Alpha Coverage: Bounding the Interconnection Gap for

Vehicular Internet Access

Presented by: Prasun Sinha Authors: Zizhan Zheng†, Prasun Sinha† and Santosh Kumar*

†The Ohio State University, * University of Memphis

Internet Access for Mobile VehiclesApplications

◦ 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

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Current Approach I (of II): Full CoverageWireless 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 Maphttp://wifi.google.com/city/mv/apmap.html

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Current Approach II (of II): Opportunistic Service via In-Situ APsPrototype

◦ 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 gapOur solution: an intermittent coverage model that

provides predictable data service to mobile users at low cost

Internet

AP

AP

AP

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

EvaluationFuture Work

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Road Network Model and Problem Statement 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 A0 µ V [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 points A in GR so that when new APs are deployed at these locations, A0 [ A provides the desired coverage.

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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

serviceChallenges

◦ Even verifying -Coverage is NP-complete since there is a reduction from HAMILTONIAN PATH to it

◦ Simplified models are needed

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Alpha Coverage w/o Route InformationA 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

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-Coverage N -Coverage

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Alpha Coverage w/o Route Information (Cont.)

Polynomial time verifiableThe 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

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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

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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

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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

Simulation Setting (Cont.)

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Simulation Results

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

Inter-contact gap (sec)

= 3000m

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Future WorkImprove 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

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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).