A Mobility Model for Studying
Wireless Communication
Raymond Greenlaw
Armstrong Atlantic State University
Savannah, GA, USA
Sanpawat Kantabutra
Chiang Mai University
Chiang Mai, Thailand
Outline
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Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 2
Introduction
• Wireless networking is becoming
prevalent because of low-cost, ease of
installation, scalability, and convenience
to users.
• We consider a model of a mobile
network; a wireless network in which the
access points themselves may be
moving.
• Such networks are of great importance
in supporting relief efforts for natural
disasters or for military field exercises.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 3
Outline
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Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 4
The Mobility Model
• Goal is to model actual mobile networks.
• Model needs to be sophisticated enough
to model complex real-life situations.
• Key features need to be abstracted out
so the model is feasible to study and
apply.
• After defining the model, a
communication protocol is defined to
interpret how the model works.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 5
Outline
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•
•
•
•
•
•
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Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 6
Definition of the Model
•
•
Model operates on a 2-dimensional
grid.
Model is an 8-tuple (S, D, U, L, R, V, C,
O), where
sm} is a finite collection
1. Set S = {s1, s2, …,
of sources, where m
N, m is the
number of sources. Corresponding to
each source
 si, for
1 ≤ i ≤ m, an initial location (xi, yi) is
specified where xi, yi
N.
2. Set D = {000, 001, 010, 101, 110} is called
directions
no
Greenlaw the
& Kantabutra
– A Mobilityand
Model correspond
for Studying Wirelessto
Communication
–7
Definition of the Model
•
Model Definition (continued)
3. Set U = {u1, u2,…, up} is a finite collection
 p N. The set
of mobile devices, where
U is called the set of users. The value p is
called the number of users.
Corresponding to each user ui, for 1 ≤ i ≤
p, an initial location
(xi, yi) is specified
where xi, yi
N.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 8
Definition of the Model
•
Model Definition (continued)
4. Let t  N. Set L = {l1, l2,…, lp} is a finite
collection of “bit strings,” where 
li
Dt
for
1 ≤ i ≤ t. Each group of three bits in li
beginning with the first three defines a
step in the given direction for the user ui’s
movement or no movement at all if the
string is 000. The value t is called the
duration of the model.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication – 9
Definition of the Model
•
Model Definition (continued)
5. Let t(i) N for 1 ≤ i ≤ m. The set R =
{r1, r2, …, rm} is a finite collection of “bit
t(i) for 1 ≤ i ≤ m.
strings,” where r
D
i
Each group of three bits in ri beginning
with the first three defines a step in a
given direction for the source si’s
movement or no movement at all if the
string is 000. The set R is called the
random walks of the mobility model.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Model Definition (continued)
6. Set V = {v1, v2, …, vm} is a finite collection
of numbers, wherevi
N. The value vi
is the corresponding number of steps from
ri per unit time that si will take. This set is
called the velocities.
7. Set C = {c1, c2, …, cm} is a finite collection
of numbers, whereci
N. The value ci
is the corresponding diameter of the
circular coverage of source si. This set is
called the coverages.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Model Definition (continued)
8. The set O = {(x1, y1, x2, y2) | x1, y1, 
x 2, y 2
N,
x2 > x1, and y2 > y1} is a finite collection of
rectangles in the plane. The set is called
the obstacles.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Remarks
– Sources in S correspond to wireless
access points and are broadcasting and
receiving signals.
– Set D represents the four possible
directions for movement in the grid, plus
no movement.
– Set U represents users with mobile
devices.
– Set L contains random walks used to
model the movement of users.
– Set R contains random walks to model the
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Remarks (continued)
– To accommodate for different source
velocities, the walks in R have different
lengths.
– Relative speeds of sources are
represented by natural numbers contained
in set V.
– Different sources will broadcast at different
signal strengths depending on a variety of
factors, available power being the main
one.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Remarks (continued)
– Various signal strengths are represented
by specifying the diameter of a circle ci for
each source indicating where its signal
can be received.
– This region is its coverage area.
– Since buildings and other obstacles may
interfere with signal transmission, the
model incorporates a set of obstacles O.
– For simplicity, only rectangular obstacles
are permitted.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Communication Protocol
– Illustrates how the model is interpreted.
– Needed so that the model works as
intended.
– Source are always on.
– Users with mobile devices are moving in
and out of the range of each other and
various sources.
– Devices would like to communicate (send
and receive messages) with one another.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Communication Protocol (continued)
– Let k > 2 and 
k
N.
– Any two sources with overlappingcoverage areas may communicate with
each other in full-duplex fashion as long
as the intersection of their overlappingcoverage area is not completely contained
inside obstacles. Those two sources are
currently in range.
– A series s1, s2, …, sk of sources are
currently in range if si and si+1 are
currently in range for
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
1 ≤ i ≤ k-1.
Definition of the Model
•
Communication Protocol (continued)
– Two mobile devices cannot communicate
directly with one another.
– A mobile device D1 always communicates
with another mobile device D2 through a
source or series of sources as defined on
the following slides.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Communication Protocol (continued)
– The mobile devices D1 at location (x1, y1)
and D2 at location (x2, y2) communicate
through a single source s located at (x3,
y3) if at a given instance in time the lines
between points
(x1, y1) and (x3, y3), and points (x2, y2) and
(x3, y3) are within the area of coverage of
s, and do not intersect with any obstacle
from O.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Communication Protocol (continued)
– The mobile devices D1 at location (x1, y1)
and D2 at location (x2, y2) communicate
through a series of sources s1 at location
(a1, b1), s2 at location (a2, b2), …, and sk at
location (ak, bk) that are currently in range
if the line between points (x1, y1) and (a1,
b1) is inside s1’s coverage area and does
not intersect any obstacle from O and the
line between points (x2, y2) and (ak, bk) is
inside sk’s coverage area and does not
intersect any obstacle from O.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Communication Protocol (continued)
– Mobility of the sources and the users are
built into this model.
– Reflects the situation in a real mobile
network where access points and users
are moving around.
– For simplicity, we implicitly assumed that
all users are moving at the same rate of
speed, whereas we explicitly modeled
sources moving at different velocities.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Definition of the Model
•
Communication Protocol (continued)
– Model can handle users moving at
different rates of speed by having some
users remain stationary while others are
moving at each step.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Outline
•
•
•
•
•
•
•
•
Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
A Sample Instance of the
Model
• Let S = {s , s , s , s }
1
2
3
4
with initial locations (2,
5),
(5, 5), (6, 4), and (5, 2)
respectively.
• Let D =
{000, 001, 010, 101,
110}.
• Let U = {u1, u2, u3} with
initial location (3, 4),
(2, 1), and (6, 2),
respectively.
• Let t = 3 and L = {l1, l2,
l3}, where li = (000,
Greenlaw & Kantabutra – A Mobility Model for Studying
Wirelessfor
Communication
000, 000)
1 ≤ i ≤ 3. –
A Sample Instance of the
Model
•
Let R = {r1, r2, r3,
r4}. For clarity, the
figure only shows r1
=
(101, 001, 101) and
omits other ri’s,
which we assume
are all (000, 000,
000) except r2
which is twice as
long.
• Let V = {1, 2, 1, 1}.
• Let C = {2, 2, 2, 4}.
Greenlaw & Kantabutra – A Mobility Model•for Studying
Wireless
Communication
Let O
= {(2,
1, 4, –
A Sample Instance of the
Model
• Three stationary
users.
• Four sources.
• One obstacle.
• s1-3 have coverage
of 2, s4 has coverage
of 4.
• s1 moves south,
east, and south with
a velocity of v1 = 1,
or one step per unit
of time.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
A Sample Instance of the
Model
• Initially, s2 and s3 are
currently in range, s2, s3,
and s4 are a series of
sources currently in
range, and sources s1
and s2 are not currently
in range.
• Initially, users u1 and u3
cannot communicate;
after three steps, u1 can
communicate with u3
through the series of
sources s1 and s4.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Outline
•
•
•
•
•
•
•
•
Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Problem Definitions
• User Communication Problem
– Instance: Mobility model (S, D, U, L, R, V,
C, O), two designated users ua and ub from
U, and a time k.
– Question: Can users ua and ub
communicate at time k?
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Problem Definitions
• Sources Reachability Problem
– Instance: Mobility model (S, D, U, L, R, V,
C, O), two designated sources sa and sb
from S, and a time k.
– Question: Are sources sa and sb in range at
time k?
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Problem Definitions
• Access Point Location Problem
– Instance: Mobility model (S, D, U, L, R, V,
C, O), two designated users ua and ub from
U, an access point diameter d, and a
natural number k.
– Question: Can users ua and ub
communicate if k or fewer access points of
diameter d are placed appropriately in the
grid?
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Problem Definitions
• Access Point Placement Problem
– Instance: Two mobility models
M = (S, D, U = {u1, u2} , L, R, V, C, O), and
M’ = (S’, D, U = {u1, u2} , L, R’, V’, C’, O’).
– Question: Can u1 and u2 communicate for
more steps in model M than they can in
model M’?
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Problem Definitions
• Obstacle Removal Problem
– Instance: Mobility model (S, D, U, L, R, V,
C, O), two designated users ua and ub from
U, and a natural number k.
– Question: Can ua and ub communicate
throughout the duration of the model if k or
fewer obstacles are removed?
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Outline
•
•
•
•
•
•
•
•
Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Conclusion
• Description of a mobility model and
several interesting decision problems
related to the model were presented.
• It would be interesting to examine the
complexity of other related problems.
• Mobility model itself can be studied
further, including extending the model to
three dimensions.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Outline
•
•
•
•
•
•
•
•
Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Acknowledgments
• Ray is very grateful to the Computer
Science Department at Chiang Mai
University for its generosity and
hospitality during his stay there during
the spring semester of 2006.
• Ray’s research was supported by a
Fulbright Lecturing/Research Fellowship.
• Ray thanks the Fulbright Commissions
of Thailand and the United States.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
Outline
•
•
•
•
•
•
•
•
Introduction
The Mobility Model
Definition of the Model
A Sample Instance of the Model
Problem Definitions
Conclusion
Acknowledgments
References
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –
References
• Paul Goransson and Raymond
Greenlaw, Secure Roaming in 802.11
Networks, Chapter 11, Elsevier, 2007.
Greenlaw & Kantabutra – A Mobility Model for Studying Wireless Communication –