Fair allocation aims13_pp upload

© 2013 UZH, CSG@IFI

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Fair Allocation of Multiple Resources Using a Non-monetary Allocation Mechanism

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

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

AIMS 2013, Barcelona, Spain, June 26, 2013

Motivation/ProblemProportionality

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 fair manner

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


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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


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Trimming Example

1.5 X

-0.5 0.5

-2.5-1.52.51.5

2.5 X

6.5 X

5.5 X0 X 0

6.5 XX

5.5 XX0 X


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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 allocationand


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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 for Allocation 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 Mäder, 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


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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

ManagedResource

Greediness

Other Metrics

BusinessIndicators

Actions, e.g., TrimmingBusinessPolicies

Monitoring

Fair allocation aims13_pp upload

Technology

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