1. Multicriteria approach to scheduling in Grids with QoS guarantees Krzysztof Kurowski 1, Jarek Nabrzyski 1, Ariel Oleksiak 1, Jan Węglarz 12 1 Poznan Supercomputing and Networking Center 2 Institute of Computing Science, Poznan University of Technology

2. Outline Introduction Architecture and model Evaluation of multi-user schedules Search algorithms Resource provider policies Experiments and results Conclusion

3. Introduction Grids -Resource provision across administrative domains -Multiple objectives of users and providers of Grids -Requirement for guaranteed quality of service Goals of this work -Optimization of total ‘satisfaction’ of Grid users -Scheduling with QoS

4. Scheduling with advance reservations Easier expression of user preferences –Mostly time and cost rather than technical details of resources Providing users with a priori information about waiting and execution times –Essential, e.g. for interactive applications Reliable calculation of resource utilization costs –Users are aware what they are charged for Realization of a quality of service (QoS) –e.g. handling jobs with deadlines

5. Multi-criteria multi-user scheduling Each user may evaluate allocations using multiple criteria –E.g. different preferences concerning resource usage cost, start time, resource speed, reliability, etc. Users may have different objectives and constraints depending on their available budgets and time obligations –Therefore common global criteria such as makespan or mean completion time not suitable Stakeholders of the Grid resource management process have different points of view –Users expects meeting their objectives such as cost, time, etc. –Resource providers are interested in high income

6. Architecture

7. Users Grid Scheduler Resource Providers j |J|+1, j |J|+2,…

8. Scenarios Scenario1: Outsourcing jobs from the so- called Virtual Organization, e.g. a community consisting of researchers from multiple universities Scenario2: Enterprise provides a facility to its employees to enable fair access to outsourced resources Scenario3: Third-party portal provides registered users equitable access to resources in the Grid

9. Model Jobs –Both serial and parallel (rigid) jobs –Non-preemptive –Do not require co-allocation however may be “big” –Various length (may be “long”) –Substantial number of jobs (rather hundreds than thousands) –Estimated duration given by users Resources –Internally homogeneous clusters –Owned by resource providers –Advance reservation capability available

10. Model Finite set of users U=u 1, u 2, …, u k Finite set of users’ jobs J = j 1,j 2,…, j n Jobs from set J compete for resources offered by resource providers RP = rp 1, rp 2,…, rp m For each job users define resource requirements and preferences Resource providers offer resources as time slots with a specified number of processors and cost

11. Model - Resource Offers J1J1 J2J2 J3J3 J4J4 J5J5 J6J6 J7J7 J8J8 J9J9 J 10 J 11 O6O6 O5O5 O7O7 O1O1 O3O3 O2O2 O4O4 O3O3 J5J5 Reservations Available time slots time CPUs Each offer is defined by o i = (t i start, t i end, r i, c i ), where O i = o i1,, o i2, …, o il, l=|O| r i - resource speed, c i - cost for allocation unit O 10 O8O8 O9O9 c1c1 c2c2 c3c3 O 11

12. Model – Problem Definition Problem –Find a schedule of jobs J of users U on resource providers’ offers O maximizing total utility and fairness Hard constraints –Resource requirements, e.g. operating system, CPU architecture, etc. –Time requirements, e.g. deadlines, etc. Soft constraints (users’ objectives) –Start time –Cost –Resource speed (CPU speed, GFLOPs, linpack benchmark) Solutions –Sets of assignments of jobs to resources within certain time slots {(j i, O nj, t start, t end ), i=1..n, j=1..k}

13. Modeling preferences of a single user Usual way of formulating requirements in Grid systems in the form of hard constraints –E.g. maximal cost and deadline However, this representation was not convenient since –It is difficult to for users to specify exact values –It gives little flexibility for a Grid scheduler 2 1GHz brsvadd -n 1024 -m hostA -u user1 \ -b 6:0 -e 8:0 Resource requirements using JSDL Advance reservation in LSF

14. Expressing preferences Reference values used to reflect end-user’s preferences Two reference values –Required: r –Desired: d If a user cannot specify reference values d=0 and r=max(g i ) is assumed Scaling function:

15. Criteria Aggregation Ordered Weighted Aggregator (OWA) –Combines minimum, maximum, and arithmetic mean –Particular behavior can be controlled setting proper weights Weights for aggregation of users’ preferences

16. Aggregation of criteria for multiple users If no information about preferences for every user Then if we treat ‘satisfaction’ of particular users as criteria r1r1 r2r2 r3r3 r4r4 U1:U1: U2:U2: cost R1 R2 R3 R1 R2 R3 R4 cost time R4 S1S1 S2S2

17. Aggregation of criteria for multiple users If preferences of multiple users are available utility of each user can be used as separate objective OWA can be used for the aggregation of criteria as, it allows to configure it by accurate setting of weights, e.g. –For w 1 = w 2 = … = w n = 1/n, OWA is an arithmetic mean –For w 1 = 1 and w 2 = … = w n = 0, OWA is a minimum The worst value is maximized OWA properties –Finds Pareto-optimal solutions if weights are non-negative –Finds equitable solutions if weights are strictly decreasing (if yi > yj then y - eyi + eyj is better than y for 0 < e < yi - yj)

18. Aggregation of criteria for multiple users - weights Quantifier “at least k%” [Yager, 1988] Can be interpreted as k% of criteria should be satisfied Formula to compute the weights proposed by [Yager, 1988] In our case a linear function used to simplify calculations and ensure strict monotonicity of weights Question: how to estimate k?

19. Heuristic for search for fair allocations Motivation –Quick answer to users’ requests –Allowing users to confirm selected allocations –May be applied developing more complex method Assumptions: –Select solutions which are the best for a given user and possibly worst for others –If there are more than one solution that satisfies a user choose the worst for others –Prefer users that did not obtain allocations matching their preferences in the past

20. Aggregation of criteria for multiple users - weights For each resource offer o i and user j j a relative utility u’ decreased by utilities of alternative offers (sorted and weighted according to decreasing utilities) is calculated j1j1 j2j2 j3j3 o1o1 111 o2o2 000 o3o3 000 j1j1 j2j2 j3j3 o1o1 101 o2o2 110 o3o3 011 j1j1 j2j2 j3j3 o1o1 10.80.5 o2o2 0.90.20.6 o3o3 0.200.3 j1j1 j2j2 j3j3 o1o1 0.50.70.13 o2o2 0.35-0.20.28 o3o3 -0.53-0.45-0.1 j1j1 j2j2 j3j3 o1o1 0.50 o2o2 0 o3o3 0 j1j1 j2j2 j3j3 o1o1 111 o2o2 -0.5 o3o3 U U’

21. Aggregation of criteria for multiple users - weights j1j1 j2j2 j3j3 o1o1 0.50.70.13 o2o2 0.35-0.20.28 o3o3 -0.53-0.45-0.1 j1j1 j2j2 j3j3 o1o1 0.50 o2o2 0 o3o3 0 j1j1 j2j2 j3j3 o1o1 111 o2o2 -0.5 o3o3 j1j1 j2j2 j3j3 o1o1 0.50.70.13 o2o2 0.7-0.20.5 o3o3 -0.53-0.45-0.1 j1j1 j2j2 j3j3 o1o1 0.50.70.13 o2o2 0.35-0.20.28 o3o3 -0.53-0.450

22. Aggregation of criteria for multiple users - using history Idea: like fair scheduling in queuing systems –Take into account historical decisions during scheduling However if we record only utility of allocated offer user is able to cheat –By submitting artificial very demanding request h i = u i * - u i, where u* was a utility of the best offer while u i of the allocated one for user i in the previous request Dynamic priority: dp i = (mean(h i ) + last(h i ))/2

23. Optimization using evolutionary algorithm Why EA? -Useful for multicriteria optimization especially for such a big number of criteria -Flexibility General approach –In the first iterations very broad search to generate possible diverse Pareto-optimal solutions -In the second part of optimization more focused search (OWA with set weights used to direct search towards fair solutions) -Specialized operators to obtain fair solutions

24. Optimization using evolutionary algorithm - representation & operators Representation -Vector of assignments: Operators –Mutations: Exchange of allocations: one is changed to a similar one (still Pareto-efficient) so that other job gets satisfactory solution Using heuristic described before for part of jobs –Crossover: Random exchange of allocations, Exchanging allocations trying to skip the most unfair ones

25. Results Comparison with traditional methods with preferences in the form of hard constraints MCT+ED - earliest due date + minimum completion time GR+LSF - Largest First + Graham algorithm MC - multi-criteria assignment of single jobs MU- multi-user

26. Policies of resource providers The main goal is to maximize income Requests may come from more then single source –Some of them are Grid schedulers –Local users may submit jobs Resource providers reserve offered resources for a certain time; after that time offer is not valid Parameters of policies –Fraction of resources offered to Grid scheduler(s) –Expiring time of initial reservations –Cost policy

27. Results Percentage of resources offered to a Grid scheduler Overbooking: offering x% of available resources to more than one consumer

28. Conclusion Model for scheduling in Grids with advance reservations shown Formulation of the problem as maximizing satisfaction (total utility and fairness) of multiple users A framework for solving multicriteria problem including: –Setting appropriate weights to obtain schedule satisfying more users –Simple heuristic to allocate jobs to offered resources –Evolutionary algorithm that optimizes aggregated satisfaction of users Experimental results

29. Future work More experiments and improvements of the evolutionary algorithm Theoretical analysis of heuristics and measures Dealing with imprecision of estimated runtimes Further study of resource provider policies Implementation in real environment in progress: GRMS and OpenDSP