Transcript Beyond Dominant Resource Fairness David Parkes (Harvard) Ariel Procaccia (CMU) Nisarg Shah (CMU) Motivation • Allocation of multiple resources (e.g., CPU, RAM, bandwidth) • Users have heterogeneous demands • Today:

Beyond Dominant
Resource Fairness
David Parkes (Harvard)
Ariel Procaccia (CMU)
Nisarg Shah (CMU)
Motivation
• Allocation of multiple
resources (e.g., CPU, RAM,
bandwidth)
• Users have heterogeneous
demands
• Today: fixed bundles (slots)
• Allocate slots using single
resource abstraction
2
The DRF mechanism
• Assume proportional demands (a.k.a.
Leontief preferences)
• Example:
o
o
o
User wishes to execute multiple
that requires 2 CPU and 1 RAM
Indifferent between 5 CPU and 2 RAM,
and 2 GB
Happier with 4.2+2.1
• Dominant resource fairness [Ghodsi
et al. 2011]: equalize largest
shares
3
DRF animated
User 1
alloc.
User 2
alloc.
Total
alloc.
4
Properties of DRF
• Pareto optimality
• Envy freeness: users do not want to
swap allocations
• Sharing incentives (a.k.a. fair
share, proportionality, IR): users
receive at least as much value as
an equal split
• Strategyproofness: reporting true
demands is a dominant strategy
• Exciting application of fair
division theory!
5
Indivisible tasks
• Demands specified as fraction
of resource r that user i needs
to run one instance of its task
• User’s utility strictly
increases with number of
complete instances of task
6
PO+SI+SP are incompatible
User 1
demand
User 2
demand
Allocation
User 1
demand
User 2
demand
Allocation
7
Envy freeness
• PO and EF are trivially
incompatible
• Need to relax the notion of
envy freeness [Budish 2011,
Lipton et al. 2004, Moulin and
Stong 2002]
• Envy freeness up to one bundle
(EF1) = i does not prefer j’s
after removing one copy of i’s
task
• Theorem: PO+EF1+SP impossible
8
Sequential Minmax
•
•
•
•
SI+EF1+SP trivial
SI+PO+SP, EF1+PO+SP impossible
Can we achieve PO+SI+EF1?
The SEQUENTIAL MINMAX mechanism:
allocate at each step to
minimize maximum allocated
share after allocation
• Theorem: Mechanism is PO+SI+EF1
9
Sequential Minmax illustrated
User 1
demand
User 1
alloc.
User 2
demand
User 2
alloc.
Total
alloc.
10
Discussion
• Additional results in paper
o
o
An extension of DRF to settings
zero demands and endowments,
satisfies group strategyproofness
Lower bounds on social welfare
maximization
• Current work: dynamic fairness
11