A Standard Measure of Mobility for Evaluating Mobile Ad Hoc Network PerformanceByJoseph CharboneauKarthik Raman

MANET

Unpredictable topology changes. Performance related to efficiency of

routing protocol.Performance studies are done with

simulations.

Performance Measure

ProblemThere 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 onAverage speedMaximum speedPause timeRate of link changesMobility factor

ProblemStill no unified quantitative measure of mobility.

Performance Measure (Cont.)

The study approached in this paper is a solution for unified quantitative measure of mobility.

SolutionUse 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.ni(t), 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

Rij(t)=F(dij(t)) Where F(.) is a function of the distance.

Remoteness (Cont.)

Requirements that function F(.) must meet.

a. F(0)=0, limx→∞F(x)=1

b. dF(x)/dx ≥ 0 for all x ≥ 0

c. dF(x)/dx|x=0=0

d. limx→∞dF(x)/dx=0

e. dF(x)/dx|x=R ≥ dF(x)/dx for all x ≥ 0

Remoteness (Cont.)

Requirements of function F(.) defined.a. Normalizes F(.) to have a unity maximum value.b. Guarantees that the remoteness is monotonically

increasing function of distance.c. and d. give the boundary condition of F(.), which

guarantee that the remoteness of a node at extreme locations does not change with movement.

e. 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.

F(x) = 1/Γ(r)

With λ=(r-1)/R where r can be a non-integer. r is the sensitivity to the remoteness at

communication range.

x

r rxde

0

1 2,0,

Mobility Measure

Mobility measure is defined in terms of the time derivatives of the remoteness.

N is the number of nodes and Mi(t) is a measure of the relative movement of other nodes seen by i.

1

0

)(1

)(

N

i

i tMN

tM

1

0

))((1

1)(

N

j

iji tdFdt

d

NtM

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

dttMT

M

0

)(1

Mobility Measure (Cont.)

If the function chosen for F(.) is the function discussed earlier then the mobility measure function will be.

1

0

)(1

)(

N

i

Gi

G tMN

tM

1

0

' ))(()(1

1)(

N

j

ijijGi tdftd

NtM

Mobility Measure (Cont.)

If the function chosen for F(.) is the identity function then the mobility measure function will be.

1

0

)(1

)(

N

i

Ii

I tMN

tM

1

0

' )(1

1)(

N

j

ijIi td

NtM

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 & speedSpeed uniformly distributed between min and

max speedsPauses 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 ΔtSpeed and direction are uniformly distributed

between their min and max valuesAt 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.

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.)

Simulation Results (Cont.)