controlled mobility in sensor networks final defense 2009...

Ryo Sugihara

Department of Computer Science and Engineering

University of California, San Diego

Final defense

2009/06/05

Controlled M

obility in Senso

r Netw

ork

s

2

Senso

r netw

ork

applica

tions

•Majority are “data-collection”applications

–Moving data from sensor nodes to base station

3

Appro

ach

es fo

r data collection

•Direct transm

ission

–Each node directly

communicates with BS

–Difficult due to

•Lim

ited comm. range

•Large energy consumption

•Multihopforw

arding

–Spanning tree rooted at BS

–Forw

ard other nodes’data

–Issues

•Unbalanced energy

consumption

•Sparse/disconnected

netw

orks

Base station

Sensor nodes

Base station

Sensor nodes

4

Altern

ative appro

ach

for data collection

•“D

ata m

ule”approach

–Mobile node travels across the sensor field while

collecting data from sensor nodes

–Pros

•Low & balanced energy consumption at each node

•Applicable to sparse/disconnected netw

orks

–Cons

•Larger data delivery latency

–Latency from the tim

e of data

generation (@sensor) until the tim

e

it is delivered to the BS

–Strongly affected by

data m

ule’s m

ovement

Base station

Data m

ule

Sensor nodes

Optimizing DM’s m

otion is critical for im

proving data delivery latency

5

Optimizing Data M

ule’s m

otion is Difficu

lt

?

?

?

Path

?

Speed?

Sch

edule?

Forw

ard

ing?

Our solution:

Data Mule Scheduling (DMS) problem framework

-Problem too hard and complex

-Many variations in problem settings

6

Data M

ule Sch

eduling (DMS) pro

blem fra

mework

•Key idea: D

ivide into subproblems

–Forw

arding

•How each node forw

ards data to neighbors

–Path selection

•Which trajectory the data m

ule follows

–Speed control

•How the data m

ule changes the speed along the path

–Job scheduling

•From which sensor the data m

ule collects data at certain tim

e

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

)

Path

sele

ction

node A

node B

node C

Forw

ard

ing

Data m

ule

Communication range

7

Covera

ge of DMS pro

blem fra

mework

1-D

DMS:

"Pure

" Data M

ule Appro

ach

:

"Hybrid" Data M

ule Appro

ach

:Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

Path

sele

ction

node A

node B

node C

Forw

ard

ing

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

)

When the path is fixed/given

Use only data m

ule to collect data from sensor nodes

Combine data m

ule and m

ultihopforw

arding approaches

8

Outline of th

e talk

1-D DMS

23 4

1

Extended DMS

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

Path

sele

ction

node A

node B

node C

Forw

ard

ing

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

)

9

Outline of th

e talk

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

Path

sele

ction

node A

node B

node C

Forw

ard

ing

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

) 1-D DMS

23 4

1

Extended DMS

10

Outline: 1

-D DMS pro

blem

•Idea of DMS form

ulation

•Mobility m

odels

–Basic cases: Constant speed, Variable speed

–Generalized

•Basic cases

–Optimal algorithms

–Non-existence

of optimal algorithms

•Generalized m

obility m

odel

–NP-hardness

–Heuristic algorithm

–Lower bound analysis

–Polynomial tim

e approximation scheme

11

B

Idea of DMS form

ulation

•Assumptions

–Communication is possible only within the intervals

–Node location, communication range/tim

e are given

A

C

Data m

ule

Communication

range

Data m

ule's path

Loca

tion

A B CeB

eC

eA

Communication tim

eNode

12

Term

inology and definitions

Tim

e

A BeB

CeC

eA

Jobs

Release tim

eDeadline

Feasible interval

Execution tim

eSim

ple jobs

Loca

tion

A B C

eB

eC

eA

Location jobs

Sim

ple

location jobs

General

location jobs

In job scheduling …

In DMS (Data Mule Scheduling) problem …

DeD

General jobs

DeD

Execution tim

e

Release location

Deadline location

Feasible location interval

13

B

Idea of DMS form

ulation (1/2)

•Consider communication as a location job

–Location constraint: Feasible location intervals

–Tim

e constraint: Execution tim

e

A

C

Data m

ule

Communication

range

Data m

ule's path

Loca

tion

A B CeB

eC

eA

Execution tim

eLocation jobs

14

Idea of DMS form

ulation (2/2)

Loca

tion

A B CeB

eC

eA

Location jobs

Tim

e

A'

B'

C'

eB

eC

eA

Jobs

+ Tim

e-speed profile

(i.e., chan

ge of speed over time)

Set of

Location jobs

Set of jobs

Tim

e

A'

B'

C'

eB

eC

eA

Jobs

Faster speed

•Location job is m

apped to "job" when the speed is given

–Job scheduling problem

15

1-D

DMS pro

blem

•Determ

ine

–Tim

e-speed profile

–Schedule

that minim

ize the travel tim

e

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

)

16

Mobility m

odels

•Constant speed

–Maintain the initial speed

•Variable speed

–Can change the speed in the range

•Generalized (V

ariable speed with acceleration constraint)

–Follow acceleration constraint

Speed

Tim

e

Speed

Tim

e

Speed

Tim

e

(a) Constant speed

(b) Variable speed

(c) Generalized

(Variable speed with

acceleration constraint)

[vmin,vmax]

|dv(t)/dt |≤amax

17

Solving 1-D

DMS: D

efinitions

•Offline scheduling

–Decision with complete knowledge about all the jobs

•Feasible (location) intervals, execution tim

e

•Online scheduling

–Decision with knowledge about the jobs that are already released

•i.e., No inform

ation about the jobs released in the future

•Feasible

–Feasible schedule: Every job completes by its deadline

–A set of jobs is feasiblewhen there is a feasible schedule

•Algorithm A

is an optimalschedulin

g algorithm

–When a set of jobs has a feasible schedule, A

always finds it

18

Job sch

eduling

•Sim

ple jobs (i.e., one feasible interval)

–Earliest due date (EDD) algorithm is an optimal online scheduling alg.

•“Always execute the job with the earliest deadline”

•General jobs (i.e., multiple feasible intervals)

–No optimal online algorithm: Proof by an adversary argument

•An adversary can m

ake any online schedulers fail by releasing a new job

–Offline: Linear programming (LP) form

ulation

2zTim

e

1e 2e 3e

25

x

11

x12

x 22

x23

x13

x14

x15

x

33

x34

x35

x36

x26

x27

x

[Jackson 1955, Liu and Layland1973, Stankovicet al. 1995]

19

1-D

DMS: B

asic ca

ses

time

t 1t 2

job 1

: e 1

job 2

: e 2

job 3

: e 3jo

b 4

: e 4

(Consta

nt speed, V

ariable

speed)

Pr: set of release tim

e

Pd: set of deadlin

e

A set of simple jobs

is feasible

Processor demand

for any

Feasible interval of job

•Sim

ple location jobs

–Optimal offline algorithms

–Using the notion of “Processor demand”

•def: Sum of execution tim

e of jobs that are contained in the interval

•Feasibility test [B

aruahet al. 1993] [Yaoet al. 1995]

•General location jobs

–LP form

ulation

20

1-D

DMS: G

enera

lize

d

•NP-hard for general location jobs

–Reduction from PARTITION

•Input: Set of variables

•Question: D

oes exist s.t. ?

–Proof by constructing 1-D DMS problem from PARTITION instance

•Idea: M

ap binary choice (in PARTITION) to stop/skip choice (in 1-D DMS)

83

54

12

14

921

Location

Location

(Variable

speed w

/ accel. c

onstrain

t)

A

21

Constru

cting 1-D

DMS pro

blem

Location

(I) Subset choices

(II) Stop points

(III) Equalizers

I-1

I-2

I-n

II-1

II-2

II-3

II-(n+1)

II-(n+2)

II-(n+3)

II-(2n+1)

III-1

III-2

2V

nV

1V

′2

V′

nV

′1

p1q

nq

2p

2q

1p

1q

nq

2p

2q

1V

Range #1

Range #2

()

∑+

=i

in

qp

L2

2(

)∑

+=

ii

nq

pL

0

Location job

Ahas a

valid

partitio

n

Min

imum

tra

vel tim

e o

f th

e

corr

espondin

g 1

-D D

MS

pro

ble

m

equals

22

Summary: C

omplexity of 1-D

DMS pro

blem

1-D DMS

(vmin> 0)

Non-existent

(karbitrary)

NP-hard in the

strong sense

Non-existent

(fixed k

≥2)

NP-hard

Non-existent

Open

Generalized

(Variable speed

with acceleration

constraint)

Non-existent

LP

(vmin= 0)

Variable speed

Non-existent

LPNon-existent

Constant speed

Non-existent

LPEDD algorithm

[Jackson 1955, Liu & Layland1973,

Stankovicet al. 1995]

Preemptive Job Scheduling

Online

Offline

Online

Offline

General jobs

Sim

ple jobs

Contributions

Hard problems

Design heuristic algorithm

Design polynomial tim

e approximation scheme

EDD-with-Stop

23

PTAS for Genera

lize

d 1-D

DMS w

/ simple jobs

•Polynomial tim

e approximation scheme (PTAS)

–(1+

ε) approximation ratio for any ε>0

•Kinodynamicmotion planning

–Basic idea for designing PTAS

•Discretize

time, position, velocity

•Find the shortest path by breadth-first search

•Our contribution:

–Modify this for the 1-D DMS problem

•Taking “feasibility condition”into consideration

()ss& ,

()g

g& ,

Find fastest trajectory

subject to

max

max

)(

)(

at

p

vt

p

≤≤

∞∞

&&&

()

ixL

max

norm

-≡

∞

[Donald et al. FOCS 1988, JACM 1993]

Kinodynam

icMotion Planning

24

Algorith

m design

•Location is discretizedat “Dominant points”

–Release/deadline locations + start/end

–Observation: Feasibility is solely dependent on the travel tim

e betw

een

dominant points

•Quantization at the dominant points

–Speed

–“Cumulative execution tim

e”

•Total tim

e that the data m

ule spent on executing the jobs

•Feasibility condition is exp

ressed using cumulative execution tim

e

•Dynamic programming

Location

A B Ce B e Ce A

Location jobs0

L Execution tim

e

Dom

inant poin

ts

25

Summary: 1

-D DMS

•Form

ulated the 1-D m

otion optimization problem

as a scheduling problem

•Obtained theoretical results

–Efficient optimal algorithms, LP form

ulations

–Non-existence of optimal algorithms

–NP-hardness results

–PTAS


Ryo Sugiharaand Rajesh K. G

upta

“Optimal Speed Control of Mobile Node for Data Collection in Sensor Netw

orks”

to appear in IEEE Transactions on Mobile Computing


upta

“Speed Control and Schedulin

g of Data Mules in Sensor Netw

orks”

under submission to ACM Transactions on Sensor Networks


upta

“Complexity of Motion Planning of Data Mule for Data Collection in W

ireless Sensor Netw

orks”

under submission to Theoretical Computer Science

26

Outline of th

e talk

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

Path

sele

ction

node A

node B

node C

Forw

ard

ing

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

) 1-D DMS

23 4

1

Extended DMS

27

Path

selection

•Objective: Find a path s.t. the induced 1-D DMS

problem has the m

inim

um travel tim

e

•Problem: Difficult to find such a path

–Relation betw

een path and travel tim

e is unclear

–Infinite choices of path

•Idea: Sim

plify the problem as a graph problem

–Find the shortest tour that covers all labels

s

1

23

4

5

28

LABEL-C

OVERIN

G TOUR

•Find the shortest “label-covering”tour

•NP-hard

–TSP is a special case of this problem

•TSP: Traveling Salesm

an Problem

•Approximation algorithm:

–Find a TSP tour (exact or approximate)

–Choose the shortest label-covering tour obtained by

shortcuttingthe TSP tour

•While preserving label-covering property

•Using dynamic programming

29

Analysis of appro

xim

ation factor

•Construct a TSP tour from optimal label-covering tour

•Every non-visited point is within at most distance r

A

C

BD

E

F

G

G’

F’

E’

D’

TOPT_LC

: Appro

x. fa

cto

r of TS

P a

lgorith

m

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r = 1

r = 20

r = 50

r = 100

r = 200

r = 300

Example

(Sim

ulation on Matlab, 40 nodes)

31

Sim

ulation experiments

•Methods and parameters

–Using Matlab

–20 nodes randomly deployed in circular area (radius: 500m)

–Each node has data that needs 10 secs

for transm

ission

–Data m

ule m

ovement:

m/s

–Average of 100 trials

Pro

posed a

lgorith

m s

uccessfu

lly e

xplo

its larg

er com

munic

ation range

Total travel time (sec)

Com

munic

ation range

0

100

200

300

400

500

600

700

020

40

60

80

100

120

No rem

ote

com

munic

ation, consta

nt speed

e.g

., [S

om

asundara

et al. 2

004], [Xin

g e

t al. 2

007]

Rem

ote

com

munic

ation, consta

nt speed, sto

p to tra

nsm

ite.g

., [M

a &

Yang 2

007]

Rem

ote

com

munic

ation, vis

it a

ll nodes, variable

speed

e.g

., [Zhao e

t al. 2

003]

Proposed

32

Summary: P

ath

selection

•Form

ulated path selection problem as a graph

problem and presented an approximation algorithm

•Demonstrated the algorithm exp

loits the broader

communication range better than previously

proposed algorithms


upta

“Improving the Data Delivery Latency in Sensor Netw

orks with Controlled Mobility”

in 4th IEEE Distributed Computation in Sensor Systems (DCOSS), SantoriniIsland, 2008.

Best Paper Award

in Systems Track


upta

“Path Planning of Data Mules in Sensor Netw

orks”


33

Outline of th

e talk

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

Path

sele

ction

node A

node B

node C

Forw

ard

ing

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

) 1-D DMS

23 4

1

Extended DMS

34

Forw

ard

ing pro

blem

•Hyb

rid data m

ule approach

–Combine m

ultihopforw

arding and data m

ule approaches

–More

flexibleenergy-latency trade-off

•In the DMS problem framework

–Use “Forw

arding”problem

Energ

y c

onsum

ption

at each n

ode

Data

deliv

ery

late

ncy

Data

mule

Multih

op

forw

ard

ing

Large energy consumption,

Small latency

Small energy consumption,

Large latency

35

Forw

ard

ing pro

blem: Idea

•Assume: N

ode can forw

ard data to its neighbors

–Within given energy consumption limit

•Data m

ule does not need to visit "empty" nodes

–"Empty" nodes: forw

ard all data to neighbors; have no remaining data

to send to the data m

ule

•Data m

ule can possibly take a shorter path when each node

forw

ards more data toward the base station

–Empirically, shorter path results in shorter latency

36

Incom

ing

Outg

oin

g

Rx

xi

jij

jji

≤′+

+∑

∑λ

Linear pro

gra

m form

ulation

•Given

–: D

ata generation rate at i-th

node

–Elimit: Energy consumption limit (per node, per unit tim

e)

–Es, Er: Energy consumption to send/receive unit data

–R: Bandwidth

•Objective: M

inim

ize

–di: N

ode i 's distance from the base station

–: D

ata remaining at node i after forw

arding

•Subject to:

–Energy consumption constraint:

–Bandwidth constraint:

node j

x ij

node i

∑′

ii

id

λ

()

limit

ij

ijs

jji

rE

xE

xE

≤′

++

∑∑

λ

iλ′

∑∑

−+

=′j

iji

jji

ix

xλ

λ

iλ

Forw

ard

ing

rate

37

Sim

ulation resu

lts: Connected netw

ork

Avg. la

tency (B

ase s

tation)

Avg. la

tency (D

ata

mule

)

Avg. la

tency (Tota

l)

Data

mule

’s tra

vel tim

e

Data delivery latency (sec)

0

100

200

300

400

500

Energ

y c

onsum

ption lim

it (x E

)

Energ

y c

onsum

ption w

hen e

ach n

ode

only

sends its

ow

n d

ata

(i.e

., N

o forw

ard

ing)

010

20

30

40

50

"Pure

" data

mule

:

Avg

late

ncy =

432.8

1 s

ec

Elimit= E

"Pure

" m

ultih

op

forw

ard

ing:

Avg

late

ncy =

4.1

7 s

ec

Elimit= 49E

Sim

ulation environments:

Matlabfor solving the problem

ns2 for simulation

38

Sim

ulation resu

lts: Disco

nnected netw

ork

Data delivery latency (sec)

0

100

200

300

400

500

Energ

y c

onsum

ption lim

it (x E

)

Energ

y c

onsum

ption in

pure

data

mule

appro

ach

010

20

30

40

50

600

Avg. la

tency (D

ata

mule

)

Data

mule

’s tra

vel tim

e

"Pure

" data

mule

:

Avg

late

ncy =

513.0

7 s

ec

Elimit= E

39

Summary: F

orw

ard

ing

•Hybrid data m

ule approach is exp

ressed in

the DMS problem framework

–By using Forw

arding subproblem

•LP-based form

ulation realizes energy-latency

trade-off


upta

“Optimizing Energy-Latency Trade-off in Sensor Netw


in INFOCOM Mini-conference, Rio de Janeiro, 2009.

40

Outline of th

e talk

Speed c

ontrol

Speed

Tim

e

Job s

chedulin

g

Location

A B

Execution tim

eLocation job

Tim

e

Execution tim

e

A’

B’

C’

Job

Tim

e

A’

B’

C’

Path

sele

ction

node A

node B

node C

Forw

ard

ing

C

e(A

)

e(B

)

e(C

)

e(A

)

e(B

)

e(C

) 1-D DMS

23 4

1

Extended DMS

41

Extended DMS

•Multiple Data Mules

–1-D DMS

–Path selection

•Partially-known Communication Range

–Hybrid connectivity m

odel

–Semi-online scheduling algorithms

42

Extended DMS

•Multiple Data Mules

–1-D DMS

–Path selection

•Partially-known Communication Range


odel

–Semi-online scheduling algorithms

43

Partially-known communication range

[Ganesanet al. 2002]

r

•Motivation: Fixed range connectivity m

odel

is not very realistic

44

Connectivity m

odels

•Fixed range

–Sim

ple

–Not realistic

•“Shadowing”model in ns2

–Harder for algorithm design

–Still not very realistic [Lee et al. 2007]

•Spatially independent Gaussian

noise

•Proposed: “Hyb

rid”

–Small fixed range + unknown

range

r

Distance (m)

Probability of

successful reception

Distance (m)

Probability of


r

Distance (m)

Probability of


?

45

NodeHybrid connectivity m

odel

•Assumption:

–Communication is possible

•in the vicinity of node (known communication range)

•in some area around that (unknown communication range)

–Data m

ule knows if it can communicate with the node

from the current location

46

Partially-known comm. range

Location

Known comm. range

Unkn

own comm. range

Data m

ule’s path

•Idea: S

emi-online sch

eduling

–Offline scheduling with known comm. range

–Opportunistically exp

loit unknown comm. range

•As in online scheduling

•Algorithms

–1-D Semi-online algorithm

•Dynamically update speed

–2-D Semi-online algorithm

•Dynamically update path & speed

47

Idea of 2-D

Semi-online Algorith

m

A

BC

DE

P

Node 1

Known comm. range

Unknown comm. range

Data m

ule’s path

Node 2

Job execution in offline schedule

Actual job execution

48

BS

Example

(Sim

ulation on Matlab, 20 nodes)

49

Sim

ulation resu

lts

Exectim

e

=10[sec]

Dense deployment

Sparse deployment

0

500

1000

1500

2000

2500

3000

00.2

0.4

0.6

0.8

1

r K/rU

Data mule's travel time (sec)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

00.2

0.4

0.6

0.8

1

r K/rU


0

500

1000

1500

2000

2500

3000

3500

00.2

0.4

0.6

0.8

1

r K/rU


0

200

400

600

800

1000

1200

1400

1600

00.2

0.4

0.6

0.8

1

r K/rU


Exectim

e

=30[sec]

Offline 1-D Semi-online

2-D Semi-online

r Ur K

Known comm. range

Unkn

own comm. range

Less

More

Uncertainty

50

Summary: P

artially-known comm. range

•Presented a realistic connectivity m

odel


odel

•Designed semi-online scheduling algorithms

–More perform

ance im

provement in environments

with larger uncertainty

51

Oth

er to

pics in the disse

rtation

•1-D DMS



•QP form

ulation + SDP

relaxation

–Periodic data

generation case

•Path selection


•ILP form

ulation +

relaxations

•Forw

arding

–Distributed algorithm

•Extended DMS

–Multiple Data Mules case

•1-D DMS

•Path selection

–Partially-known

communication range

•Periodic case

•ns2 sim

ulation

52

Conclusion

•Designed the Data Mule Scheduling (DMS) problem as a

problem framework for motion optimization of data m

ules

–Exp

ressive:

•Fixed path, Pure data m

ule approach, H

ybrid data m

ule approach

•Various connectivity/m

obility m

odels

–Effective

•for theoretical analysis:

–Extracted optimally-solvable cases (1-D DMS for basic cases)

–Identified hard cases and designed approximate/heuristic algorithms

•for perform

ance im

provement:

–as demonstrated by sim

ulation exp

eriments

–Flexible:

•Accommodates other form

ulations: Path selection, Forw

arding

–Extensible:

•Multiple DMs

•Partially-known comm. range

53

6m

Dissertation writing and Defense

3m

Sim

ulation study

Submit to IPSN (08 Nov) / MobiHoc

(08 Nov) / MobiCom

(09 Mar)

3m

DMS with uncertainty

Real-w

orld

consideration

Submit to RTSS (08 May)

Ongoing

2m

Hyb

rid approach

Submitted to DCOSS (08 Feb)

Done

Path selection

Tech. report (07 Oct),

Submit to IEEE TMC (08 Mar)

Done

1-D DMS

Establishing

theoretical

foundation

Deliverables

Status

Work

time

Item

Stage

Planned tim

eline (as of Mar. 2008)

54

Relation w/ Speed

Scaling

TCS (under submission)

PTAS

TMC (to appear),

Heuristic algorithm

Complexity analysis

TOSN1, TOSN2

(under submission)

Multiple Data Mules

TOSN2 (under submission)

INFOCOM Mini-conf. (09 Apr)

DCOSS (08 Jun),

TOSN2 (under submission)

TOSN1 (under submission),

TCS (under submission)

Actual

Sim

ulation study

Submit to IPSN (08 Nov) /

MobiHoc(08 Nov) / MobiCom

(09 Mar)

DMS with uncertainty

Submit to RTSS (08 May)

Hyb

rid approach

Submitted to DCOSS (08 Feb)

Path selection

Tech. report (07 Oct),

Submit to IEEE TMC (08 Mar)

1-D DMS

Deliverables (incl. Planned)

Item

Plan/A

ctual

55

Futu

re W

ork

•Open case on complexity analysis

•Relaxing the assumptions

•Different problem settings/form

ulations

•Connections betw

een DMS and other areas

56

e.g.) Speed sca

ling pro

blem

•Speed scaling problem for processor energy m

anagement

–Scheduling problem

•Execution tim

e given as “# units of work”

–Processor speed s(t) is variable

–Objective: M

inim

ize energy consumption

•Benefits

–Speed scaling �

DMS

•Variable speed: Based on the algorithm for speed scaling [Y

aoet al. 1995]

–DMS �

Speed scaling

•“Rate-constrained speed scaling”(a.k.a. “Optimistic feasible DVS”[Yuan & Qu2005] )

–Constraint on the rate of processor speed change

•Apply the PTAS for Generalized 1-D DMS

t 1t 2

Tim

e (sec)

A B CRB

RC

RA

Jobs

0T # units of work

Pro

cessor sp

eed (units/sec)

W

Processed workload

W=∫t2

t1

s(t)dt

s∗(t)=argmin

s(t)

∫T

0

P(s(t))dt

57

Publica

tions

•Programming m

odels for sensor netw

orks

–“Programming Models for Sensor Netw

orks: A Survey”

in ACM Transactions on Sensor Networks, vol.4, issue 2, M

ay 2008

•1-D DMS

–“O

ptimal Speed Control of Mobile Node for Data Collection in Sensor Netw

orks”

to appear in IEEE Transactions on Mobile Computing

–“Speed Control and Scheduling of Data Mules in Sensor Netw

orks”


–“Complexity of Motion Planning of Data Mule for Data Collection in W

ireless Sensor Netw

orks”

under submission to Theoretical Computer Science

•Path selection

–“Improving the Data Delivery Latency in Sensor Netw


in 4th IEEE Distributed Computation in Sensor Systems (DCOSS), SantoriniIsland, 2008.

Best Paper Award

in Systems Track

–“Path Planning of Data Mules in Sensor Netw

orks”


•Forw

arding

–“O

ptimizing Energy-Latency Trade-off in Sensor Netw


in Proceedings of the 28th Annual Conference of the IEEE Communications Society (INFOCOM) Mini-

conference, Rio de Janeiro, 2009.

58

BACKUP

59

Pre

vious work

on data m

ule appro

ach

•Problems of previous work

–Without perform

ance guarantee; Lacking theoretical foundation

–Oversim

plifying assumptions

Heuristic;

Constant +

Stop

Path

[Xing et al., 07]

Heuristic; Stop to

communicate

Constant +

Stop

Path

[Ma, Yang, 07]

Heuristic; A

ssume

negligible comm. tim

e

Constant

Path

[Ma, Yang, 06]

NP-hardness; H

euristic

algorithm

Constant +

Stop

Path

[Somasundaraet al., 04]

Adaptive heuristic

algorithm

Variable

Speed

[Kansalet al., 04]

Heuristic algorithm

Variable

Path +

Speed

[Zhao et al., 03]

Remarks

Instant

move/stop

Speed of

data m

ule

Comm. only

at node

Assumptions

Problems

60

1-D

DMS: C

lose

r look

A B

Location

C

Location

Speed

Tim

e

Tim

e

A B C

Input: S

et of lo

cation jobs

Tim

e-S

peed p

rofile

(Solu

tion for th

e p

roble

m)

Correspondin

g Job Scheduling p

roble

m

Tim

e

Tim

e-L

ocation p

rofile

(dete

rmin

ed b

y T

ime-S

peed p

rofile

)

Execution tim

e

Execution tim

e

Location job

Job

e(A)

e(B)

e(C)

e(A)

e(B)

e(C)

61

1-D Basic

62

Adversary arg

ument

•Proving non-existence of optimal online algorithm for

general jobs

–If p < 1, adversary sets

•Job 1 cannot be finished

–If p = 1, adversary sets

•Job 2 cannot be finished

job 1

: e(1

) = 1

job 2

: e(2

) = 1

Tim

e

(job 3

: e(3

) = 1

)

01

23

p 1-p

63

1-D General

64

is slower than exactlyby aiseconds

–Choice of (i) or (ii) im

poses additional a

isecondsto Range #1 or #2

Location

Zero

-length

feasib

le location inte

rvals

PQ

AB

CD

pi

qi

pi

qi

Sta

rtG

oal

Range #

1R

ange #

2

Forc

e d

ata

mule

to s

top

II-A

II-B

II-C

II-D

Bin

ary

choic

e for ai

I-i

Location job

Case (i)

Case (ii)

Sto

p in R

ange #

1

Sto

p in R

ange #

2

Constru

cting 1-D

DMS pro

blem (1/3)

65

Constru

cting 1-D

DMS pro

blem (2/3)

•Location jobs III-1and III-2

enforce the “additional

time”to be same for each range

–Giving a valid

partition of A

Location

Sta

rtG

oal

Range #

1R

ange #

2

I-1

Location job

I-2

I-3

I-n

Additio

nal tim

e

III-1

III-2

66

Heuristic algorith

m for genera

l ca

se (1/2)

•Sim

plify

–Convert all general location jobs to sim

ple location jobs

–Proportionally distribute the execution tim

e

•Maximize

–Increase the speed until a tight intervalis found

•Tight interval: Processor demand = interval length

Location

Speed

Full

accel/decelat th

e m

axim

um

rate

Location

Speed

Tig

ht in

terv

al

Accel

inte

rval

Decel

inte

rval

Pla

teau inte

rval

Pro

c. dem

and =

tim

e d

ura

tion

Genera

l

location job

A

Execution

tim

e

Execution

tim

eSim

ple

location job

A1

A2

A3

67

Heuristic algorith

m for genera

l ca

se (2/2)

•Trim

–Elim

inate all fixed intervalsfrom remaining jobs

•Fixed interval: Intervals that the speed is already determ

ined

•Execution tim

e of each location job is changed accordingly

•Recursion

–Repeat from “Maximize”for the remaining intervals

Location

Speed

Recurs

ively

maxim

ize

Accelin

terv

al

Location

Decelin

terv

al

Location

Location

Tig

ht in

terv

al

Location

Speed

Tig

ht in

terv

al

Accelin

terv

al

Decelin

terv

al

Pla

teau inte

rval

68

Example: G

enera

lize

d m

odel

Location job

Job Job

Speed

control

Job

schedulin

g

(Variable

speed w

/ accel. c

onstrain

t)

heuristic

solu

tion

69

Analysis of lower bound

•We want to know how good a heuristic solution is

–Compare it to global optimal solution?

•Problem: H

ard to obtain

–Idea: U

se its lower boundfor comparison

•Global optimal solution is above the lower bound

•Method 1: O

nly for simple jobs case

–Based on processor demand analysis

–LP form

ulation

•Method 2: For any cases

–QP (Quadratic Programming) form

ulation

–SDP (SemidefiniteProgramming) relaxation

•Convex optimization; solved efficiently

Solution space of

original Q

P problem

Solution space of

SDP relaxation problem

Global optimal

solution

Optimal solution

of relaxation problem

70

QP and SDP relaxation

Minim

ize

subject to

QP (Quadratic Program)

Minim

ize

subject to

Equivalent QP problem

Minim

ize

subject to

SDP (SemidefiniteProgram) relaxation

All eigenvaluesof A

are non-negative

Positive semidefiniteness

Relax

Equivalent (Schurcomplement)

Componentw

iseinner product of matrices

(Frobeniusinner product)

71

Experiments

•Methods and parameters

–Location jobs (#: 5~20)

•Feasible location interval: random location, length randomly chosen from 0~20m

•Execution tim

e: 10 secs

–Total travel length: (10~40) x (# location jobs)

–Data m

ule m

ovement:

–Average of 100 trials

0

0.51

1.5

510

15

20

Num

ber of lo

cation jobs

Total travel time (normalized)

Heuristic

Lower bound (LB-M

axSpeed)

0

0.51

1.52

10

20

30

40

Node d

eplo

ym

ent density


Heuristic

Lower bound (LB-M

axSpeed)

0

0.51

1.5

12

3

Num

ber of fe

asib

le location

inte

rvals

(per jo

b)


Heuristic

Lower bound (SDP)

Lower bound (LB-M

axSpeed)

Heuristic a

lgorith

m p

roduces g

ood s

olu

tions v

ery

clo

se to low

er bound

dense

spars

e

72

PTAS

73

Kinodynamic

motion planning

•Donald, Xavier, Canny, Reif(FOCS 1988, JACM 1993)

•Basic idea for designing PTAS

–Discretize

time, position, velocity

•Sufficient to consider only piecewise-extremal(“bang-bang”) controls

•Directed graph connecting each grid point is induced

–Find the shortest path in the graph

•By breadth-first search

()ss& ,

()g

g&,

+=

+

++

=+

ττ

ττ

τ

at

pt

p

at

pt

pt

p

)(

)(

21)

()

()

(2

&&

&in

teger m

ultip

le o

f 2

21τ

a

inte

ger m

ultip

le o

f τ

a

Fin

d a

faste

st traje

cto

ry s

ubje

ct to

max

max

)(

)(

at

p

vt

p

≤≤

∞∞

&&&

()

ixL

max

norm

-≡

∞

74

DVS

75

Connections betw

een DMS and Speed sca

ling

•Both problems are “scale-parameterized”

–1-D DMS problem

•Scaled by data m

ule’s speed

–Speed scaling problem

•Scaled by processor’s speed

Variable

Fixed

ei

RiVariable

Fixed

76

Pro

blem definition

•Generalized 1-D DMS for simple location jobs

–Input:

•Set of simple location jobs

–release location

–deadline location

–execution tim

e

•Constraints on data m

ule’s m

otion

–Maximum absolute acceleration

–Maximum speed

–Output:

•Minim

um travel tim

e to finish all the jobs

max

max

)(

0

)(

vt

x

at

x

≤≤

≤

&

&&

ir id ie

Location

A B Ce B e Ce A

Location jobs0

L Execution tim

e

(loc, speed)=

(0,0

)(loc, speed)=

(L,0

)

77

Time

0t1t

Processor speed

0s

1s

atbt

ps msns

+D −D

)(

*t

s)

(ts

78

Speed sca

ling pro

blem

•Scheduling problem

–Execution tim

e given as “# units of work”

•Processor speed s(t) is variable

•Power consumption P(s) is a convex func. of processor speed

–Im

plication: Executing a job with slower speed is m

ore energy efficient

•Objective: M

inim

ize energy consumption

Tim

e (sec)

A B CRB

RC

RA

Jobs

0T # units of work

Pro

cessor sp

eed (units/sec)

W

t 1t 2 Consumed energy

Processed workload

W=∫t2

t1

s(t)dt

E=∫t2

t1

P(s(t))dt

s∗(t)=argmin

s(t)

∫T

0

P(s(t))dt

79

Benefits

•Speed scaling �

DMS

–Variable speed

•Based on the algorithm for speed scaling [Y

aoet al. 1995]

•DMS �

Speed scaling

–Rate-constrained speed scaling

•Constraint on the rate of processor speed change

–a.k.a. “Optimistic feasible DVS”[Yuan & Qu2005]

•Apply the PTAS for Generalized 1-D DMS

80

Path Selection

81

Path

selection as a gra

ph pro

blem

•Labeled edge

–e.g.) Edge (1,3) has label {1,2,3}, since the edge intersects with

the comm. range of node 1,2,3

•Find the shortest tour that covers all labels

–Equivalent to “DM’s path intersects with the comm. range of all nodes”

s

1

23

4

5

82

Choosing the cost m

etric

•Observation from exp

eriments

–“Path length m

easured by Euclidean distance

is strongly

correlated with the travel tim

e”

Exec. tim

e (e)

Comm. range (r)

Radius (d)

100

150

500

20

10

150

500

2

100

10

500

150

500

150

Correlation coefficient

Correlation coefficient

(a) 5 nodes

(b) 20 nodes

Exec. tim

e (e)

Comm. range (r)

Radius (d)

100

150

500

20

10

150

500

2

100

10

500

150

500

150

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Num. edge

Euclidean

distance

Uncovered

distance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Num. edge

Euclidean

distance

Uncovered

distance

83

Sim

ulation experiments

•Matlab+ ns2

–On Matlab, solve Forw

arding & DMS problem

–Generate ns2 script that describes data m

ule’s m

otion

plan and communication schedule

•Measure the data delivery latency

–Varying energy consumption limit (Elimit)

84

Forwarding

85

Forw

ard

ing pro

blem

•Motivation:

–Add flexibility to energy-latency trade-off

•Solution:

–Hybrid data m

ule approach

•Combine m

ultihopforw

arding and data m

ule approaches

–In the DMS problem framework

•Use “Forw

arding”problem

Energ

y c

onsum

ption

at each n

ode

Data

deliv

ery

late

ncy

Data

mule

Multih

op

forw

ard

ing

Large energy consumption,

Small latency

Small energy consumption,

Large latency

86

Examples

Elimit= E

(Avg. la

tency: 432.8

1sec)

"Pure" data m

ule approach

Energ

y c

onsum

ption w

hen e

ach n

ode o

nly

sends its

ow

n d

ata

(i.e

., N

o forw

ard

ing)

87

Examples

Elimit= 2E

(Avg. la

tency: 358.1

5sec)

88

Examples

Elimit= 5E

(Avg. la

tency: 215.2

6sec)

89

Examples

Elimit= 10E

(Avg. la

tency: 95.4

2sec)

90

Examples

Elimit= 25E

(Avg. la

tency: 39.8

8sec)

91

Examples

Elimit= 49E

(Avg. la

tency: 4.1

7sec)

"Pure" multihopforw

arding approach

92

Multiple DM

93

Multiple Data M

ules Case

•1-D –Identical paths

•"Symmetric schedule“is optimal for basic cases

–Arbitrary paths

•LP form

ulation for basic cases

•Heuristic for Generalized (acceleration constrained) model

•2-D –k-Label Covering Tour problem

•minim

ize the m

aximum tour length

–Approximation algorithm

•based on k-SPLITOUR algorithm for k-TSP


•ILP form

ulation + relaxations

94

(a) Symmetric

1 2

Location

ll2

l3

0

Location job

Location

Speed

DM#1,2

22

31

et

×+

(b) Asymmetric

Location

Speed

Location

DM#1

DM#2

et

t+

+2

1

et

t+

+2

1

alal

at

alal

at

22

22

22

21

==

==

DM’s travel time

95

0

1000

2000

3000

4000

5000

6000

12

34

Num

ber of data

mule

s (k)

Maximum path length

0

1000

2000

3000

4000

5000

6000

050

100

150

Com

munic

ation range (r)

Maximum path length

Overlay

Partitio

nPro

posed

ILPcover

LPC

PM

axC

ost

Low

er bounds

96

0

100

200

300

400

500

600

700

800

900

1000

12

34

Num

ber of data

mule

s (k)

Maximum travel time

0

200

400

600

800

1000

1200

050

100

150

Com

munic

ation range (r)

Maximum travel time

0

200

400

600

800

1000

1200

1400

12

34

Num

ber of data

mule

s (k)

Maximum travel time

0

200

400

600

800

1000

1200

1400

1600

1800

050

100

150

Com

munic

ation range (r)

Maximum travel time

0

500

1000

1500

2000

2500

3000

12

34

Num

ber of data

mule

s (k)

Maximum travel time

0

500

1000

1500

2000

2500

050

100

150

Com

munic

ation range (r)

Maximum travel time

Overlay

Partitio

nPro

posed

e =

30

e =

60

e =

10

97

Semi-online

98

Semi-online sch

eduling algorith

ms

•1-D algorithm

–Make offlin

e plan

–At each location,

•When there is a planned schedule, follow it

•Otherw

ise,

–Move at the m

aximum speed, and

–Execute any available job

•2-D algorithm

–1-D + Change the path

•Guaranteed to be better than the offline algorithm

99

Sim

ulation experiments

•Im

plemented on ns2

•Designed sim

ple communication protocol

–Scheduled data collection

•Request-response per packet

–Opportunistic data collection

•Broadcast "advertise" packet

100

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Average data delivery latency (sec)

Offline

Periodic 2D semi-online

Dense

λ=100 λ=500

Sparse

λ=100 λ=500

Main resu

lts

101

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

Offline

Sem

i-

online

r K= 20m (Reception prob.: 99.9%)




Dense,

λ = 100 Bytes/sec

Dense,

λ= 500 Bytes/sec

Sparse,

λ= 100 Bytes/sec

Sparse,

λ= 500 Bytes/sec

Overe

stim

ating comm. range

102

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

0

0.2

0.4

0.6

0.81

1.2

12

34

56

78

910

Period

Collection rate

Offline

Sem

i-

online

320 Kbps (M

easured)

480 Kbps (M

easured x 1.5)

640 Kbps (M

easured x 2.0)

Dense,

λ = 100 Bytes/sec

Dense,

λ= 500 Bytes/sec

Sparse,

λ= 100 Bytes/sec

Sparse,

λ= 500 Bytes/sec

Overe

stim

ating bandwidth

controlled mobility in sensor networks final defense 2009...

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