1. Jaroslaw Kutylowski 1 HEINZ NIXDORF INSTITUTE University 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

2. Jaroslaw Kutylowski 2 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Motivation & Problem traffic jam How to notify other cars on the road about traffic jam?

3. Jaroslaw Kutylowski 3 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Motivation & 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

4. Jaroslaw Kutylowski 4 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Agenda 1.Model & System Architecture 2.Size approximation 3.Broadcast 4.Experimental evaluation

5. Jaroslaw Kutylowski 5 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & 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

6. Jaroslaw Kutylowski 6 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & System Architecture Division in geographic sectors For evaluations we assume sector length of 250 meters

7. Jaroslaw Kutylowski 7 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & 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

8. Jaroslaw Kutylowski 8 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & System Architecture Time division between size approximation, leader election and broadcast Size approximation Leader election Broadcast one time unit

9. Jaroslaw Kutylowski 9 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & 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

10. Jaroslaw Kutylowski 10 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & 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

11. Jaroslaw Kutylowski 11 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & 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)

12. Jaroslaw Kutylowski 12 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Model & System Architecture Every node hears a successful transmission with probability p r … sector with traffic jam Leader transmits broadcast message

13. Jaroslaw Kutylowski 13 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Size approximation Leader election needs approximate number of stations in sector Upper bound on number of stations in sector known – N max Multi-round algorithm each round has duration of M j steps every active station chooses randomly step to transmit in a round each station counts number of successful transmissions if station has successful transmission – station gets inactive

14. Jaroslaw Kutylowski 14 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Size approximation Defining parameters M j and number of rounds First possibility Compute M j so that the expected number of successful transmission per time step in each round is maximized For M j we compute the expected number of stations which get inactive S j – computation of M j+1 relies on it Disadvantage: deviations from expectation can cause low approximation ratio

15. Jaroslaw Kutylowski 15 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Size approximation Second possibility Taking deviations into account –using more rounds –giving better reliability Why? we can compute the deviation of S j from its expectation -- number of stations which get inactive with high probability computation of M j+1 gets more reliable

16. Jaroslaw Kutylowski 16 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Size 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

17. Jaroslaw Kutylowski 17 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Size approximation Take n=N max =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

18. Jaroslaw Kutylowski 18 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Broadcast Algorithm Leader transmits message if it has not been resent from its sector often enough No acknowledgements Key problem unreliability of wireless link (parameter p r ) transmission from sector S to S+1 –only a fraction of nodes from sector S+1 received message

19. Jaroslaw Kutylowski 19 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Broadcast 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

20. Jaroslaw Kutylowski 20 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Broadcast 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

21. Jaroslaw Kutylowski 21 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Final approximation c computed numerically, dependent on smallest number of stations in sector expected Broadcast

22. Jaroslaw Kutylowski 22 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Broadcast 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

23. Jaroslaw Kutylowski 23 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Experimental 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 reached the first sector average time 31 unit time slots (3.1 second)

24. Jaroslaw Kutylowski 24 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Conclusion 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

25. Jaroslaw Kutylowski 25 HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity Thank you for your attention! International Graduate School of Dynamic Intelligent Systems