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



Algorithms and ComplexityMotivation & Problem

traffic jam

How to notify other cars on the road about traffic jam?



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



Algorithms and ComplexityAgenda

1. Model & System Architecture

2. Size approximation

3. Broadcast

4. Experimental evaluation



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




Division in geographic sectors

For evaluations

we assume sector length of 250 meters




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




Time division between size approximation, leader election and broadcast

Size approximation

Leader election

Broadcast

one time unit




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




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




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)




Every node hears a successful transmission with probability pr

…

sector with traffic jam

Leader transmits broadcast message



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




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




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




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




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



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




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




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




Final approximation

c computed numerically, dependent on smallest number of stations in sector expected

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



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)



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




Thank you for your attention!Thank you for your attention!

International Graduate School of Dynamic Intelligent Systems

Reliable Broadcasting without Collision Detection… … in an Automotive Scenario

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