How Fair is your Queue

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 March, 2004 Fairness in Queues, H. Levy, CS, TAU

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

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! Fairness in Queues, H. Levy, CS, TAU

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? Fairness in Queues, H. Levy, CS, TAU

5. Short Long “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 Fairness in Queues, H. Levy, CS, TAU

6. Short(S) Long (L) 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! Fairness in Queues, H. Levy, CS, TAU

7. This? Or This? 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? Fairness in Queues, H. Levy, CS, TAU

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) Fairness in Queues, H. Levy, CS, TAU

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

10. 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? Fairness in Queues, H. Levy, CS, TAU

11. 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? Fairness in Queues, H. Levy, CS, TAU

12. Conflicting (disturbing) Views Fair (Fairest?)  Unfair  Unfair (most?)  Fair  Fairness in Queues, H. Levy, CS, TAU

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 Fairness in Queues, H. Levy, CS, TAU

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

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

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

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

18. L L 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 reverseorder of seniority (LIFO) is most unfair • Pushing a juniorahead of seniorreduces fairness Fairness in Queues, H. Levy, CS, TAU

19. S Theorem 3: L 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 jobreduces fairness Fairness in Queues, H. Levy, CS, TAU

20. L S 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. Fairness in Queues, H. Levy, CS, TAU

21. How good: (service time) How bad: (waiting time) How bad: Property 5: BoundsHow bad (good) can it be? • Bound on individual discrimination • Use for scale of reference / sanity check Bound on system discrimination: Fairness in Queues, H. Levy, CS, TAU

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). Fairness in Queues, H. Levy, CS, TAU

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! Fairness in Queues, H. Levy, CS, TAU

24. 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. Fairness in Queues, H. Levy, CS, TAU

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

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 Fairness in Queues, H. Levy, CS, TAU

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

28. FIFO: 0.9 LIFO: 0.15 RAQFM: account for all factors - bridge the gap Seniority + service time differences play role (MOST CASES!)  RAQFM agrees with ordinary person Service time differencesvery radical (A few cases)  RAQFM agrees with Wierman & Harchol Balter Fairness in Queues, H. Levy, CS, TAU

29. 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. Fairness in Queues, H. Levy, CS, TAU

30. 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 servicerequirement • 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 Fairness in Queues, H. Levy, CS, TAU

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