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