Transcript Algorithms for Radio Networks 08 Feb 2006 15th Lecture Christian Schindelhauer
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]
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Mobility in Wireless Networks
Models of Mobility – Cellular – Random Trip – Group – Combined – Non-Recurrent – Particle based Discussion – Mobility is Helpful – Mobility Models and Reality
HEINZ NIXDORF INSTITUTE
University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 2
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
HEINZ NIXDORF INSTITUTE
University of Paderborn Algorithms and Complexity Christian Schindelhauer [Bai and Helmy in Wireless Ad Hoc Networks 2003] Zur Anzeige wird der QuickTime™ Dekompressor „TIFF (LZW)“ benötigt.
Algorithms for Radio Networks 3
Models of Mobility Random Waypoint Mobility Model
[Johnson, Maltz 1996] move directly to a randomly chosen destination choose speed uniformly from stay at the destination for a predefined pause time
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University of Paderborn Algorithms and Complexity Christian Schindelhauer [Camp et al. 2002] Algorithms for Radio Networks 4
Random Waypoint Considered Harmful
[Yoon, Liu, Noble 2003] move directly to a randomly chosen destination choose speed uniformly from stay at the destination for a predefined pause time Problem: – If v min =0 then the average speed decays over the simulation time
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 5
Random Waypoint Considered Harmful
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University of Paderborn Algorithms and Complexity Christian Schindelhauer The Random Waypoint (V min ,V max , T wait )-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 v i from (V min , V max ] • Go from (x,y) to (x’,y’) with speed v i • Wait at (x’,y’) for time T wait .
• (x,y) (x’,y’) What one might expect – The average speed is (V min + V max )/2 – Each point is visited with same probability – The system stabilizes very quickly All these expectations are wrong!!!
Algorithms for Radio Networks 6
Random Waypoint Considered Harmful
What one might expect – The average speed is (V min + V max )/2 – Each point is visited with same probability
HEINZ NIXDORF INSTITUTE
University of Paderborn Algorithms and Complexity Christian Schindelhauer Reality – The average speed is much smaller • Average speed tends to 0 for V min = 0 – The location probability distribution is highly skewed – The system stabilizes very quickly All these expectations are wrong!!!
– The system stabilizes very slow • For V min stabilizes = 0 it never Why?
Algorithms for Radio Networks 7
Random Waypoint Considered Harmful The 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 R max with the current position as center 2. Assumption: Set the pause time to 0: T wait = 0 This increases the average speed supports our argument
HEINZ NIXDORF INSTITUTE
University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 8
Random Waypoint Considered Harmful The average speed is much smaller
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University of Paderborn Algorithms and Complexity Christian Schindelhauer The probability density function of speed of each node is then for given by since f V (v) is constant and Algorithms for Radio Networks 9
Random Waypoint Considered Harmful The average speed is much smaller
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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
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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
The average speed of a single node:
HEINZ NIXDORF INSTITUTE
University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 12
Models of Mobility Problems 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
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 13
Models of Mobility Combined Mobility Models
[Bettstetter 2001]
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 14
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
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 15
Models of Mobility: Particle Based Mobility: Pedestrians
Speed: – f: sum of all forces – : individual fluctuations Target force: – Wanted speed v 0 Social territorial force and direction e 0 Attraction force (shoe store) Pedestrian force (overall):
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 16
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
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 17
Models of Mobility Particle Based Mobility: Vehicles
Vehicles use 1 dimensional space Given – relative distance to the predecessor – relative speed to the predecessor Determine – Change of speed
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Algorithms for Radio Networks 18
Models of Mobility: Particle Based Mobility: Pedestrians
Similar as in the pedestrian model
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University of Paderborn Algorithms and Complexity Christian Schindelhauer Each driver watches only the car in front of him No fluctuation s(v i ) = d i + T i v i , d i is minimal car distance, T i h(x) = x , if x>0 and 0 else, R i is break factor is security distance s i (t) = (x i (t)-x i-1 (t)) - vehicle length Δv i = v i -v i-1 where Algorithms for Radio Networks 19
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
Positive impacts of mobility: Improves coverage of wireless sensor networks Helps security in ad hoc networks
HEINZ NIXDORF INSTITUTE
University of Paderborn Algorithms and Complexity Christian Schindelhauer 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 22
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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