Alpha Coverage: - PowerPoint Presentation

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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 MemphisSlide2

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

Slide3

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+ APs1 Mbps upload and download rate Not very practical for large scale deployment due to the prohibitive cost of deployment and management

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Google

Wifi

Coverage Map

http://wifi.google.com/city/mv/apmap.htmlSlide4

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)ProblemsOpportunistic service, no guaranteeUnpredictable interconnection gap

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Our solution: an intermittent coverage model that provides predictable data service to mobile users at low cost

Internet

AP

AP

APSlide5

Roadmap Alpha Coverage – An Intermittent Coverage ModelA general definition – intuitive but intractable Two simplifications

Alpha Network Coverage (



N

-Coverage)Applies when route information is unknown Ex: Burglar trackingAllows a factor log (n) approximationAlpha Path Coverage (P -Coverage) Applies when route information is given Ex: bus trace in DieselNet, cached model in MobisteerAllows a more efficient factor log (n) approximationEvaluationFuture WorkSlide6

Road Network Model and Problem Statement Model

Model a road network

R

as an undirected graph

G

R 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 A

0 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.6

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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. FeaturesProvides a guarantee on the worst case inter-contact gapProvides an estimation of the cumulative data serviceChallengesEven verifying -Coverage is NP-complete since there is a reduction from HAMILTONIAN PATH to itSimplified 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 8

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

= 5

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-Coverage



N

-

CoverageSlide9

Alpha Coverage w/o Route Information (Cont.)Polynomial time verifiable

The optimization problem (

N

-Cover) is NP-hard

Reduction from VERTEX COVER restricted to triangle-free, 3-connected, cubic planar graphsO(log |V|) approximationAssumption: New APs are deployed only at the vertices of GR (real or artificial road intersections) Introducing a factor of 2Reduce 

N -Cover to node version low diameter graph decomposition

GVY algorithmHigh computation time complexity for large networks

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

= 2Slide10

Alpha Coverage with Route InformationMotivation: 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 databaseEx 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-hardO(log |V|) approximation: reduce P -Cover to Minimum Set Cover

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Simulation Setting Road network

A

4

km x

4

km region around the center of Franklin County, OHAbout 1000 intersections, 1300 road segments Obtained from 2007 Tiger/Line Shapefiles + Mercator projection

Moving scenariosRestricted 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

100m11Slide12

Deployment methodsP –Coverage

Rand-1: a set of randomly selected vertices of

G

R

Rand-2: a set of points on randomly selected edges of

GRRand-3: the region is divided into 50m x 50m cells; APs are deployed at the centers of a set of randomly selected cells.12

An instance of 

P -Cover,  = 3000

m

Simulation Setting (Cont.)Slide13

Simulation Results

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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



(m)

CDF

Standard deviation (sec)Slide14

Future WorkImprove the efficiency of 

N

-

Coverage

Combinatorial algorithms for fractional vertex

multicut Connected -CoverageConnect each AP to at least one of the gateways with Internet backhaulJoint Coverage and connectivity optimizationA 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 graphsO(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 2Step1: 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).

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