User Mobility Model based on Street Pattern G. Paschos E. Vagenas S. Kotsopoulos

University of Patras - Greece

Introduction This is a mobility model for cellular communications ‡ The analysis is based on the street pattern of the cell area ->urban environment ‡

Monte Carlo simulation of vehicle movement ->statistical processing ‡ Parameter extraction ->mobility model ‡

Design Goals ‡ ‡ ‡

To develop a modern mobility model To incorporate the street pattern To use the model in order to calculate Sojourn Time statistics using an area map Our Model Knowledge of user behaviour

Sojourn Time Statistics

…further processing

Sojourn Time

Sojourn Time ‡

Remaining Sojourn Time

The sojourn time statistics are very important for the teletraffic analysis

Assumptions The model is applied in an urban environment with relatively low traffic ‡ The vehicles float rather than move ‡ Velocity, Delays, Traffic etc are considered statistic values with fixed parameters ‡ The Sojourn time follows a gamma distribution* ‡

*[1]

Hong and Rappaport, “Traffic model and performance analysis of cellular radio telephone with prioritized and nonprioritized handoff procedures” [2] R. Guerin, “Channel occupancy time distribution in a cellular radio system” [3] Bratanov and Bonek, “Mobility Model of Vehicle-Borne Terminals in Urban Cellular Systems”

systems

The gamma distribution 0.007

a −1

x f gamma (x ) = e a Γ(a )b

Sojourn Time p.d.f. for new call and handover call

0.006 0.005

Remaining Sojourn Time (new call) Sojourn Time (handover call)

0.004

⎧ a = 1.1 ⎨ ⎩b = 132

0.003 0.002 0.001 0

0

200

400

600

800

1000

Sojourn Time (sec)

1200

⎧a = 2.1 ⎨ ⎩ b = 86

−

x b

Results from the Monte Carlo Simulation -3

9

x 10

8

p.d.f.

7 6 5

Simulation data Sojourn Time Remaining Sojourn Time

4 3 2 1 0 0

200 400 600 800 1000 Sojourn Time - Remaining Sojourn Time (sec)

1200

The Model

Implementation Assumptions The pattern is firstly considered square ‡ The velocity follows a gaussian distribution ‡ The driver decides upon turning left or right or going straight ahead ‡ There is a three state delay in every crossroad. ‡

„ „ „

No delay for priority road A small delay for a non priority road An average delay for a traffic light

Analysis Diagram

Parameters Selection ‡

The traffic parameter ptr „ „

‡

An indicator of traffic lights percentage and/or priority crossings Usually 0.5 to

The Area of Block Ab „ „

Ab=a^2 Relative to Cell Radius

Results 450

1.2 a values of gamma pdf for a new call

b values of gamma pdf for a new call

1.15

400

1.1

350

1.05

300

1

250

0.95

0.85 0.8 1600

200

0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.9

4600

7600

10600

13600

16600

0.2 0.3 0.4 0.5 0.6 0.7 0.8

150 100 19600

Area of city Block Ab

50 1600

4600

10600

13600

16600

b values of gamma pdf for a handover call

a values of gamma pdf for a handover call

300

0.2 0.3 0.4 0.5 0.6 0.7 0.8

3

250 2.5

200

1.5

1 1600

150

0.2 0.3 0.4 0.5 0.6 0.7 0.8

2

4600

7600

10600

13600

Area of city Block Ab

16600

19600

Area of city Block Ab

350

3.5

7600

100 50

19600

0 1600

4600

7600

10600

13600

Area of city Block Ab

16600

19600

The model a nc

⎧⎪1.1034 − 0.311e −0.0001428571⋅ Ab , p tr ∈ [0.1,0.4 ) =⎨ ⎪⎩1.05374 + 0.1241525 ⋅ p tr − 0.311e −0.0001428571⋅ Ab , p tr ∈ [0.4,0.9]

bnc = 53.60435 + 70.2435 ⋅ ptr + (85.37414 + 495.558231⋅ ptr )e −0.00027405247⋅ Ab

ahc = 4 + 0.54 ⋅ ptr − (3.2 + 0.48 ⋅ ptr )e

(

)

− 4.5⋅10 −5 +1.3⋅10 −5 ⋅ ptr Ab

bhc = 34 + 32 ⋅ ptr + (82 + 400 ⋅ ptr )e −0.000261224⋅ Ab

A case study

Future Work The model will be extended to cover nonsquare street pattern ‡ The curve fitting will be performed using a genetic algorithm and a semantic function toolkit ‡ Measurements will take place in the case study area to validate and calibrate the model ‡

Thank you End of Presentation