HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Algorithms for Radio Networks
Winter Term 2005/2006
08 Feb 2006
15th Lecture
Christian Schindelhauer
[email protected]
1
HEINZ NIXDORF INSTITUTE
Mobility in Wireless Networks
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 Models of Mobility
– Cellular
– Random Trip
– Group
– Combined
– Non-Recurrent
– Particle based
 Discussion
– Mobility is Helpful
– Mobility Models and Reality
Algorithms for Radio Networks
2
Models of Mobility
Random Trip Mobility
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Random Walk
Random Waypoint
Random Direction
Boundless Simulation Area
Gauss-Markov
Probabilistic Version of the Random Walk Mobility
City Section Mobility Model
Zur Anzeige wird der QuickTime™
Dekompressor „TIFF (LZW)“
benötigt.
[Bai and Helmy in
Wireless Ad Hoc
Networks 2003]
Algorithms for Radio Networks
3
Models of Mobility
Random Waypoint Mobility Model
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
[Johnson, Maltz 1996]
 move directly to a randomly chosen destination
 choose speed uniformly from
 stay at the destination for a predefined pause time
[Camp et al. 2002]
Algorithms for Radio Networks
4
HEINZ NIXDORF INSTITUTE
Random Waypoint Considered Harmful
[Yoon, Liu, Noble 2003]
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 move directly to a randomly
chosen destination
 choose speed uniformly from
 stay at the destination for a
predefined pause time
 Problem:
– If vmin=0 then the average
speed decays over the
simulation time
Algorithms for Radio Networks
5
HEINZ NIXDORF INSTITUTE
Random Waypoint Considered Harmful
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 The Random Waypoint (Vmin,Vmax, Twait)-Model
– All participants start with random position (x,y) in [0,1]x[0,1]
– For all participants i  {1,...,n} repeat forever:
•
•
•
•
•
Uniformly choose next position (x’,y’) in [0,1]x[0,1]
Uniformly choose speed vi from (Vmin, Vmax]
Go from (x,y) to (x’,y’) with speed vi
Wait at (x’,y’) for time Twait.
(x,y)  (x’,y’)
 What one might expect
– The average speed is (Vmin + Vmax)/2
– Each point is visited with same probability
– The system stabilizes very quickly
 All these expectations are wrong!!!
Algorithms for Radio Networks
6
HEINZ NIXDORF INSTITUTE
Random Waypoint Considered Harmful
What one might expect
– The average speed is
(Vmin + Vmax)/2
– Each point is visited with
same probability
– The system stabilizes very
quickly
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Reality
– The average speed is much
smaller
• Average speed tends to 0 for
Vmin = 0
– The location probability
distribution is highly skewed
– The system stabilizes very
slow
• For Vmin = 0 it never
stabilizes
All these expectations are
wrong!!!
Why?
Algorithms for Radio Networks
7
Random Waypoint Considered Harmful
The average speed is much smaller
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 Assumption to simplify the
analysis:
1. Assumption:
 Replace the rectangular area
by an unbounded plane
 Choose the next position
uniformly within a disk of
radius Rmax with the current
position as center
2. Assumption:
 Set the pause time to 0:
Twait = 0
 This increases the average
speed
 supports our argument
Algorithms for Radio Networks
8
Random Waypoint Considered Harmful
The average speed is much smaller
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 The probability density function of speed of each node is then for
 given by
 since fV(v) is constant and
Algorithms for Radio Networks
9
Random Waypoint Considered Harmful
The average speed is much smaller
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 The Probability Density Function (pdf) of travel distance R:
 The Probability Density Function (pdf) of travel time:
Algorithms for Radio Networks
10
Random Waypoint Considered Harmful
The average speed is much smaller
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 The Probability Density Function (pdf) of travel time:
Algorithms for Radio Networks
11
Random Waypoint Considered Harmful
The average speed is much smaller
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 The average speed of a single node:
Algorithms for Radio Networks
12
Models of Mobility
Problems of Random Waypoint
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
In the limit not all positions occur
with the same probability
If the start positions are uniformly
at random
– then the transient nature of
the probability space changes
the simulation results
Solution:
– Start according the final
spatial probability distribution
Algorithms for Radio Networks
13
Models of Mobility
Combined Mobility Models
[Bettstetter 2001]
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Algorithms for Radio Networks
14
Models of Mobility:
Particle Based Mobility
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Motivated by research on mass
behavior in emergency situations
– Why do people die in mass
panics?
Approach of [Helbing et al. 2000]
– Persons are models as
particles in a force model
– Distinguishes different
motivations and different
behavior
• Normal and panic
Algorithms for Radio Networks
15
Models of Mobility:
Particle Based Mobility: Pedestrians
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Speed:
– f: sum of all forces
– : individual fluctuations
Target force:
– Wanted speed v0 and direction e0
Social territorial force
Attraction force (shoe store)
Pedestrian force (overall):
Algorithms for Radio Networks
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Models of Mobility:
Particle Based Mobility: Pedestrians
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
This particle based approach predicts
the reality very well
– Can be used do design panicsafe areas
Bottom line:
– All persons behave like mindless
particles
Algorithms for Radio Networks
17
Models of Mobility
Particle Based Mobility: Vehicles
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 Vehicles use 1dimensional space
 Given
– relative distance to the
predecessor
– relative speed to the
predecessor
 Determine
– Change of speed
Algorithms for Radio Networks
18
Models of Mobility:
Particle Based Mobility: Pedestrians
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 Similar as in the pedestrian model
 Each driver watches only the car in front of him
 No fluctuation




s(vi) = di + Ti vi, di is minimal car distance, Ti is security distance
h(x) = x , if x>0 and 0 else, Ri is break factor
si(t) = (xi(t)-xi-1(t)) - vehicle length
Δvi = vi-vi-1
 where
Algorithms for Radio Networks
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Models of Mobility
Particle Based Mobility: Vehicles
Reality
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Simulation
with GFM
Algorithms for Radio Networks
20
Discussion:
Mobility is Helpful
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
 Positive impacts of mobility:
 Improves coverage of wireless sensor networks
 Helps security in ad hoc networks
 Decreases network congestion
– can overcome the natural lower bound of throughput of
– mobile nodes relay packets
– literally transport packets towards the destination node
Algorithms for Radio Networks
21
Discussion:
Mobility Models and Reality
Discrepancy between
– realistic mobility patterns and
– benchmark mobility models
Random trip models
– prevalent mobility model
– assume individuals move
erratically
– more realistic adaptions exist
• really realistic?
– earth bound or pedestrian
mobility in the best case
HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Group mobility
– little known
– social interaction or physical
process?
Worst case mobility
– more general
– gives more general results
– yet only homogenous
participants
– network performance
characterized by
crowdedness
Algorithms for Radio Networks
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HEINZ NIXDORF INSTITUTE
University of Paderborn
Algorithms and Complexity
Christian Schindelhauer
Thanks for your attention!
End of 15th lecture
Next exercise class:
Next mini exam
Oral exams
Last meeting
Tu 15 Jan 2006, 1.15 pm, F1.110
Mo 13 Feb 2006, 2pm, FU.511
Tu 20 Feb/We 22 Feb.2006
(email: [email protected])
Mo 06 Mar 2006, 7pm, 11. Gebot,
Winfriedstrasse, Paderborn
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