Delay Analysis of Large-scale Wireless
Sensor Networks
Jun Yin, Dominican University, River Forest, IL, USA,
Yun Wang, Southern Illinois University Edwardsville, USA
Xiaodong Wang, Qualcomm Inc. San Diego, CA, USA
1
Outline
Introduction
 Delay analysis

–
Hop count analysis


–
One –dimensional
Two –dimensional
Source – destination delay analysis


Random source –destination
Delay from multi-source to sink
–
–

Flat architecture
Two-tier architecture
Conclusion
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Web-enabled toaster +
weather forecaster
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/science/nature/1264205.st
m
IP picture frame
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World’s smallest web server
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Internet phones
1-3
Wireless Sensor network : The
next big thing after Internet



Recent technical advances have enabled the
large-scale deployment and applications of
wireless sensor nodes.
These small in size, low cost, low power sensor
nodes is capable of forming a network without
underlying infrastructure support.
WSN is emerging as a key tool for various
applications including home automation, traffic
control, search and rescue, and disaster relief.
Wireless Sensor Network
(WSN)

WSN is a network consisting of hundreds or
thousands of wireless sensor nodes, which
are spread over a geographic area.
 WSN has been an emerging research topic
–
–
–
VLSI  Small in size, processing capability
Wireless  Communication capability
Networking  Self-configurable, and coordination
WSN organization


Flat vs. hierarchical
Homogenous vs. Heterogeneous
Delay is important for WSN



It determines how soon event can be
reported.
Delay is determined by numerous
network parameters: node density,
transmission range; the sleeping
schedule of individual nodes; the
routing scheme, etc.
If we can characterize how the
parameters determine the delay, we
can choose parameters to meet the
delay requirement.
7
Outline
Introduction
 Delay analysis

–
Hop count analysis


–
One –dimensional
Two –dimensional
Source – destination delay analysis


Random source –destination
Delay from multi-source to sink
–
–

Flat architecture
Two-tier architecture
Conclusion
Our approach

Firstly, we try to characterize how network
parameters such as node density,
transmission range determine the hop
count;
 Then we consider typical traffic patterns in
WSN, and then characterize the delay.


Random source to random destination
Data aggregation in two-tier clustering architecture
Outline
Introduction
 Delay analysis

–
Hop count analysis


–
One –dimensional
Two –dimensional
Source – destination delay analysis


Random source –destination
Delay from multi-source to sink
–
–

Flat architecture
Two-tier architecture
Conclusion
Modeling

Randomly deployed WSN is modeled
as:
–
–


Random geometric graph
2-dimensional Poisson distribution
Nodes are deployed randomly.
The probability of having k nodes located with in
the area of rs 2 around the event :
Shortest path routing: One
dimensional case

At each hop, the next hop is the farthest
node it can reach.
L
r0

r0 :Transmission range
r: per-hop progress
P[r   ]  1  P[r   ]  e
   r0  
P[r   ]  e  r0  
12
E[r ]  r0 
1  e  r0
 L 
H 

 E (r ) 

Two-dimensional case

Per-hop progress
2
r0

1
r1
r2
Average per-hop progress in 2D case
P[   ]  1  P[   ]  e
P[   ]  2e

  r0 2  2

  r0 2  2

 r0
E[r ] 
  P[r   ] cos dd
0 0


14/50
Average per-hop progress as node
density increases
Numeric and simulation results
It shows that our analysis
can provide a better
approximation on hop

count than
.
Hop count between fixed S/D distance under
various transmission range
r0
15
Hop count simulations
Hop count between various S/D distance
It shows that our
analysis can provide a
better approximation on
hop count than  .
r
Outline
Introduction
 Delay analysis

–
Hop count analysis


–
One –dimensional
Two –dimensional
Source – destination delay analysis


Random source –destination
Delay from multi-source to sink
–
–

Flat architecture
Two-tier architecture
Conclusion
Per-hop delay and H hop delay
In un-coordinated WSN, per-hop
delay is a random variable between 0
and the sleeping interval (Ts).
 Per-hop delay is denoted by d:

Ts
E (d ) 
2
Ts
2
Ts
1
 (d )   [s  E (d )] ds 
Ts
12
0
2
Random source/dest traffic
Distance distribution
between random S/D
pairs in a square area of
L*L:
4   2
2
PS / D ( )  4  L  2L  
L 2
2
Hop count between random S/D pairs
19
Heterogeneous WSN

Sensor nodes might have different
capabilities in sensing and wireless
transmission.
http://intel-research.net/berkeley/features/tiny_db.asp
Random deployment of
heterogeneous WSN
N1 = 100
N2 = 300
L = 1000m
21
Modeling

The deploying area of WSN: a square of
(L*L).
 The probability that there are m nodes
located within a circular area of r 2 is:
(r 2 ) m  r 2
P( , m, r ) 
e
m!

Node density of Type I and Type II nodes:
N1
1 
,
L*L
22/50
N2
2 
L*L
2-tier structure
Type II node chooses the closest Type
I node as its clusterhead:
Clusterhead
23
Voronoi diagram
Distance distribution
Distance distribution
between a Type II sensor
node to its closest Type I
sensor node:
P(v   )  21e
1 2
Average distance:
E (v ) 
2
1
PDF of the distance to from Type II
sensor node to its clusterhead
24/50
Average delay in 2-tier WSN
Average delay:
E ( D)  E E d | H  h 
Ts

2
2 L

0
v
P (v )
dv
F ( , r0 , 2 )
Ts

F ( , r0 , 2 ) 1
Per-hop progress
25
Summary on delay analysis

The relationship between node density,
transmission range and hop count is
obtained.
 Per-hop delay is modeled as a random
variable.
 Delay properties are obtained for both flat
and clustering architecture.
26/50
Conclusion
Analysis delay property in WSN;
 It covers typical traffic patterns in
WSN;
 The work can provide insights on
WSN design.

27/50
Thanks.
Questions?
28
Random source to central sink
node
Laptop computer
29
Incremental aggregation tree
30
Hop count analysis (Key
assumptions)
31