Alpha Coverage: Bounding the Interconnection Gap for Vehicular Internet Access

1. Alpha Coverage: Bounding the Interconnection Gap for Vehicular Internet Access Presented by: PrasunSinha Authors: ZizhanZheng†, PrasunSinha† and Santosh Kumar* †The Ohio State University, * University of Memphis

2. Internet Access for Mobile Vehicles • Applications • Infotainment • Cargo tracking • Burglar tracking • Road surface monitoring • Current Approaches • Full Coverage • Wireless Wide-Area Networking (WWAN) • Fully Covered WiFi Mesh • Opportunistic Service • Roadside WiFi

3. Current Approach I (of II): Full Coverage • Wireless Wide-Area Networking • 3G Cellular Network • 3GPP LTE (Long Term Evolution) • WiMAX • Either long range coverage (30 miles) or high data rates (75 Mbps per 20 MHz channel) • 3 Mbps downlink bandwidth reported in one of the first deployments in US • Google WiFi for Mountain View • 12 square miles, 400+ APs • 1 Mbps upload and download rate • Not very practical for large scale deployment due to the prohibitive cost of deployment and management Google Wifi Coverage Map http://wifi.google.com/city/mv/apmap.html

4. Current Approach II (of II): Opportunistic Service via In-Situ APs • Prototype • Drive-Thru Internet (Infocom’04,05) • In-Situ Evaluation • DieselNet (Sigcomm’08, Mobicom’08) • Interactive WiFi connectivity (Sigcomm’08) • Cost-performance trade-offs of three infrastructure enhancement alternatives (Mobicom’08) • MobiSteer (Mobisys’07) • Handoff optimization for a single mobile user in the context of directional antenna and beam steering • Cabernet (Mobicom’08) • Fast connection setup (QuickWiFi) and end-to-end throughput improvement (CTP) • Problems • Opportunistic service, no guarantee • Unpredictable interconnection gap Internet AP AP AP Our solution: an intermittent coverage model that provides predictable data service to mobile users at low cost

5. Roadmap • Alpha Coverage – An Intermittent Coverage Model • A general definition – intuitive but intractable • Two simplifications • Alpha Network Coverage (N-Coverage) • Applies when route information is unknown • Ex: Burglar tracking • Allows a factor log (n) approximation • Alpha Path Coverage (P-Coverage) • Applies when route information is given • Ex: bus trace in DieselNet, cached model in Mobisteer • Allows a more efficient factor log (n) approximation • Evaluation • Future Work

6. Road Network Model and Problem Statement v1 v2 v3 • Model • Model a road network R as an undirected graph GR with edge length at most  (by inserting artificial intersections if needed). • Model a movement as a path on GR (not necessarily ending at intersections). • Model access points as points on GR (modeling the worst case of communication range). • Given GR and A0µV [GR] that models a set of APs previously deployed • Determine if the deployment provides the desired coverage (to be defined), and if not • Find a minimum set of pointsA in GR so that when new APs are deployed at these locations, A0[A provides the desired coverage. v4 v5 v9 v8 v6 v7 v1 v2 v3 s v4 v5 v9 t v7 v8 v6

7. Alpha Coverage: an Intermittent Coverage Model • A deployment provides -Coverage to a road network R if any path of length  on GR touches at least one point representing an access-point. • Features • Provides a guarantee on the worst case inter-contact gap • Provides an estimation of the cumulative data service • Challenges • Even verifying -Coverage is NP-complete since there is a reduction from HAMILTONIAN PATH to it • Simplified models are needed

8. Alpha Coverage w/o Route Information • A deployment provides Network Coverage of distance  ( N-Coverage for short)if any path f(a,b) with dist(a,b) (graph distance) at least  is covered by at least one AP • –Coverage implies  N–Coverage, but not vice versa s s v1 v1 v2 v2 v3 v3 t t v5 v9 v9 v4 v4 v5 -Coverage N -Coverage  = 5 v7 v8 v6 v7 v8 v6

9. Alpha Coverage w/o Route Information (Cont.)  = 2 v1 v2 v3 • Polynomial time verifiable • The optimization problem ( N-Cover) is NP-hard • Reduction from VERTEX COVER restricted to triangle-free, 3-connected, cubic planar graphs • O(log |V|) approximation • Assumption: New APs are deployed only at the vertices of GR (real or artificial road intersections) • Introducing a factor of 2 • Reduce  N-Cover to node version low diameter graph decomposition • GVY algorithm • High computation time complexity for large networks v4 v5 v9 v6 v7 v8 v1 v3 v4 v6 v8

10. Alpha Coverage with Route Information • Motivation: use route information to design a more efficient algorithm • Assumption: a set of paths F is given where |F| = O(p(|V|)) • Ex 1) a set of shortest paths obtained from a road network database • Ex 2) a set of most frequently traveled paths learned from historical traffic data • Decompose each given path into -paths • A deployment provides Path Coverage of distance  ( P-Coverage for short) if any -path in F is covered by at least one AP. • Polynomial time verifiable, the optimization problem is still NP-hard • O(log |V|) approximation: reduce P-Cover to Minimum Set Cover

11. Simulation Setting • Road network • A 4km x 4km region around the center of Franklin County, OH • About 1000 intersections, 1300 road segments • Obtained from 2007 Tiger/Line Shapefiles + Mercator projection • Moving scenarios • Restricted random way point: each movement follows a shortest path and has length at least  • 5 mobile nodes, moving 1 hour each, 10 scenarios • Various speed limits • Ns-2 simulation • The transmission range of each AP is 100m

12. Simulation Setting (Cont.) • Deployment methods • P–Coverage • Rand-1: a set of randomly selected vertices of GR • Rand-2: a set of points on randomly selected edges of GR • Rand-3: the region is divided into 50m x 50m cells; APs are deployed at the centers of a set of randomly selected cells. An instance of P -Cover,  = 3000 m

13. Simulation Results Standard deviation (sec) CDF Inter-contact gap (sec) = 3000m  (m) • 21 APs are used • The maximum gap for P-Coverage is about 214 sec, bounded by the time spent on two adjacent moves • The maximum gap for a random deployment can be larger than 2000 sec

14. Future Work • Improve the efficiency of  N-Coverage • Combinatorial algorithms for fractional vertex multicut • Connected -Coverage • Connect each AP to at least one of the gateways with Internet backhaul • Joint Coverage and connectivity optimization • A bound on the number of hops to gateways • (,)-Coverage: Enabling Assured Data Service • Guarantees that each user moving through a path of length  has access to at least  units of data. • Challenges: variable data rates, traffic density, and contact durations; unknown association schedules

15. Alpha Coverage w/o Route Information (Cont.) • Polynomial time verifiable • The optimization problem, called N-Cover, is NP-hard • There is a reduction from VERTEX COVER restricted to triangle-free, 3-connected, cubic planar graphs • O(log |V|) approximation: reduce N-Cover to Minimum Vertex Multicut • Assumption: New APs are deployed only at the vertices of GR (real or artificial road intersections) => introducing a factor 2 • Step1: Find the set of -pairs, treat their midpoints as terminals • Step2: Solving the fractional vertex multicut problem -- the dual of node version maximum multicommodity flow problem • Step 3: Rounding the solution by low diameter graph decomposition (GVY).