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

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

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

Advantages of Histogram-Based Approach Scalable E.g. 1500-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

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.

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

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

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

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 ((270+650)/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

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

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

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.

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

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

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