1. 3/24//2004Fairness in Queues, H. Levy, CS, TAU1 How Fair is your Queue March, 2004 Hanoch Levy School of Computer Science, Tel Aviv University Jointly with Benjamin Avi-Itzhak, RUTGERS University David Raz, Tel-Aviv University

2. 3/24//2004Fairness in Queues, H. Levy, CS, TAU2 Why QUEUES? Not Fair!!! To provide FAIRNESS in waiting/service This is more Fair… Sophisticated queues to address fairness issues

3. 3/24//2004Fairness in Queues, H. Levy, CS, TAU3 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!

4. 3/24//2004Fairness in Queues, H. Levy, CS, TAU4 How Important is fairness in 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? FAIRNESS INHERENT/CRUCIAL part of queues

5. 3/24//2004Fairness in Queues, H. Levy, CS, TAU5 So – What is the problem? Short Long Take social-science/economics utility-fairness measures and apply to queues The difficulty (B): Size vs. seniority dilemma HOW??? What is the PIE? A moving target… The difficulty (A): Whom to compare a customer against? The problem in a nutshell: Short vs. Long

6. 3/24//2004Fairness in Queues, H. Levy, CS, TAU6 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! Short(S) Long (L)

7. 3/24//2004Fairness in Queues, H. Levy, CS, TAU7 Motivation / Questions (2): Do You like your supermarket? How fair is a scheduling policy? E.g: FIFO LIFO Or This? This? Multiple Queue (Multi server) Single queue (multi server) Queues by job size?

8. 3/24//2004Fairness in Queues, H. Levy, CS, TAU8 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)

9. 3/24//2004Fairness in Queues, H. Levy, CS, TAU9 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

10. 3/24//2004Fairness in Queues, H. Levy, CS, TAU10 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?

11. 3/24//2004Fairness in Queues, H. Levy, CS, TAU11 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?

12. 3/24//2004Fairness in Queues, H. Levy, CS, TAU12 Conflicting (disturbing) Views View Policy Ordinary person Queueing theory (WHB 03) FIFO LIFO (preemptive) Unfair (most?) Fair Unfair Fair (Fairest?)

13. 3/24//2004Fairness in Queues, H. Levy, CS, TAU13 Basic Requirements of a Queue Fairness measure 1.Aim for standard: Have a consistent view/intuition 2.Deal with individual, scenario, and system 3.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 4.Yields to analysis

14. 3/24//2004Fairness in Queues, H. Levy, CS, TAU14 RAQFM: A Resource Allocation Queueing Fairness Measure Aims at meeting these requirements In particular: –Long vs. Short –Seniority vs. service times S L

15. 3/24//2004Fairness in Queues, H. Levy, CS, TAU15 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)

16. 3/24//2004Fairness in Queues, H. Levy, CS, TAU16 Basic Properties of RAQFM Resource allocation is proper = zero-sum discrimination (work conserving, non idling) System measure of discrimination: aggregate statistics of –Eliminate: Expected discrimination –Reasonable: distance from mean, Var(D), E[|D-E[D]|]. –Measure of Unfairness Individual discrimination:

17. 3/24//2004Fairness in Queues, H. Levy, CS, TAU17 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!!

18. 3/24//2004Fairness in Queues, H. Levy, CS, TAU18 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 LL

19. 3/24//2004Fairness in Queues, H. Levy, CS, TAU19 Property 3: Service Time (identical arrival times) Single server queue Arrival times are all identical Service times are arbitrary 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 S L

20. 3/24//2004Fairness in Queues, H. Levy, CS, TAU20 Property 4: More advanced The Long vs. Short case Single server queue Long and short arrive at different times S L Fairness of two orders depends on relative seniority and relative service times.

21. 3/24//2004Fairness in Queues, H. Levy, CS, TAU21 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) Bound on system discrimination: How bad:

22. 3/24//2004Fairness in Queues, H. Levy, CS, TAU22 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).

23. 3/24//2004Fairness in Queues, H. Levy, CS, TAU23 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!

24. 3/24//2004Fairness in Queues, H. Levy, CS, TAU24 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.

25. 3/24//2004Fairness in Queues, H. Levy, CS, TAU25 Individual discrimination under FIFO: M/M/1 ( conditioned on # customers found ahead) Discrimination as a function of # customers found at queue Utilization Time to cry Traffic jam at 4AM Indifferent Time to smile Empty super- market Friday noon

26. 3/24//2004Fairness in Queues, H. Levy, CS, TAU26 System Unfairness: Compare operation policies System Unfairness as a function of system load Empty system: everyon e is alone LIFO: Severe seniority discriminatio n FIFO: no seniority discriminatio n PS: Absolut e Fairness !

27. 3/24//2004Fairness in Queues, H. Levy, CS, TAU27 How other measures relate: Bridging the gap LIFO (preemptiv e) FIFO Queueing theory ( WHB 2003 ) Ordinary person View Policy Unfair Fair Unfair Fair Wierman & Harchol-Balter (2003) –FIFO (FCFS) – is UNFAIR –LIFO (preemptive) – is FAIR SeniorityService times

28. 3/24//2004Fairness in Queues, H. Levy, CS, TAU28 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 FIFO: 0.9 LIFO: 0.15

29. 3/24//2004Fairness in Queues, H. Levy, CS, TAU29 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.

30. 3/24//2004Fairness in Queues, H. Levy, CS, TAU30 Summary Fairness is fundamental for queueing systems No agreed upon measure exists RAQFM is a queueing fairness measure that: 1.Has a consistent view 2.Deals with individuals, scenario, and system 3.Accounts for both seniority and service requirement 4.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 5.Yields to analysis We analyzed a large variety of queueing systems Much more work is needed

31. 3/24//2004Fairness in Queues, H. Levy, CS, TAU31 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…