Post on 22-May-2020
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
–Heuristic algorithm
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
Ryo Sugiharaand Rajesh K. G
upta
“Speed Control and Schedulin
g of Data Mules in Sensor Netw
orks”
under submission to ACM Transactions on Sensor Networks
Ryo Sugiharaand Rajesh K. G
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
30
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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
Ryo Sugiharaand Rajesh K. G
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
Ryo Sugiharaand Rajesh K. G
upta
“Path Planning of Data Mules in Sensor Netw
orks”
under submission to ACM Transactions on Sensor Networks
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
Ryo Sugiharaand Rajesh K. G
upta
“Optimizing Energy-Latency Trade-off in Sensor Netw
orks with Controlled Mobility”
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
–Hybrid connectivity m
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
successful reception
r
Distance (m)
Probability of
successful reception
?
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
Data mule's travel time (sec)
0
500
1000
1500
2000
2500
3000
3500
00.2
0.4
0.6
0.8
1
r K/rU
Data mule's travel time (sec)
0
200
400
600
800
1000
1200
1400
1600
00.2
0.4
0.6
0.8
1
r K/rU
Data mule's travel time (sec)
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
–Hybrid connectivity m
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
–Heuristic algorithm
–Lower bound analysis
•QP form
ulation + SDP
relaxation
–Periodic data
generation case
•Path selection
–Lower bound analysis
•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”
under submission to ACM Transactions on Sensor Networks
–“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
orks with Controlled Mobility”
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”
under submission to ACM Transactions on Sensor Networks
•Forw
arding
–“O
ptimizing Energy-Latency Trade-off in Sensor Netw
orks with Controlled Mobility”
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
Total travel time (normalized)
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)
Total travel time (normalized)
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
–Lower bound analysis
•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%)
r K= 30m (Reception prob.: 98.4%)
r K= 40m (Reception prob.: 93.6%)
r K= 50m (Reception prob.: 85.1%)
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