate (srcrelay and relay dest)

Two-hop relay per node throughput : Θ(nλ)

Aggregate meeting rate at a destination: nλ

Grossglauser and Tse’s results: Θ(nλ)=Θ(1) when λ = 1/n (i.e., speed 1/√n, radio range 1/√n)

Motion correlation (w/ flight len [O(r),O(1)]) still preserves meeting rate

Source to Relay Relay to Destination

Sou

rce

Des

tinat

ion

Food (=source)

Ants (=relays)


2-Hop Relay: Delay Analysis

Source to relay node (Dsr), and then relay to dest (Drd) Dsr = avg. inter-any-contact time to a random relay Drd = avg. residual inter-contact time (relay

dest) Mean residual inter-contact time (Drd) = E[T2] / 2E[T]

>> T is a random variable for inter-contact time

Random Direction (RD): E[T2] = O(1/λ2) Drd=O(1/λ)

Random Walk (RW): E[T2] = O(logn*1/λ2) Drd=O(logn/λ)

Average 2-Hop Delay: D(n) = [O(1/λ), O(logn/λ)]

As flight distance increases, average delay decreases monotonically

Inspection paradox (length bias): source tends to sample a longer inter-

contact interval between relay and dest nodes

Time

SrcRelay

Inter-contact history: RelayDest

Source

Relay

Destination

Source to Relay

Relay to Dest


2-Hop Relay: Buffer Requirement

Little’s law: buffer = (rate) x (delay)

Required buffer space per node: B = [Θ(n), Θ(nlogn)]

Rate*delay = Θ(nλ)* [1/λ, logn/λ] = [Θ(n), Θ(nlogn)] Recall: random direction (1/λ) and random walk (logn/λ)

Motion correlation requires more buffer space Correlation increases burstiness of relay traffic

Impact of limited buffer space on throughput Limited buffer of Θ(K) at each relay node is fairly shared by all

sources Relay node carries a packet to a certain dest with prob. K/B Throughput per source = Θ(nλ*K/B)

Delay: [Θ(1/λ), Θ(logn/λ)]

S1

S2 R

Θ(n) srcs

RelayS3

D1

D2

D3

Θ(n) dests

Rate: Θ(nλ)


Simulation: Throughput

Degree of correlation via average flight distance L L=250m high correlation power law head + exponential tail L=1000m low correlation almost exponential

Throughput is independent of the degree of correlations

Average throughput per node as a function of # nodes

Th

rou

gh

pu

t p

er

nod

e (

kb

ps)

5000m*5000m area

# of nodes <=100Radio range =

250m802.11 w/ 2Mbps

CCDF of inter-contact time (20m/s)

L=250m

log-linear

L=1000m

L=250m

Exp

Inte

r-con

tact

tim

e C

CD

F

Log-log


Simulation: Inter-any-contact Time

Inter-any(k)-contact time: inter-contact time to any of k nodes

Invariance property: avg inter-contact time is independent of correlation

Residual inter-contact time: source probes a random point of the inter-meeting times between relay and destination

Average Inter-contact time Average residual inter-contact time

20m/s

30m/s

20m/sL=250m

20m/sL=1000m

30m/sL=250m

30m/sL=1000m

Number of relay nodes (k) Number of relay nodes (k)


Simulation: Buffer Utilization

Burstiness of relay traffic increases with the degree of correlation

S S D D D S S D

N=3 N=2

Relay node’s contact historyTime

# consecutive encounters (N)

S Source

D DestinationN=2

Cumulative dist of # consecutive encounters

L=

25

0

L=

10

00

Number of consecutive encounters (N)

P(N

<=

X)


Conclusion

Impact of correlated motion patterns on DTN scaling properties

DTN model: inter-contact rate + motion correlation via flight distance

Flight distance of Ω(r); i.e., min travel distance ~ one’s radio range Considered mobility ranges from Random Walk to Random Direction

Main results:

Throughput is independent of motion correlation Delay monotonically increases with the degree of correlation Buffer requirement also increases with the degree of correlation Correlation increases burstiness of relay traffic

Future work:

Applying results to DTN multicast scenarios Scaling properties of inter-domain DTN scenarios

Documents

Scaling Properties of Delay Tolerant Networks with Correlated Motion Patterns Uichin Lee, Bell Labs/Alcatel-Lucent Soon Y. Oh, Mario Gerla (UCLA) Kang-Won