1. Histogram-Based Density Discovery in Establishing Road Connectivity
Kevin Lee, Jiajie Zhu, Jih Chung Fan, Mario Gerla
University of California, Los Angeles VNC, 10/28/09

2. Why Do We Need Density?
Using density information to avoid traps in VANET
What is the relationship between density and connectivity? D ?
What is a good density algorithm that allows us to establish accurate connectivity of the road? S
Nodes bunched up at the intersection => Can’t assume uniform density
Credit: M. Fiore and J. H¨arri, ACM MobiHoc 2008

3. Histogram-Based Density Discovery Algorithm
Break up the roads into segments
Nodes within a segment keep track of density in that segment in P2P fashion
Nodes keep a histogram of density Ni for other segments by broadcast
Road is connected if
Get the density from node whose distance is closest to the segment center just because nodes at the segment center know better the density of the road segment 1 2 1 2 1 2
Segment center 1 2 ? 1 2 1 2 1 2

4. Advantages of Histogram-Based Approach
Scalable
E.g meter road, 250-meter segment length
The number of segments is 6 (1500/250)
P2P can only store 6 cars, not enough
More accurate
Each segment size is smaller than the road length
Connectivity correlates better with segment density than road density
Need a slide on [Seg/Radio Range]
NOT CONNECTED

5. Why Optimal Segment Size?
No fluctuation of density due to influx of cars
A histogram of segment densities correlates well with road connectivity
Note that Optimal Segment Size is NOT necessarily the radio range
Imagine in the extreme case where a car’s radio range covers multiple segments. Every time a car moves in and out, that segment’s density has to be updated. This kind of frequent update does not make road connectivity any more accurate.

6. Density Accuracy
Intuition: Given a car’s Spd and convergence time Conv, it should stay within the segment (thus not change the density of a segment)
SegSizeopt >= Conv * Spd
The convergence time is the time that a car knows the density of ALL segments

7. Convergence Time Convergence time does NOT vary with segment size
Convergence time varies with either traffic or road length
RL 900m
RL 1000m

8. Minimum Segment Size
Extrapolate the relationship between road length and convergence, density and convergence
Use [SegSizeopt >= Conv * Spd] to obtain relationship between SegSizeopt, road length, and density

9. Connectivity Accuracy
Places upperbound on the optimal segment size
Definition: the number of runs that are identified correctly/total number of runs
1,000 runs
300 runs are connected, 270 are identified correctly
700 runs are not, 650 are identified correctly
92% accurate (( )/1000)
30 false negatives
50 false positives
As the road length approaches to the road length, it becomes peer to peer. Connectivity accuracy actually decreases
For some segment size x
False negatives: not connected when in fact it is
False positive: connected when in fact it is not
Note that connectivity accuracy is the majority opinion of the nodes on the road segment

10. Segment Size vs. Connectivity Accuracy
Connectivity accuracy drops when segment size increases
Periodic rise and drop due to last segment not evenly divisible by segment size
RL 900m
RL 1000m
Radio range can cover despite there is no car in the last segment. May indicate that the road is disconnected when in fact it is not (false negatives). The false negatives increase until the last segment size is greater than the radio range.
Maximum segment size is before the first drop in connectivity accuracy because connectivity generally drops
SegSizemax = 325m
SegSizemax = 375m

11. Optimal Segment Size
For each road length and density, find SegSizemin and SegSizemax
Average is SegSizeopt
Use average for sensitivity. Can also use SegSizemax.

12. Evaluation
Connectivity accuracy between P2P and histogram- based approach
Road Percentage Connectivity (RPC) vs. Connectivity Accuracy (CA)
If road is connected, CA = RPC
If road is not, CA = 1 – RPC
Broadcast overhead between P2P and histogram- based approach
1,000 traces from VanetMobiSim
RPC, road percentage connectivity, tells how many percentages of the cars say the road is connected. If the road is actually connected, it is RPC. If it not, it is 1- RPC.
The mobility traces were generated by VanetMobiSim [27], an open source and freely available realistic vehicular traffic
generator for network simulators.

13. Connectivity Accuracy between P2P and Histogram
P2P underperforms when density is low
This is due to sparse density that models cluster behavior

14. Broadcast Overhead between P2P and Histogram
Broadcast/node/sec
P2P has scalability issue as it needs to keep track of unique cars

15. Conclusion Systematic way to obtain optimal SegSize
Evaluation shows histogram-based scheme’s scalability