1 heinz nixdorf institute university of paderborn algorithms and complexity christian...
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Algorithms for Radio Networks 3 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Christian Schindelhauer Models of Mobility Random Trip Mobility Random Walk Random Waypoint Random Direction Boundless Simulation Area Gauss-Markov Probabilistic Version of the Random Walk Mobility City Section Mobility Model [Bai and Helmy in Wireless Ad Hoc Networks 2003]TRANSCRIPT
1
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Algorithms for Radio NetworksWinter Term 2005/2006
01 Feb 200614th Lecture
Christian [email protected]
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
Brownian Motion (microscopic view)– speed and direction are chosen randomly in each time step
(uniformly from and [0, 2] )
Random Walk – macroscopic view– memoryless– e.g., for cellular networks– movement from cell to cell– choose the next cell randomly– residual probability
Models of MobilityBrownian Motion, Random Walk
[Camp et al. 2002]
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
Models of MobilityRandom Waypoint Mobility Model
[Camp et al. 2002]
[Johnson, Maltz 1996]
Algorithms for Radio Networks 6
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 7
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 8
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 9
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 10
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 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 distance R:
The Probability Density Function (pdf) of travel time:
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HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityChristian Schindelhauer
Thanks for your attention!End of 12th lectureNext lecture: We 08 Feb 2006, 4pm, F1.110Next exercise class: Th 09 Feb 2006, 1.15 pm, F2.211 or Tu 14 Jan 2006, 1.15 pm, F1.110Next mini exam Mo 13 Feb 2006, 2pm, FU.511