Fair Coalitions for Power-Fair Coalitions for Power-Aware RoutingAware Routing

ARO Review ARO Review April 2004April 2004

Carl A. GunterCarl A. GunterUniversity of PennsylvaniaUniversity of Pennsylvania

Joint with Ratul Guha and Saswati Joint with Ratul Guha and Saswati SarkarSarkar

Overview of ProjectsOverview of Projects Secure and Open Embedded DevicesSecure and Open Embedded Devices

– Designing software for smart cardsDesigning software for smart cards Models and protection measures for DoS and Models and protection measures for DoS and

network resource management network resource management – DoS preventionDoS prevention– Power managementPower management

Privacy and Access ControlPrivacy and Access Control– Secure web servicesSecure web services– WorkflowWorkflow– Location Based ServicesLocation Based Services

Secure TunnelsSecure Tunnels– Ipsec and symbolic simulation Ipsec and symbolic simulation

Carl Gunter

Alwyn Goodloe

Michael McDougall

Benefits of Power-Aware Benefits of Power-Aware RoutingRouting

Sharing between wireless nodes has Sharing between wireless nodes has well-proven benefitswell-proven benefits– Routing can yield two orders of Routing can yield two orders of

magnitude in power savingsmagnitude in power savings Some sharing can be achieved by Some sharing can be achieved by

direct designdirect design Other sharing can be achieved by Other sharing can be achieved by

adapting to context and exploiting ad adapting to context and exploiting ad hoc opportunities for mutual benefithoc opportunities for mutual benefit

Reason for Savings from Reason for Savings from RoutingRouting

Power costs for wireless transmission Power costs for wireless transmission are proportional to a power of the are proportional to a power of the distance over which the transmission distance over which the transmission must occurmust occur

Transmitting a packet a distance of Transmitting a packet a distance of dd is proportional to is proportional to d d 44

ExampleExample

d

e

f

e 4 + 2f 4 < d 4

Benefit RegionBenefit Region

B C

A benefits by routing through B but not by routing through C

Default RoutingDefault Routing

(-2,0) (-1,0) (0,0)

(2,.5)

(1,1)

Cost for red: 20Cost for brown: 19

Optimal Power Aware Optimal Power Aware RoutingRouting

(-2,0) (-1,0) (0,0)

(2,.5)

(1,1)

1 2

2

1.73

1

Cost for red: 9 Benefit for red: 20-9=11Cost for brown: 3.6 Benefit for brown: 19-3.6=15.4 Benefit for network: 11+15.4=26.4

CoalitionsCoalitions

Sharing between individual nodes may be Sharing between individual nodes may be beneficial because of a relationship beneficial because of a relationship between the nodesbetween the nodes– Common ownerCommon owner– Common purposeCommon purpose

Given a group of sharing nodes, when is it Given a group of sharing nodes, when is it worthwhile to collaborate with another worthwhile to collaborate with another group?group?

We refer to a sharing arrangement We refer to a sharing arrangement between two or more groups as a between two or more groups as a coalitioncoalition

Coalitions do Not Benefit Pairs Coalitions do Not Benefit Pairs of One-Member Groupsof One-Member Groups

Only the red group can benefit from shared routing!

Multi-Member Groups May Multi-Member Groups May Benefit from CoalitionsBenefit from Coalitions

This routing allows both groups to benefit from shared routing.

This Benefit Can Be This Benefit Can Be SubstantialSubstantial

50 nodes randomly located and randomly formed into groups

But it May Not be EqualBut it May Not be Equal

This routing allows both groups to benefit from shared routing,but the red nodes have more opportunity to benefit.

Optimal Routing Provides Greatest Optimal Routing Provides Greatest Benefit to the Network at the Expense Benefit to the Network at the Expense

of Fairnessof Fairness

Units are in watts. Each axis represents the benefit for a group

But What is Fair?But What is Fair?

How should groups that can benefit How should groups that can benefit from forming a coalition share the from forming a coalition share the mutual benefit?mutual benefit?

Approach: use Approach: use max-min fairnessmax-min fairness, an , an idea from fair routing developed for idea from fair routing developed for wireline networks.wireline networks.

Max-Min FairnessMax-Min Fairness

A A benefit vectorbenefit vector is a pair is a pair (x(x11,…,x,…,xnn)) where where xxii is a benefit to party is a benefit to party ii..

A benefit vector is A benefit vector is feasiblefeasible if it can be if it can be realized by a possible sharing.realized by a possible sharing.

A feasible benefit vector A feasible benefit vector (x(x11,…,x,…,xnn)) is is max-max-min fairmin fair if for each if for each ii, , xxii cannot be increased cannot be increased while maintaining feasibility without while maintaining feasibility without decreasing decreasing xxjj for some for some jj for which for which xxjj x xii..

A A fair coalition routingfair coalition routing is a routing that is a routing that induces a max-min fair benefit vector.induces a max-min fair benefit vector.

TheoremTheorem

The following properties hold for fair The following properties hold for fair coalition routing for any collection of coalition routing for any collection of groups:groups:

1.1. There is always a unique max-min fair There is always a unique max-min fair benefit vector.benefit vector.

2.2. This vector can be calculated efficiently This vector can be calculated efficiently using linear programming techniques.using linear programming techniques.

3.3. When there are two groups, the When there are two groups, the components of the benefit vector are components of the benefit vector are equal.equal.

Max-Min Fair GeometryMax-Min Fair Geometry

Max-Min Fair Benefit VectorFeasible BenefitVectors

Fair Coalition RoutingFair Coalition Routing

(-2,0) (-1,0) (0,0)

(2,.5)

(1,1)

1 2

1.78

.22

.78

Cost for red: 9 Opt Benefit for red: 20-9=11Cost for brown: 3.6 Opt Benefit for brown: 19-3.6=15.4 Opt Benefit for network: 11+15.4=26.4

Fair benefit for red: 11.9Fair benefit for brown: 11.9Fair benefit for the network: 23.8Cost of fairness: 26.4-23.8=2.6

1 2

21

How Much Does Fairness How Much Does Fairness Cost?Cost?

Average cost is 18% compared to the average benefit of 46%

Two Counter-Intuitive Two Counter-Intuitive ObservationsObservations

There are instances where three There are instances where three groups can form a beneficial coalition groups can form a beneficial coalition even when no pair of the groups can. even when no pair of the groups can.

Fairness sometimes entails routing Fairness sometimes entails routing away from the access point.away from the access point.

Three but Not TwoThree but Not Two

Routing Away from the Access Routing Away from the Access PointPoint

(-2,0) (-1,0) (0,0)

(2,.5)

(1,1)

1 2

.27.73

1.73

Trust IssuesTrust Issues

Groups must be Groups must be able to able to economically economically enforce routing for enforce routing for their members and their members and trusted coalition trusted coalition partners.partners.

How much does How much does this cost?this cost?

Experiment with Experiment with IPSec on laptopsIPSec on laptops

80

82

84

86

88

90

92

94

96

Time in Minutes

PlainAuthEncr

Future WorkFuture Work

Negotiation and middleware.Negotiation and middleware. Mobility (incremental re-routing).Mobility (incremental re-routing). Families of sensors.Families of sensors. Other forms of sharingOther forms of sharing

– MemoryMemory

Fresh Perspectives on Fresh Perspectives on DesignDesign

Power efficiency and routing are Power efficiency and routing are central concepts.central concepts.

New paradigms involve significant New paradigms involve significant architectural latitude.architectural latitude.

Game-theoretic and economic Game-theoretic and economic perspectives provide foundations for perspectives provide foundations for scalability and measurement.scalability and measurement.