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Online Scheduling in Grids 1 Uwe Schwiegelshohn, 2 Andrei Tchernykh, 1 Ramin Yahyapour 1 Technische Universität Dortmund, Germany uwe.schwiegelshohn@udo.edu, ramin.yahyapour@udo.edu 2 CICESE Research Center, Ensenada, Baja California, Mexico chernykh@cicese.mx

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online scheduling in grids

Online Scheduling in Grids

1Uwe Schwiegelshohn, 2Andrei Tchernykh, 1Ramin Yahyapour

1Technische Universität Dortmund, Germany

uwe.schwiegelshohn@udo.edu, ramin.yahyapour@udo.edu

2CICESE Research Center, Ensenada, Baja California, Mexico

chernykh@cicese.mx

CIRM-Marseille-Luminy, May 12 - 16, 2008

computational grid
Computational Grid

(by Christophe Jacquet)

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grid model
Grid Model
  • An encompassing and precise representation of a Grid is usually too complex to address various problems occurring in Grids.
  • Application of a suitable model that considers important properties of a Grid.

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grid model4
Grid Model

The Grid contains m machines.

Machine Mihas size mi if it comprises miprocessors.

All processors in the Grid are identical.

  • Each job J is described by a triple :
    • release date,
    • size (degree of parallelism),
    • execution time on processors.

Job must be executed on processors on one machine without interruption (space sharing mode).

GPm | sizej | Cmax

Pm | rj, sizei | Cmax is referred to as PS

while the scheduling on a set of parallel machines

GPm | rj,sizei | Cmax is referred to as MPS.

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list scheduling
List Scheduling

Non clairvoyant scheduling

Time

Processors

Processors

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List Scheduling

Cmax(LIST)=17

Cmax*=9

Time

Processors

Processors

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List Scheduling on Parallel Processors

Cmax(LIST)/Cmax* ≤ 2-1 / m

  • All jobs are sequential and have release date 0.
    • Graham 1966
  • Jobs have release date 0 and may be parallel.
    • Garey, Graham 1975
  • Jobs are parallel and submitted over time (online scheduling)
    • Naroska, Schwiegelshohn 2002

Does the same bound hold for Grids as well?

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applicability to grids
Applicability to Grids

There is no polynomial time algorithm that always produces schedules S with

Cmax(S)/Cmax ∗ < 2

for

GPm | sizei | Cmax

and all input data unless P = NP.

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applicability to grids9
Applicability to Grids
  • 2 machines with m processors each
  • All jobs have processing time 1 and different degrees of parallelism
    • Total requirement of all jobs: 2m processors
  • Consider an arbitrary algorithm A.

machine 1

machine 2

Cmax (A)=1  Cmax*=1: optimal solution

machine 1

machine 2

Cmax (A)=2 and Cmax *=2: optimal solution

Cmax (A)=2 and Cmax *=1: optimal solution

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applicability to grids10
Applicability to Grids

How do we know whether Cmax*=2 applies?

  • Partition: NP-hard
  • There is no algorithm A with polynomial time complexity guaranteeing Cmax(A)/Cmax* < 2.

Scheduling in Grids is inherently more difficult than

scheduling on a single parallel processor.

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List Scheduling in the Grid

Cmax(LIST)=4

Time

Machines with different numbers of processors

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List Scheduling in the Grid

Cmax*=2

Time

Machines with different numbers of processors

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Problems of List Scheduling

  • Cmax(LIST)/Cmax* = (k+1)/2
  • Analysis of the problem
    • Jobs with little parallelism occupy large machines which are not available for highly parallel jobs.
    • In case of few highly parallel jobs it is inefficient to prevent jobs with little parallelism from using these large machines.
  • Simple approach
    • Increased priority for highly parallel jobs
    • Arranging jobs in descending order of their parallelism
      • Fairness is neglected.

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sorting in order of parallelism

Few available processors

for parallel jobs

Predominantly execution

of sequential jobs

Sorting in Order of Parallelism

Time

Processors

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does ordering the jobs help
Does Ordering the Jobs Help?
  • We are interested in an algorithm that does not use a single list of jobs.
    • Some machines are blocked from executing some jobs under certain circumstances.

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does ordering the jobs help17
Does Ordering the Jobs Help?
  • We assume a machine indexing such that mi−1 ≤ miholds

Three sets of jobs are considered

    • Set Ai contains all jobs that cannot execute on the previous (next smaller) machine and require more than 50% of the processors of machine Mi.
    • Set Bi contains all jobs that cannot execute on the previous machine but require at most 50% of the processors of machine Mi.
    • Set Hi contains all jobs that require more 50% of the processors of machine Mi but can also be executed on the previous machine.

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grid scheduling algorithm
Grid Scheduling Algorithm

1. The machines are arranged in ascending order of processor numbers.

2. A job is assigned to the first machine that can execute it.

Group A: >= half of the processors on this machine are required.

Group B: < half of the processors on this machine are required.

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grid scheduling algorithm19
Grid Scheduling Algorithm

3. Any machine applies a priority order when selecting jobs for execution:

Jobs of its group A

Jobs of its group B

Jobs that are enabled for execution on its previous machine.

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Performance of the Algorithm

  • Theoretical evaluation
    • Cmax(LIST)/Cmax* < 3 in the offline case
    • Cmax(LIST)/Cmax* < 5 in the online case

U.Schwiegelshohn, A.Tchernykh, R.Yahyapour

Online Scheduling in Grids. IEEE, IPDPS’08, 2008

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conclusion
Conclusion
  • Common list scheduling does not work well in Grids.
  • Jobs should receive priority on the machines that provide the right amount of parallelism.
  • Jobs with less parallelism are only executed on these machines if better suited jobs are not available.
  • The presented algorithm has a constant worst case bound and relatively small gap.

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two level grid model

Workload

Grid

Broker

Allocation

Local queue

Local queue

Local queue

Local scheduler

Local scheduler

Local scheduler

node

node

node

Two Level Grid Model

We regard MPS as two stage (two layer) scheduling MPS = MPS_Allocation + PS.

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allocation
Allocation

For each job:

firstbe the minimum i such that node is able to execute a job .

lastis the maximum i

set of nodes first, first+1, . . . , last is a set M-available.

m1

m2

m3

m4

m5

mm

first(Jj) = 2

last(Jj) = m

M-available

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allocation25
Allocation

If last is the minimum r such that

m1

m2

m3

m4

m5

mm

first(Jj) = 2

last(Jj) = 5

M-admis

last(Jj) = m

M-available

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a*m(f0,m)

(1-a)*m(f0,m)

a*m(f,m)

(1-a)*m(f,m)

1 f0 fl0 l m

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For a set of machines with identical processors, and for a set of rigid jobs with admissible range

the competitive factor of Min_LB-a+ Best_PS is

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competitive factor
Competitive factor

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competitive factor29
Competitive factor

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competitive factor30
Competitive factor
  • A.Tchernykh, U.Schwiegelshohn, R.Yahyapour, N.Kuzurin.
  • Online Hierarchical Job Scheduling in Grids.
  • IEEE, CoreGrid’08, EuroPar, 2008

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