# Presentation: 483002

## Empirical Analysis of the Mobility Factor for the Random Waypoint Model

**1542 Case Studies**

- Jabin Song and Leonard E. Miller
*Wireless Communication Technologies Group*
*Advanced Network Technologies Division*
*NIST, 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)

*M**i*
*MF* for node *i*
- Average change of the distance to all other nodes during a sample time (***t*)
*T = K****t*
*N*: Number of nodes
*d**ij*(*t*): Distance between nodes *i* and *j* at time *t** *
*MF*
- Average *MF* of the nodes in the network
-    where *d**ij*(*t*) is the distance between nodes *i* and *j* at time *t** *and *N* is the number of nodes.

## 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**

- [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

## 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