How Fair is your Queue Principles of Queue fairness measurement

1
How Fair is your QueuePrinciples of Queue
fairness measurement
Hanoch Levy School of Computer Science, Tel Aviv
University
Based on work with Benjamin Avi-Itzhak, RUTGERS
University David Raz, Tel-Aviv University Eli
Brosh, Columbia
Imperial College, December 2006
2
Why Fairness in Queues?
Why Queues?
Not Fair!!!
To provide FAIRNESS in waiting/service
Queue A Fairness Management Facility
3
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
4
Why Us? (Applications)

• Daily life queues

• Call centers
• Computer systems
• Web servers

5
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

6
So What is the problem?

• Take social-science 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
7
Queue Model (single server)
8
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

9
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!

10
Designing a Metrics - Keep in mind

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

• Applications

11
The Physical Factors
12
How fair is your queue?

1. I flip service orderYou rank how fair 1-10

• Seniority
• Size

13
Size and Seniority preference principles (TESTS)

• Seniority
• Size

14
Size and Seniority preference principles (TESTS)

• Seniority principle/ TEST
• Weak All jobs same service times ? ailt aj ? more
  fair Ji before Jj
• Strong Ji and Jj same service times
• Extended increase with aj- ai

• Service-requirement principle / TEST
• Weak All jobs same arrival times ? silt sj ? more
  fair Ji before Jj
• Strong Ji and Jj same arrival times
• Extended increase with sj- si

15
How Scheduling policies meet the principles (are
fair by principle)
FCFS LCFS ROS (random) Shortest job first longest job first
Seniority - - - -
Service requirement - - - -
16
Recall the issues
The difficulty (B) Size vs. seniority dilemma
The difficulty (A) Whom to compare a customer
against?
17
Whom should a customer be compared to
1

• Seniority
• Size

Locality of Reference
18
Measure 0 Waiting time variance

• Does not account for size
• Not LOCAL

19
Review of Measures (jobs based)

• Seniority based

20
Measure 1 Order (seniority) Fairness

• Gordon (87), 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

21
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

22
Measure 2 Service-time fairness Slow-Down
Based

• Wierman Harchol-Balter (03)
• Slow-down S(x)T(x)/x
• Belief Customers waiting time (soj. Time)
  should be proportional to service time ?
  slow-down equal
• Motivation PS is fair, PS ES(x) 1/(1-?)
• Approach Policy is fair if ES(x) 1/(1-?) for
  all x
• Analysis -- M/G/1, many policies.

23
Service-time Fairness Results

• Classification (not measure) of a large variety
  of policies
• Any preemptive size based policy is always unfair
  (all loads all service dists).
• All non-size based non-preemptive policies are
  always unfair for service time dist defined on
  neighborhood of zero (short jobs discriminated).
• Age based policies are always unfair
• FCFS is always UNFAIR
• LCFS (preemptive) PS are always FAIR

24
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 / no
  temporality!
• Advantage relatively simple analysis

• Applications Computer systems (?)

25
Measure 3 A Resource Allocation Approach (Raz,
Avi-Itzhak Levy 04)

• Focus on server resources (aim at equal division)

• Summary statistics of discrimination ? system
  unfairness

26
Resource allocation Fairness Results

• Adhering to tests
• STRONG Seniority service test YES
• WEAK Service-time service test YES
• STRONG Service-time service test NOT
• ONLY MEASURE which is LOCAL

27
Resource allocation Fairness Results (2)

• PS most fair
• Reacts to both s.time and seniority
• FCFS gt LCFS (seniority dominant)
• FCFS lt PLCFS (s. time dominant)

28
Individual discrimination under FIFO M/M/1(
conditioned on customers found ahead)
Indifferent

• Discrimination as a function of customers found
  at queue

29
Measure 4 SlowDown Q Fairness (Revisit Slow-Down)

• Brosh, Avi-Itzhak-Levy (05)
• Slow-down S(x)T(x)/x
• Want a measure
• Want to account for seniority
• Take Var T(x) x c where c is a normalization
  constant
• Analysis -- M/G/1, many policies.
• Admits Tests not local
• Convenient for analysis / large systems

30
What to pick? Go by the application
Service critical Airline reservation, Call center, Line for bread Order fairness
Delay sensitive, seniority-blind customers Computer systems (?) service time fairness
Delay sensitive, variable service time Call centers, Supermarkets, Banks, Computer systems Resource allocation fairness or SQF
31
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

32
THANK YOU