Copyright © 2002 OPNET Technologies, Inc. 1 Random Waypoint Mobility Model Empirical Analysis of the…

Copyright © 2002 OPNET Technologies, Inc. 1

Random Waypoint Mobility Model

Empirical Analysis of the Mobility Factor for the Random Waypoint Model1542 Case Studies

Jabin Song and Leonard E. MillerWireless Communication Technologies GroupAdvanced Network Technologies DivisionNIST, Gaithersburg, MD



Introduction• Evaluation of performance of various wireless ad hoc network

routing protocols– Largely done via simulation– Node mobility model

» One aspect of a simulation scenario» Determines how frequently links change» Relates to the performance (e.g., affects overhead traffic for maintenance of routes)» Need a mobility measure to characterize the motion of nodes and to compare

simulations → Mobility Factor (MF)

• In this paper,– OPNET simulations are performed for random waypoint mobility model– Used a slightly modified equation for MF of Larsson and Hedman [7]– Provide useful guidance for designing simulation scenario for ad hoc

network[7] T. Larsson and N. Hedman, “Routing Protocols in Wireless Ad-hoc Networks-A Simulation Study,” Master’s Thesis at Lulea University of

Technology, Stockholm, 1998.



Random Waypoint Mobility Model• Operation

– Select a random destination (within the specified area)– Select a random speed (0 < v ≤ max_speed)– Move– After reaching the destination, pause a random time (0 < p ≤ max_pause_time)

• Process Model



Mobility Factor (MF)• Mi

– MF for node i– Average change of the distance to all other nodes during a sample time (t)

» T = Kt» N: Number of nodes» dij(t): Distance between nodes i and j at time t

• MF– Average MF of the nodes in the network

where dij(t) is the distance between nodes i and j at time t and N is the number of nodes.

N

iiM

NMF

1

1

1

0

1 1K

i i ik

M A k t A k tK t

N

jiji td

NtA

1

)(1

1)(



Simulation and Results• Simulation Parameters

• Results– Relationship between MF and the maximum node speed– Results for single-hop connectivity– Results for multi-hop connectivity

Parameters Values

Simulation Time 1 hour (and 10 minutes)

Maximum Speed 1 ~ 10 m/s

Pause Time 1 second

Transmission Range 250 meters

Network Area 1 km2 (1 1 kilometer)

Number of Nodes 20



MF vs. Maximum Speed of Nodes

•Each symbol represents an independent simulation run.

•“Average” is the mean value of 20 independent runs.•MF is almost a linear function of speed.



Results for Single-Hop Connectivity (1/3)

• Analytical Results– Node distribution of random waypoint

mobility model» Not uniform distribution [12]

Peak in the middle of the area Decrease to zero at the border of the area Symmetric in all directions from the

center Density function of node’s position:

where D D square area

– E{# Neighbors} = 4.69» Agrees well with the simulation

result

Avg. Number of Neighbors

2 23 2 3 2

( , )6 6 6 6

XYf x y x x y yD D D D

[12] C. Bettstetter and C. Wagner, “The Spatial Node Distribution of the Random Waypoint Model,” Proc. 1st German Workshop on Mobile Ad-Hoc Networks (WMAN’02), Ulm, Germany, March 25-26, 2002.

Not a function of MF



Results for Single-Hop Connectivity (2/3):

Single-Hop Connectivity Change Rate•For a node pair, a single-hop connectivity change

occurs when they either move into or out of transmission range from each other.

•Single-hop connectivity change rate has a linear relationship with MF.



Results for Single-Hop Connectivity (3/3)

Avg. Duration of Single-Hop Connection (sec)

Distributions of Single-Hop Connection Duration•Duration is normalized (multiplied)

by the maximum node speed.•“Total” is the distribution for all values of the maximum node speeds.

•For different maximum speeds, the normalized distributions are very similar.

Inversely proportional to MF



Results for Multi-Hop Connectivity (1/3)• Assumption

– Multi-hop connectivity of a pair of nodes holds if there exists at least one single/multi-hop path between them.

– Example» Connection between node A and D: single-hop → two-hop link» No multi-hop connectivity change

C

D

A

B

E

C

D

AA

B

E

Node A'sTransmission Range

Node B'sTransmission Range

Node A'sTransmission Range

Node B'sTransmission Range



Results for Multi-Hop Connectivity (2/3)

Multi-Hop Connectivity Change Rate

Avg. Number of Multi-Hop Connections

Not a function of MF Almost a linear function of MF



Results for Multi-Hop Connectivity (3/3)

Avg. Duration of Multi-Hop Connection (sec)

Inversely proportional to MF



Conclusion• Studied relationship between the MF and various aspects of ad hoc network

– Via OPNET simulation of the random waypoint mobility model» Relationship between MF and the maximum node speed: Linear function of MF» Single-hop connectivity

Average number of neighbors: • Not a function of MF and agrees well with the analytical result shown in the paper

Single-hop connectivity change rate:• Strong linear relationship with MF

Average duration of single-hop connections:• Inversely proportional to MF

Distributions of single-hop connection durations:• Very similar independent of the maximum node speed

» Multi-hop connectivity Average number of multi-hop connections:

• Not a function of MF Multi-hop connectivity change rate:

• Linear relationship with MF Average duration of multi-hop connections:

• Inversely proportional to MF

– Can be used for simulation evaluation of ad hoc routing protocols

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Copyright © 2002 OPNET Technologies, Inc. 1 Random Waypoint Mobility Model Empirical Analysis of the…