Quantifying Fairness in Queueing Systems: Principles

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Quantifying Fairness in Queueing Systems
Principles Applications Approaches
Hanoch Levy School of Computer Science, Tel Aviv
University
Jointly with Benjamin Avi-Itzhak, RUTGERS
University David Raz, Tel-Aviv University
HETNETs July, 2004
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Why Fairness in Queues?
Why Queues?
Not Fair!!!
To provide FAIRNESS in waiting/service
Queue A Fairness Management Facility
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Why Fairness in Queues? (2)

• Fairness inherent/crucial part of queues

• Recent studies, Rafaeli et. al. 2003
  (experimental psychology)
• Experiments on humans in queue scenarios
• Fairness in queue is very important to people
• Perhaps even more than delay itself!

The issue
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Outline

• Queue Model
• Job-Based systems, Flow-Based systems
  applications
• The performance issue Delay vs. Service
• The granularity level How fine
• The physical entities seniority, service
  requirement, resources
• The Fairness Measures Overview properties
• Application perspective

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Queue Model (single server)
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Job-Based vs. Flow-BasedApplications

• JOB BASED
• Customer Job
• Applications
• Networking Application level equipment Web
  server, file server
• Supermarket, Bank, public office alike
• Call center
• Computer system

• FLOW BASED
• Customer Flow
• Applications
• Networkingnetwork level equipment
• Routers, gateways, load-balancers

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History Queueing Theory and Fairness

• Queueing theory Decades of research
• Delay of individual
• Practical Applications many diverse
• Fairness in queues
• Many importance statements
• Importance of fairness Larson (1988), Palm
  (1953), Mann (1969), Whitt (1984), Rothkopf
  Rech (1987)
• Very little analysis (job fairness)
• Morris Wang (85).
• Avi-Itzhak Levy (96)
• Bender, Chakrabarti . Muthukrishnan (1998),
  Wierman Harchol-Balter (2003), Harchol-Balter
  et. al. (2003)
• Raz, Levy, Avi-Itzhak (2004)

Exception Flow Fairness

• ? We know only little about queue (job) fairness!
  
• ? More complex than measuring individual delay!

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Designing a Metrics - Keep in mind

• To be used by
• Researchers
• Designers / operators
• Customers (appeal to)

• Applications

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The performance issues Delay vs. Service

• Delay
• Job delay (waiting time, sojourn time)
• Traditional queueing-theory measure
• The major factor when service is guaranteed

• Job (service) Completion
• Have the job done
• Less popular in queueing theory
• Applies when service is not guaranteed
• Ticket line for scarce tickets

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Granularity of Fairness Evaluation

• At what granularity level, should fairness be
  evaluated

• Individual
• Scenario
• System (steady state)

• All are important
• Individual, scenario build confidence (scale of
  reference) in metrics
• System to evaluate systems/policies
• Note All exist for individual waiting times

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Dealing with StochasticsActual measures vs.
Expected values

• Actual measure
• Fairness evaluated for every scenario
• Expectation used to summarize scenarios

• Expected values
• Expected performance per customer class evaluated
• Classes compared to each other gt fairness

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The Physical Factors
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Size and Seniority preference principles
(requirements)

• Seniority
• Size

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Size and Seniority preference principles
(requirements)

• Seniority principle
• Weak All jobs same service times ? if ailt aj
  then more fair to complete service of Ji before
  Jj
• Strong Ji and Jj same service times

• Service-requirement principle
• Weak All jobs same arrival times ? if silt sj
  then more fair to complete service of Ji before
  Jj
• Strong Ji and Jj same arrival times

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How Scheduling policies meet the principles (are
fair by principle)
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The Size vs. Seniority Dilemma

• Mr. Short vs. Mrs. Long
• Is it more fair to serve Short ahead of Long? By
  how much?

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Review of Measures (jobs based)

• Seniority based

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Measure 1 Order (seniority) Fairness

• Avi-Itzhak Levy (96)
• Axioms (for G/D/1) what happens to unfairness
  measure when interchanging customers
• P1 Monotonicity in seniority difference of
  interchanged neighbors
• P2 Reversibility of neighbor interchange
• P3 Independence on position and time
• P4 Fairness change is not affected by customers
  not interchanged
• P4G interchange of non-neighbors

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Order Fairness results

• ai - Arrival time of customer i
• Di - Waiting displacement of customer i
• C gt 0, arbitrary constant
• Expected fairness per customer

• FCFS most fair (LCFS least)

• Thm Let (W, W) be the steady state waiting
  time under (policy, FIFO), then

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Order Fairness Properties Applicability

• Good for
• S. times identical
• S. times dont matter
• Issue is Job completion
• Applications
• Scarce-ticket lines
• Some call-centers

• FCFS is most fair (LCFS least)
• Intuition concepts
• Peoples strong belief in order fairness

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Measure 2 service-time Fairness

• Bender, Chakrabarti . Muthukrishnan (1998),
  Harchol-Balter et. al. (2003)
• Wierman Harchol-Balter (2003)
• Propose a Fairness Criterion
• Emphasis on service requirement
• Slowdown for job of size x compute ET(x)/x
• If the slowdown is lower then 1/(1-?) for all x
  and ? - FAIR
• Classification of a large variety of policies

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Service-time Fairness Results

• Classification (not measure) of a large variety
  of policies
• Conclusion
• FCFS is Always UNFAIR
• LCFS (preemptive) is FAIR

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S. time Fairness Properties Applicability

• Good for
• A. times identical
• A. times not known / dont see the queue
• Your size is always the same
• Issue is wash seniority by averaging.
• Advantage relatively simple analysis

• Applications Computer systems (?)

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Measure 3 Resource Allocation Fairness

• Raz, Levy, Avi-Itzhak (04)
• Aim at the dilemma between size and seniority
• Focus on fair share of resources
• Ideal At t, each customer deserves 1/N(t) of
  system resources (N(t) customers(t))
• Compare warranted service with granted service

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Resource allocation Fairness Results

• PS most fair
• Reacts to both s.time and seniority
• S.times identical Fairness monotone in seniority
• A. times identical Fairness monotone in s.times
• FCFS gt LCFS (seniority dominant)
• FCFS lt LCFS (s. time dominant)

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Resource Allocation Fairness Applicability

• Good for
• S. times and A. times arbitrary
• Issue is Waiting times

• Applications
• Waiting lines where resources guaranteed
• Call centers (non-scarce resources)
• Web services
• Supermarkets
• Airport services

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Job-Based vs. Flow-BasedApplications

• JOB BASED
• Customer Job
• Applications
• Networking Application level equipment Web
  server, file server
• Supermarket, Bank, public office alike
• Call center
• Computer system

• FLOW BASED
• Customer Flow
• Applications
• Networkingnetwork level equipment
• Routers, gateways, load-balancers

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A word on flow-based measures

• Deal with flows (of packets)
• Interested mainly in throughput
• Literature
• Fair bandwidth allocation (network)
• MinMax fairness (Jaffe (81))
• Proportional Fairness (Kelly (97))
• Fair Scheduling
• Weighted Fair Queueing (WFQ)
• Demers, Keshav and Shenker (1990), Greenberg and
  Madras (1992), Parekh (1992), Parekh and Gallager
  (1993), (1994), Golestani (1994), Rexford,
  Greenberg and Bonomi (1996), Bennet and Zhang
  (1996), others.

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Measure 4 PS proximity WFQ/RFB literature

• Scheduling fairness measures
• Worst Case deviation from PS (extreme values)
• Relative Fairness Bound (Golestani (94))

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Measure 4 PS proximity WFQ/RFB literature

• Absolute Fairness Bound (AFB) (Greenberg and
  Madras (1992) and Keshav (1997))

• Maximum (time) discrepancy between schedule and
  PS
• Applying to jobs
• Try PS completion discrepancy of job
• LCFS FCFS infinity!
• Most non-PS based (non-WFQ) infinity! (SJF, LJF,
  SRPT..)
• Good for very precise PS imitations

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What fits? Go by the application
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Concluding remarks

• Fairness in Queues is important
• Measures must
• Fit applications
• Agree with ones intuition / be consistent
• Researcher, designer, customer
• Yield to analysis
• Research of subject in its infancy
• Much more to study
• Scheduling policies
• Weights
• Multiple queues /servers
• Complex structures
• Relations between measures
• Other measures

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Closing Words Why Study Fairness in Queues (5
reasons)

• The Fundamental (Q fairness)
• Isnt fairness why we have queues (for human
  services) in the first place?
• The Scientific evidence (Rafaeli et. al. 2003)
• Fairness in queues important to people / perhaps
  gt delay
• The Inductive reasoning
• WFQ 10s of papers fairness on O(1)
  microsecond jobs!!
• The Challenge
• We know very little on Queue fairness
• The problem is harder than Q delay!

• The Practical Relax your nerves