Transcript A Standard Measure of Mobility for Evaluating Mobile Ad Hoc

A Standard Measure of
Mobility for Evaluating
Mobile Ad Hoc Network
Performance
By
Joseph Charboneau
Karthik Raman
MANET
Unpredictable topology changes.
 Performance related to efficiency of
routing protocol.

 Performance
simulations.
studies are done with
Performance Measure

Problem
 There
are many mobility models but not a
unified quantitative “measure” of mobility.
 Ex.
A is the performance of protocol R1 using model
M1.
 B is the performance of protocol R2 using model
M2.
 There are two different models used so results
can’t be compared between A and B.

Performance Measure (Cont.)

Other studies are based on
 Average
speed
 Maximum speed
 Pause time
 Rate of link changes
 Mobility factor

Problem
 Still
no unified quantitative measure of
mobility.
Performance Measure (Cont.)
The study approached in this paper is a
solution for unified quantitative measure of
mobility.
 Solution

 Use
a standard that is flexible and consistent.
Flexible because the mobility measure can be
customized by using a remoteness function.
 Consistent because mobility measure has a linear
relationship to link change rate.

Remoteness

Remoteness is based on the distance
between two nodes.
i = 0,1,…,N-1, represent the location
vector of node i at time t.
 dij(t)=|nj(t)-ni(t)| is the distance between node i
to j at time t.
 Remoteness is defined by
 ni(t),
Rij(t)=F(dij(t))
 Where F(.) is a function of the distance.

Remoteness (Cont.)

Requirements that function F(.) must
meet.
a.
b.
c.
d.
e.
F(0)=0, limx→∞F(x)=1
dF(x)/dx ≥ 0 for all x ≥ 0
dF(x)/dx|x=0=0
limx→∞dF(x)/dx=0
dF(x)/dx|x=R ≥ dF(x)/dx for all x ≥ 0
Remoteness (Cont.)

Requirements of function F(.) defined.
a.
b.
c.
e.
Normalizes F(.) to have a unity maximum value.
Guarantees that the remoteness is monotonically
increasing function of distance.
and d. give the boundary condition of F(.), which
guarantee that the remoteness of a node at
extreme locations does not change with
movement.
Makes the remoteness most sensitive to the
movement of a node at communication range.
Remoteness (Cont.)

One function of F(.) that meets all of the
requirements is.
x
 F(x)

r 1  
d , x  0, r  2
= 1/Γ(r)   e
0
λ=(r-1)/R where r can be a non-integer.
 r is the sensitivity to the remoteness at
communication range.
 With
Mobility Measure

Mobility measure is defined in terms of the time
derivatives of the remoteness.



M (t ) 
1
N
N 1
 M (t )
i
i 0
1
M i (t ) 
N 1
N 1

j 0
d
F (dij (t ))
dt
N is the number of nodes and Mi(t) is a measure of the relative
movement of other nodes seen by i.
Mobility Measure (Cont.)


The mobility measure M(t) represents the
average amount of the relative movement of
the nodes in the network at time t.
For a network in steady state, the time average
of mobility measure can be used.
T
1
M 
T

0
M (t )dt
Mobility Measure (Cont.)

If the function chosen for F(.) is the function
discussed earlier then the mobility measure
function will be.
 M G (t ) 
 M iG (t ) 
1
N
N 1

M iG (t )
i 0
1
N 1
N 1

j 0
dij' (t )  f (dij (t ))
Mobility Measure (Cont.)

If the function chosen for F(.) is the identity
function then the mobility measure function will
be.
I
 M (t ) 
I
 M i (t ) 
1
N
N 1

M iI (t )
i 0
1
N 1
N 1

j 0
dij' (t )
Mobility Measure (Cont.)

Both MG(t) and MI(t) are both mobility
measures but only MG(t) meets the given
requirements.
Mobility Models

Random Waypoint Model (RWP)
 Node
selects random destination & speed
 Speed uniformly distributed between min and
max speeds
 Pauses at destination for random time and
selects a new destination
Mobility Models (Cont.)

Random Gauss-Markov Model (RGM)
 Each
node is assigned a speed, direction and
updated every Δt
 Speed and direction are uniformly distributed
between their min and max values
 At boundary node reflects and chooses a new
random direction
Mobility Models (Cont.)

Reference Point Group Mobility Model (RPGM)
 Each
group has a logical center which defines
location, speed, direction, etc
 Defines a reference point and random motion vector
for each node in a group
 Random motion vector is updated periodically and is
given by the length and direction, distributed uniformly
over the intervals [0, RMmax] and [0, 2π)
Network Scenarios
Network Scenarios (Cont.)
Network Scenarios (Cont.)
Simulation Results
All scenarios are done with 500 seconds
warm up time and measured for the next
500 seconds.
 The first equation is based on L(t) which
defines the number of link changes.


Simulation Results (Cont.)

The formula to calculate the time average of the
normalized link change is.


If N(t) is a constant N the equation is.


If N(t) is a function of time the equation is.

Simulation Results (Cont.)
Simulation Results (Cont.)
Simulation Results (Cont.)