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Progress Report

Progress Report. 07/30. Virtual Core Scheduling Problem. For every time period, the hypervisor scheduler is given a set of virtual cores with their operating frequency. Generate a scheduling plan, such that the power consumption is minimized, and the performance is guaranteed. Scheduling Plan.

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Progress Report

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  1. Progress Report 07/30

  2. Virtual Core Scheduling Problem • For every time period, the hypervisor scheduler is given a set of virtual cores with their operating frequency. • Generate a scheduling plan, such that the power consumption is minimized, and the performance is guaranteed.

  3. Scheduling Plan • A set of ai,j which indicates the amount of time executing virtual core j on physical core i in a time interval. • The execution order of each virtual core on a physical core.

  4. Current Solution • Two phases: • Use integer programming to find a feasible set of ai,j. • Decide the execution order on each physical core. • A virtual core cannot appear in two or more physical core on the same time.

  5. Example vCPU2 (10,10,20, 20) vCPU0 (50,40,0, 0) vCPU1 (20,20,20, 20) vCPU5 (0, 0,10, 10) vCPU3 (10,10,20, 20) vCPU4 (10,10,10, 10) t=100 t=0

  6. Open-shop Problem • “Open-shop scheduling problem (OSSP) is a scheduling problem in which a given set of jobs must each be processed for given amounts of time at each of a given set of workstations, in an arbitrary order, and the goal is to determine the time at which each job is to be processed at each workstation.”[1] [1] Open-shop scheduling: http://en.wikipedia.org/wiki/Open_shop_scheduling

  7. Open-shop Problem(Cont.) • O2||Cmax can be solved in polynomial time. • ON||Cmax(N>2) • May be solved in polynomial timewhen all nonzero processing times are equal. • Otherwise, NP-hard problem. • O|pmtn| Cmax • With preemption

  8. Open-shop Model • Define: • Load of machine iMLi = • Load of job j JLj = • Lower bound on CmaxLB = max{maxmi=1MLi, maxnj=1JLj} • tight: job j(machine i) with JLj(MLi)= LB • slack: not tight, JLj(MLi)< LB

  9. Open-shop Model(Cont.) • “Decrementing Set” D • For each tight job and machine, exactly one operation. • For each job and machine with slack, at most one operation. • An operation is a job-machine pair. • Job running on the machine.

  10. Algorithm O|pmtn|Cmax • REPEAT • Calculate a decrementing set D • Calculate a maximum value △ with • △ ≦ min(i,j)∈Dpij • △ ≦ LB – MLi if i has slack and no operation in D • △ ≦ LB – JLj if j has slack and no operation in D • schedule the operations in D for △ time units in parallel • Update p, LB, ML, JL • UNTIL all operations have been scheduled

  11. Example

  12. Summary • The second part of our problem can be formulated into Open-shop problem. • Since virtual cores can preempt each other, we can apply algorithm O|pmtn| Cmaxto find a feasible scheduling in polynomial time.

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