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Fair allocation aims13_pp upload

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  • Hello my name is Patrick Poullie and I will present a mechanism to allocate multiple divisible divisble resources over multiple consumers.
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    • 1. © 2013 UZH, Slide 1 of 10 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/Problem Proportionality Algorithm Outline Conclusions
    • 2. © 2013 UZH, Slide 2 of 10 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?
    • 3. © 2013 UZH, Slide 3 of 10 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
    • 4. © 2013 UZH, Slide 4 of 10  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
    • 5. © 2013 UZH, Slide 5 of 10 Formal Definition
    • 6. © 2013 UZH, Slide 6 of 10 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
    • 7. © 2013 UZH, Slide 7 of 10 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 X 0 X 0 6.5 XX 5.5 XX 0 X
    • 8. © 2013 UZH, Slide 8 of 10 Formal Definition
    • 9. © 2013 UZH, Slide 9 of 10 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
    • 10. © 2013 UZH, Slide 10 of 10 Thank You, for Your Attention! Questions? Comments?
    • 11. © 2013 UZH, Slide 11 of 10 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
    • 12. © 2013 UZH, Slide 12 of 10 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)
    • 13. © 2013 UZH, Slide 13 of 10 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
    • 14. © 2013 UZH, Slide 14 of 10 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
    • 15. © 2013 UZH, Slide 15 of 10 Greediness Alignment Algorithm Outline Random decision or based on greediness Receive Demands Calculate Greediness Return Greediness Are resources scarce? Return bundles Trim bundles Yes No
    • 16. © 2013 UZH, Slide 16 of 10 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., Trimming Business Policies Monitoring