AIMS13 Fair Resource Allocation

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2013 UZH, CSG@IFI Slide 1 of 10

Fair Allocation of Multiple Resources Usinga Non-monetary Allocation Mechanism

Patrick Poullie, Burkhard Stiller,1 Department of Informatics IFI, Communication Systems Group CSG,

University of Zrich UZH{poullie,stiller}@ifi.uzh.ch

AIMS 2013, Barcelona, Spain, June 26, 2013

Motivation/Problem

Proportionality

Algorithm OutlineConclusions


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Motivation

Shared computing , e.g., (private) clouds or clusters,

offer different resources to consumers

CPU, RAM, mass storage, bandwidth

If offered as predefined or at least static bundles

Drawback: Some resources of some consumers are idle Advantage: guaranteed resources

If offered as shared resources

Drawback: No resources are guaranteed, when too many

consumers are active simultaneously Advantage: flexible allocation

Can both advantages be combined?


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Problem Statement

To design an allocation mechanism, that

Scales with the number of consumers and resources

Linear runtime designated

Needs minimal input information

Complete preference function may not be available

Does need no monetary compensation

Monetary compensation may not be possible or desired

Allows to receive equal share and allocates leftovers/unused

resources in a fairmanner

To define fair leftover allocation Complicated for multiple resources with different demands

Very different to scheduling


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Bundle: Share of resources a consumer receives

If resources are received beyond equal share other

resources have to be released

Greediness measures to which degree this is the case

Equal greediness is fair

Proportionality of Bundles


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Formal Definition



Greediness Alignment Algorithm

Round-based, where each round each consumer

demands a bundle

Consumers only receive bundle after the last round

Greediness is calculated and fed back to consumers

who should consider it for demand in the next round After last round every consumer receives demanded

bundle

If resources are scarce, greediness is aligned: greedy

consumers are trimmed stronger Incentive to consider feedback for next round/demand

Trimming to enforce fair leftover reallocation



Trimming Example

1.5 X

-0.5 0.5

-2.5

-1.5

2.5

1.5

2.5 X

6.5 X

5.5 X0 X 0

6.5 XX

5.5 XX0 X



Formal Definition


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Conclusions and Future Work

Scalability

Computation of greediness is linear

Minimal input information

Only demands are submitted and adapted

No monetary compensation Equal share guarantee and fair leftover reallocation

Allows to receive equal share and aligns greediness

Future Work

Trimming algorithm will be defined to optimize runtime Game theory to evaluate incentive compatibility

efficiency of allocation

and


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Thank You, for Your Attention!

Questions?

Comments?


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Related Work

A. Kumar et al Almost Budget-balanced Mechanisms

for Allocation of Divisible Resources

allocation problem on the uplink multiple access channel

Only one resource and involves biddings

R. Jain et al: An Efficient Nash-Implementation

Mechanism for Divisible Resource Allocation

auctioning bundles of multiple divisible goods (links)

Combined to path/ combination of multiple paths possible

S. Yang, B Hajek: VCG-Kelly Mechanisms forAllocation of Divisible Goods: Adapting VCG []

network operator aims to select an outcome that is efficient


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Related Work in Scheduling

Traffic Scheduling

Andreas Mder, Dirk Staehle An Analytical Model for Best-

Effort Traffic over the UMTS Enhanced Uplink

Dimitrova et al. Analysis of packet scheduling for UMTS EUL

- design decisions and performance evaluation

Focus on: time component, interference, location

Singe resource: Channel

Multi Processor Scheduling

Dan McNulty et al A Comparison of Scheduling Algorithms

for Multiprocessors

Focus on migrating task between processors

Interchangeable resources (processors)


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Related Work in Economics

S. Brams. Mathematics and Democracy: p. 271 et

seq.: Adjusted Winner

No resource dependcies

S. Brams et al. The Undercut Procedure: An Algorithm

for the Envy-free Division of Indivisible Items

Two people constrained [TP, UC]

L. Schulman, V. Vazirani Allocation of Divisible Goods

Under Lexicographic Preferences

efficiency, incentive compatibility, and fairness properties BUT lexicographic preference function


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Definition of Fairness

Not to be understood as envy freeness

Collides with other desirable criteria

Pareto efficiency

Calculation likely not scalable

Equality of defined greediness is considered fair

Every consumer releases of his equal share what he

receives from others

Strategy proofness is also not always desirable

Guarantees Pareto efficiency but cripples welfare

Mechanisms not need to be perfect but

comprehensible


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Greediness Alignment Algorithm Outline

Random decision orbased on greediness

Receive

Demands

Calculate

Greediness

Return

Greediness

Are resourcesscarce?

Return

bundles

Trim

bundles

Yes

No


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Business Policy Management

Algorithm allows to dynamically allocate resources and

to make equal/fixed share guarantees

Higher resource utilization while compliment with SLAs

Comprehensible framework to introduce dynamic

resource allocation to general terms and SLAs

Service description for fair use

Managed

Resource

Greediness

Other Metrics

Business

Indicators

Actions, e.g., TrimmingBusiness

Policies

Monitoring

AIMS13 Fair Resource Allocation

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