Collision Reconstruction Methodologies Volume 1: Collision ...
Reliable Broadcasting without Collision Detection… … in an Automotive Scenario
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Transcript of Reliable Broadcasting without Collision Detection… … in an Automotive Scenario
Jaroslaw Kutylowski 1
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and Complexity
Reliable Broadcasting without Collision Detection…
…in an Automotive Scenario
Jaroslaw Kutylowski (UPB)
Filip Zagorski (WUT)
SOFSEM 2006
International Graduate School of Dynamic Intelligent Systems
Jaroslaw Kutylowski 2
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityMotivation & Problem
traffic jam
How to notify other cars on the road about traffic jam?
Jaroslaw Kutylowski 3
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityMotivation & Problem
Design limitations
• cheap hardware– no collision detection– low transmission speed– low transmission distance– interference range = 2 x transmission distance
• hard environmental conditions– curves, big trucks – transmission failures
• reliability is necessary
Jaroslaw Kutylowski 4
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityAgenda
1. Model & System Architecture
2. Size approximation
3. Broadcast
4. Experimental evaluation
Jaroslaw Kutylowski 5
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Hardware requirements• Synchronized clocks
• Location information (GPS)
• Successful / unsuccessful transmission
– collision information to sender– no information about collision to other stations
• a collision is not undistinguishable from no transmission at all
Jaroslaw Kutylowski 6
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Division in geographic sectors
For evaluations
we assume sector length of 250 meters
Jaroslaw Kutylowski 7
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Message about traffic jam produced in start sector
Message broadcasted from one sector to the next one• Unique leader in each sector• Leader changed frequently• Only leaders retransmit information
In each sector we need• Size approximation algorithm• Leader election algorithm• Broadcast algorithm
Jaroslaw Kutylowski 8
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Time division between size approximation, leader election and broadcast
Size approximation
Leader election
Broadcast
one time unit
Jaroslaw Kutylowski 9
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Transmission distance• for size approximation and leader election
transmission distance = one sector size • for broadcast
transmission distance = two sector sizes
Interference distance• for size approximation and leader election
transmission distance = two sector size • for broadcast
transmission distance = four sector sizes
Jaroslaw Kutylowski 10
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Time division between neighbor sectors• sectors numbered with consecutive IDs• a sector executes its algorithms only if
current time unit % 5 == sector ID % 5
Sector with ID%5==0
Sector with ID%5==1
Sector with ID%5==2
Sector with ID%5==3
Sector with ID%5==4
Sector with ID%5==0
one time unit
five time units
Jaroslaw Kutylowski 11
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Time division between neighbor sectors
Fact: when a sector is transmitting, the next sector can hear it without interference from other sectors
(the next sector transmitting is in distance 5 and its interference range is at most 4 sectors)
Jaroslaw Kutylowski 12
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityModel & System Architecture
Every node hears a successful transmission with probability pr
…
sector with traffic jam
Leader transmits broadcast message
Jaroslaw Kutylowski 13
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexitySize approximation
Leader election needs approximate number of stations in sector
Upper bound on number of stations in sector known – Nmax
Multi-round algorithm
• each round has duration of Mj steps
• every active station chooses randomly step to transmitin a round
• each station counts number of successful transmissions• if station has successful transmission – station gets inactive
Jaroslaw Kutylowski 14
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexitySize approximation
Defining parameters Mj and number of rounds
First possibility
Compute Mj so that the expected number of successful transmission per time step in each round is maximized
For Mj we compute the expected number of stations which get inactive Sj – computation of Mj+1 relies on it
Disadvantage: deviations from expectation can cause low approximation ratio
Jaroslaw Kutylowski 15
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexitySize approximation
Second possibility
Taking deviations into account– using more rounds– giving better reliability
Why?
• we can compute the deviation of Sj from its expectation -- number of stations which get inactive with high probability
• computation of Mj+1 gets more reliable
Jaroslaw Kutylowski 16
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexitySize approximation
Deviation from expectation given by
Increase M so that necessary probability is reached
Deviation from expectation Probability dependent on M
Number of stations which get inactive
Jaroslaw Kutylowski 17
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexitySize approximation
Take n=Nmax=100 (worst case)
First possibility: 264 steps in 8 rounds, perfect estimation of number of stations in 45% of experiments
Second possibility: 592 steps in 7 rounds, perfect estimation in 100% of experiments
Jaroslaw Kutylowski 18
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityBroadcast
Algorithm• Leader transmits message if it has not been resent from its
sector often enough• No acknowledgements
Key problem
• unreliability of wireless link (parameter pr)
• transmission from sector S to S+1– only a fraction of nodes from sector S+1 received
message
Jaroslaw Kutylowski 19
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityBroadcast
No acknowledgements• with link unreliability an acknowledgment is not reliable• leader may have received messages – others do not
• leader acknowledges message although intuitively it should not!
leader
Jaroslaw Kutylowski 20
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityBroadcast
Investigate probability that message will be retransmitted in sector S after i rounds from hearing it from S-1
these values are hard to compute!
We develop an approximation (lower bound) for the value of
P(i,x) describes the probability that message will reach sector S+i from S for the first time in exactly x rounds
Jaroslaw Kutylowski 21
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and Complexity
Final approximation
c computed numerically, dependent on smallest number of stations in sector expected
Broadcast
Jaroslaw Kutylowski 22
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityBroadcast
Some computed values• link reliability set to • 2.5 km length road, with 10 sectors
• probability to travel this distance in 20 time slots (2 seconds) is about 0.9
Jaroslaw Kutylowski 23
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityExperimental evaluation
Helbing-type cellular automaton• link reliability set to • 6.75 km length road, with 27 sectors• traffic jam in last sector, counting arrival time in first sector
• all broadcasts reachedthe first sector
• average time 31 unit timeslots (3.1 second)
Jaroslaw Kutylowski 24
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and ComplexityConclusion
We have shown
• complete system for traffic jam notification
• size approximation algorithm– not optimized for asymptotical performance– works well for small inputs
• analysis for broadcast on a line under assumption of link unreliability
Jaroslaw Kutylowski 25
HEINZ NIXDORF INSTITUTEUniversity of Paderborn
Algorithms and Complexity
Thank you for your attention!Thank you for your attention!
International Graduate School of Dynamic Intelligent Systems