1. 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
Alternative name: “Satellite-linked Web Caches”
March, 2004
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Fairness in Queues, H. Levy

2. To provide FAIRNESS in waiting/service
Why QUEUES?
“Not Fair!!!”
“This is more Fair…”
To provide FAIRNESS in waiting/service
Sophisticated queues to address fairness issues
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Fairness in Queues, H. Levy

3. 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 don’t know how to quantify queue fairness!
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Fairness in Queues, H. Levy

4. 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: 10’s 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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Fairness in Queues, H. Levy

5. “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
Long
Short
The difficulty (A): Whom to compare a customer against?
The difficulty (B): Size vs. seniority dilemma
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Fairness in Queues, H. Levy

6. Motivation / Questions
Should Long be served ahead of Short?
Short(S)
Long (L)
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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Fairness in Queues, H. Levy

7. Motivation / Questions (2): Do You like your supermarket?
How fair is a scheduling policy?
This?
E.g:
FIFO
LIFO
Multiple Queue (Multi server)
Single queue (multi server)
Queues by job size?
Or This?
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Fairness in Queues, H. Levy

8. 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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Fairness in Queues, H. Levy

9. 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?
Call center
Web server
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Fairness in Queues, H. Levy

10. Fairness in Queues, H. Levy
Related Work(1)
Avi-Itzhak & Levy (96):
Axiomatic approach
Departure point+emphasis: 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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Fairness in Queues, H. Levy

11. Fairness in Queues, H. Levy
Recent Related Work
Wierman & Harchol-Balter (Sigmetrics 2003):
Propose a Fairness Criterion
Class-based approach: For job of size x compute E[T(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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Fairness in Queues, H. Levy

12. Conflicting (disturbing) Views
Policy
Ordinary person
Queueing theory (WHB 03)
FIFO
LIFO (preemptive)
Fair
(Fairest?) 
Unfair 
Unfair (most?) 
Fair 
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Fairness in Queues, H. Levy

13. 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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Fairness in Queues, H. Levy

14. RAQFM: A Resource Allocation Queueing Fairness Measure
Aims at meeting these requirements
In particular:
Long vs. Short
Seniority vs. service times S L
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Fairness in Queues, H. Levy

15. 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
Equal Share philosophy (“axiom”): at t:
Warranted service of
Granted service of
Individual discrimination of
(net service)
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Fairness in Queues, H. Levy

16. Basic Properties of RAQFM
Resource allocation is proper = zero-sum discrimination (work conserving, non idling)
Individual discrimination:
We are trying to use SRM to analyze the CSDS
System measure of discrimination: aggregate statistics of
Eliminate: Expected discrimination
Reasonable: distance from mean, Var(D), E[|D-E[D]|].
Measure of Unfairness
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Fairness in Queues, H. Levy

17. Property 1: Processor Sharing: Ultimate Fairness
Single server queue
Processor sharing service policy (Kleinrock (64), (67), Coffman, Muntz & Trotter (70))
Theorem 1: Under PS
 Var[D] = 0
 PS is the most fair policy!!
We are trying to use SRM to analyze the CSDS
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Fairness in Queues, H. Levy

18. 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
We are trying to use SRM to analyze the CSDS
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Fairness in Queues, H. Levy

19. Property 3: Service Time (identical arrival times)
Single server queue
Arrival times are all identical
Service times are arbitrary S L
Theorem 3:
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
We are trying to use SRM to analyze the CSDS
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Fairness in Queues, H. Levy

20. Property 4: More advanced The Long vs. Short case
Single server queue
Long and short arrive at different times S L
We are trying to use SRM to analyze the CSDS
Fairness of two orders depends on relative seniority and relative service times.
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Fairness in Queues, H. Levy

21. Property 5: Bounds How bad (good) can it be?
Bound on individual discrimination
Use for scale of reference / sanity check
How good:
(service time)
How bad:
(waiting time)
We are trying to use SRM to analyze the CSDS
Bound on system discrimination:
How bad:
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Fairness in Queues, H. Levy

22. 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).
We are trying to use SRM to analyze the CSDS
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Fairness in Queues, H. Levy

23. 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!
We are trying to use SRM to analyze the CSDS
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Fairness in Queues, H. Levy

24. Fairness in Queues, H. Levy
RAQFM is Analyzable
RAQFM yields to analysis via standard queueing theory techniques
Can compute
E[D| x] (class discrimination)
Var[D] (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.
We are trying to use SRM to analyze the CSDS
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Fairness in Queues, H. Levy

25. Individual discrimination under FIFO: M/M/1 ( conditioned on # customers found ahead)
Utilization
Indifferent
Time to smile
Empty super-market Friday noon
Time to cry
Traffic jam at 4AM
Discrimination as a function of # customers found at queue
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Fairness in Queues, H. Levy

26. 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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Fairness in Queues, H. Levy

27. How other measures relate: Bridging the gap
Wierman & Harchol-Balter (2003)
FIFO (FCFS) – is UNFAIR
LIFO (preemptive) – is FAIR
LIFO (preemptive)
FIFO
Queueing theory (WHB 2003)
Ordinary person
View
Policy
Unfair 
Fair 
Unfair 
Seniority
Service times
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Fairness in Queues, H. Levy

28. RAQFM: account for all factors - bridge the gap
Seniority + service time differences play role (MOST CASES!) 
RAQFM agrees with
ordinary person
FIFO:
LIFO:
Service time differences very radical (A few cases) 
RAQFM agrees with
Wierman & Harchol Balter
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Fairness in Queues, H. Levy

29. Fairness in Queues, H. Levy
Comparison of Methods
[AL96]: (SENIORITY)
Easy to compute
Order fairness: When the issue is ORDER
[WHB03]: (SERVICE TIMES)
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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Fairness in Queues, H. Levy

30. Fairness in Queues, H. Levy
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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Fairness in Queues, H. Levy

31. Fairness in Queues, H. Levy
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…
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Fairness in Queues, H. Levy