How Fair is your Queue

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How Fair is your Queue
Hanoch Levy School of Computer Science, Tel Aviv
University
Jointly with Benjamin Avi-Itzhak, RUTGERS
University David Raz, Tel-Aviv University
March, 2004
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Why QUEUES?
Not Fair!!!
To provide FAIRNESS in waiting/service
Sophisticated queues ?to address fairness issues
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Queueing Theory, queues and fairness

• Queueing theory Decades of very deep and
  elaborate research
• Queueing structures / policies, distributions
• Focus on delay of individual Moments/
  distribution / optimal operations, many more!
• Practical Applications Efficient control /
  operation of
• Bank, computer system, web server, telecom
• Fairness in queues
• Many statements this is fair, that system is
  unfair.
• Very little analysis (job fairness)
• Larson (1988), Palm (1953), Mann (1969), Whitt
  (1984) Discuss justice related / overtaking
• Morris Wang (85).
• Avi-Itzhak Levy (96)
• Wierman Harchol-Balter (Sigmetrics 2003)
• ? We dont know how to quantify queue fairness!

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How Important is fairness in queues?

• FAIRNESS INHERENT/CRUCIAL part of queues

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

• WFQ 10s of papers fairness among jobs whose
  duration is O(1) microsecond

• Economic value of queues of humans
• O(1) of GNP?

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So What is the problem?

• Take social-science/economics
  utility-fairness measures and apply to queues

• HOW??? What is the PIE? A moving target

• The problem in a nutshell Short vs. Long

The difficulty (A) Whom to compare a customer
against?
The difficulty (B) Size vs. seniority dilemma
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Motivation / Questions

• Should Long be served ahead of Short?

• Is it fair?

• How fair (how much fair) is it to serve Short
  Ahead of Long?

• Quantify/ Measure Fairness in Waiting lines!

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Motivation / Questions (2)Do You like your
supermarket?

• How fair is a scheduling policy?

• E.g
• FIFO
• LIFO

• Multiple Queue (Multi server)
• Single queue (multi server)
• Queues by job size?

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Motivation / Questions (3)and your airport?

• Multiple Queue (Multi server)
• Single queue (multi server)
• Smith Whitt (81), Larson (87), Rothkopf Rech
  (87), Wolff (77, 87, 88)

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Applications (computer world)

• Internet revolution Service shift to computer
  systems.
• Responsibility of control shifts to computer
  programmer/operator
• Examples
• Call centers
• Web services
• How should I operate my web-server? FIFO? LIFO?
  Priorities?

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Related Work(1)

• Avi-Itzhak Levy (96)
• Axiomatic approach
• Departure pointemphasis Seniority (Order of
  service)
• If service times are identical ? variance of
  waiting time measures fairness
• Extend to service times
• When is it good?

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Recent Related Work

• Wierman Harchol-Balter (Sigmetrics 2003)
• Propose a Fairness Criterion
• Class-based approach For job of size x compute
  ET(x)/x
• If this is bounded by 1/(1-rho) for all x ? FAIR.
  
• Results Analyze the classification for a large
  variety of policies.
• FIFO (FCFS) is Always UNFAIR
• LIFO (preemptive) is FAIR.
• When is it good?

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Conflicting (disturbing) Views
Fair (Fairest?) ?
Unfair ?
Unfair (most?) ?
Fair ?
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Basic Requirements of a Queue Fairness measure

• Aim for standard ? Have a consistent
  view/intuition
• Deal with individual, scenario, and system
• Account for both seniority and service
  requirement
• Seniority Service times are identical
• Fairness is a function of seniority
• FIFO most fair / LIFO most unfair
• Senior ahead of junior is more fair
• Service requirement Arrival times are identical
• Fairness is a function of service requirement
• Short ahead of long is more fair
• Yields to analysis

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RAQFM A Resource Allocation Queueing Fairness
Measure

• Aims at meeting these requirements
• In particular
• Long vs. Short
• Seniority vs. service times

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Approach individual discrimination

• To whom should a job be compared? (moving
  target!)
• Compare to the public.
• Focus on server resources (aim at equal division)
• Weigh the warranted service with the granted
  service

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Basic Properties of RAQFM

• Resource allocation is proper zero-sum
  discrimination (work conserving, non idling)

• Eliminate Expected discrimination
• Reasonable distance from mean, Var(D),
  ED-ED.
• Measure of Unfairness

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Property 1 Processor Sharing Ultimate Fairness

• Single server queue
• Processor sharing service policy (Kleinrock (64),
  (67), Coffman, Muntz Trotter (70))

• ? VarD 0
• ? PS is the most fair policy!!

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Property 2 SENIORITY (identical service times)

• Single server queue
• Service times are all identical
• Arrival times are arbitrary
• Theorem 2
• Serving by order of seniority (FIFO) is most fair
• Serving in reverse order of seniority (LIFO) is
  most unfair
• Pushing a junior ahead of senior reduces fairness

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Property 3 Service Time (identical arrival
times)

• Single server queue
• Arrival times are all identical
• Service times are arbitrary

• Serving shortest job first (SJF) is most fair
• Serving Longest job first (LJF) is most unfair
• Pushing a large job ahead of small job reduces
  fairness

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Property 4 More advancedThe Long vs. Short case

• Single server queue
• Long and short arrive at different times

• Fairness of two orders depends on relative
  seniority and relative service times.

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Property 5 BoundsHow bad (good) can it be?

• Bound on individual discrimination
• Use for scale of reference / sanity check

• Bound on system discrimination

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Property 6 Locality of Comparison

• Measure can be evaluated by comparing all
  customers (across busy periods)
• Unique to RAQFM within a large function family.
• Important for fairness One should compare only
  relevant customers (within busy periods).

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Property 7 Discrimination Monotonic in Service
time

• THM For an arbitrary system, if service decision
  is independent of service time, then
• Discrimination monotonically increases with
  service time (deterministic)
• Larger customers get preferential service
• Discrimination monotonically increases with
  service time distribution
• ? justification to the prioritization of short
  jobs!

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RAQFM is Analyzable

• RAQFM yields to analysis via standard queueing
  theory techniques
• Can compute
• ED x (class discrimination)
• VarD (system unfairness)
• Conducted analysis for M/M/1 type Variety of
  service orders (FIFO, LIFO, ROS, more).
• Conducted analysis for Multi-queue / multi-class
  systems.

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Individual discrimination under FIFO M/M/1(
conditioned on customers found ahead)
Indifferent

• Discrimination as a function of customers found
  at queue

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System Unfairness Compare operation policies
PS Absolute Fairness!
LIFO Severe seniority discrimination
Empty system everyone is alone
FIFO no seniority discrimination

• System Unfairness as a function of system load

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How other measures relateBridging the gap

• Wierman Harchol-Balter (2003)
• FIFO (FCFS) is UNFAIR
• LIFO (preemptive) is FAIR

• Seniority

• Service times

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RAQFM account for all factors - bridge the gap
Seniority service time differences play
role (MOST CASES!) ? RAQFM agrees with
ordinary person
Service time differences very radical (A few
cases) ? RAQFM agrees with Wierman Harchol
Balter
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Comparison of Methods

• AL96 (SENIORITY)
• Easy to compute
• Order fairness When the issue is ORDER
• WHB03 (SERVICE TIMES)
• Easy to compute
• When jobs do not see each other / do not care of
  each other.
• RAQFM (SENIORITY SERVICE TIMES)
• Somewhat harder to compute
• When issue is waiting time. Also for ORDER
  fairness.

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Summary

• Fairness is fundamental for queueing systems
• No agreed upon measure exists
• RAQFM is a queueing fairness measure that
• Has a consistent view
• Deals with individuals, scenario, and system
• Accounts for both seniority and service
  requirement
• Admits logically to special cases
• Service times are identical
• Senior ahead of junior is more fair
• Arrival times are identical
• Short ahead of long is more fair
• Yields to analysis
• We analyzed a large variety of queueing systems
• Much more work is needed

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Closing Words

• Thank you
• If you have applications at which fairness is
  relevant we will be glad to hear.

• Whenever you enjoy the queues of your
  supermarket / bank / airport / give us a call