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Algorithms for Radio Networks Winter Term 2005/2006 08 Feb 2006 15th Lecture. Christian Schindelhauer [email protected]. Mobility in Wireless Networks. Models of Mobility Cellular Random Trip Group Combined Non-Recurrent Particle based Discussion Mobility is Helpful - PowerPoint PPT Presentation
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1
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Algorithms for Radio NetworksWinter Term 2005/2006
08 Feb 200615th Lecture
Christian Schindelhauer
Algorithms for Radio Networks 2
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Mobility in Wireless Networks
Models of Mobility
– Cellular
– Random Trip
– Group
– Combined
– Non-Recurrent
– Particle based Discussion
– Mobility is Helpful
– Mobility Models and Reality
Algorithms for Radio Networks 3
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of MobilityRandom Trip Mobility
Random WalkRandom WaypointRandom DirectionBoundless Simulation AreaGauss-MarkovProbabilistic Version of the Random Walk MobilityCity 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 4
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
move directly to a randomly chosen destination choose speed uniformly from stay at the destination for a predefined pause time
Models of MobilityRandom Waypoint Mobility Model
[Camp et al. 2002]
[Johnson, Maltz 1996]
Algorithms for Radio Networks 5
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian 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
Random Waypoint Considered Harmful[Yoon, Liu, Noble 2003]
Algorithms for Radio Networks 6
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Random Waypoint Considered Harmful
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 7
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
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
All these expectations are wrong!!!
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
Why?
Algorithms for Radio Networks 8
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Random Waypoint Considered HarmfulThe average speed is much smaller
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 9
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Random Waypoint Considered HarmfulThe average speed is much smaller
The probability density function of speed of each node is then for
given by
since fV(v) is constant and
Algorithms for Radio Networks 10
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Random Waypoint Considered HarmfulThe average speed is much smaller
The Probability Density Function (pdf) of travel distance R:
The Probability Density Function (pdf) of travel time:
Algorithms for Radio Networks 11
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Random Waypoint Considered HarmfulThe average speed is much smaller
The Probability Density Function (pdf) of travel time:
Algorithms for Radio Networks 12
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Random Waypoint Considered HarmfulThe average speed is much smaller
The average speed of a single node:
Algorithms for Radio Networks 13
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of MobilityProblems of Random Waypoint
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 14
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of MobilityCombined Mobility Models [Bettstetter 2001]
Algorithms for Radio Networks 15
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of Mobility:Particle Based Mobility
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 16
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of Mobility:Particle Based Mobility: Pedestrians
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 17
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of Mobility:Particle Based Mobility: Pedestrians
This particle based approach predicts the reality very well
– Can be used do design panic-safe areas
Bottom line:– All persons behave like mindless
particles
Algorithms for Radio Networks 18
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of MobilityParticle Based Mobility: Vehicles
Vehicles use 1-dimensional space
Given– relative distance to the
predecessor– relative speed to the
predecessor Determine
– Change of speed
Algorithms for Radio Networks 19
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of Mobility:Particle Based Mobility: Pedestrians
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 20
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Models of MobilityParticle Based Mobility: Vehicles
Reality Simulationwith GFM
Algorithms for Radio Networks 21
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Discussion: Mobility is Helpful
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 22
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
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
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
23
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Thanks for your attention!End of 15th lectureNext exercise class: Tu 15 Jan 2006, 1.15 pm, F1.110Next mini exam Mo 13 Feb 2006, 2pm, FU.511Oral exams Tu 20 Feb/We 22 Feb.2006
(email: [email protected])Last meeting Mo 06 Mar 2006, 7pm, 11. Gebot,
Winfriedstrasse, Paderborn