1Uwe Schwiegelshohn, 2Andrei Tchernykh, 1Ramin Yahyapour

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Online Scheduling in Grids

• 1Uwe Schwiegelshohn, 2Andrei Tchernykh, 1Ramin
  Yahyapour
• 1Technische Universität Dortmund, Germany
• uwe.schwiegelshohn_at_udo.edu, ramin.yahyapour_at_udo.ed
  u
• 2CICESE Research Center, Ensenada, Baja
  California, Mexico
• chernykh_at_cicese.mx

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

(by Christophe Jacquet)
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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 Model
The Grid contains m machines. Machine Mi has
size mi if it comprises mi processors. 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
Non clairvoyant scheduling
Time
Processors
Processors
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List Scheduling
Cmax(LIST)17
Cmax9
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
There is no polynomial time algorithm that always
produces schedules S with Cmax(S)/Cmax lt 2
for GPm  sizei  Cmax and all input data
unless P NP.
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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 2
machine 1
Cmax (A)1 ? Cmax1 optimal solution
machine 2
machine 1
Cmax (A)2 and Cmax 2 optimal solution
Cmax (A)2 and Cmax 1 optimal solution
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Applicability to Grids

• How do we know whether Cmax2 applies?
• Partition NP-hard
• There is no algorithm A with polynomial time
  complexity guaranteeing Cmax(A)/Cmax lt 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
Cmax2
Time
Machines with different numbers of processors
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Problems of List Scheduling

• Cmax(LIST)/Cmax (k1)/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
Time
Processors
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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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Online Job Stealing Scheduling in Grids
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Does Ordering the Jobs Help?

• We assume a machine indexing such that mi-1 mi
  holds
• 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
2. A job is assigned to the first machine that
can execute it. Group A gt half of the
processors on this machine are required.
Group B lt half of the processors on this
machine are required.
1. The machines are arranged in ascending order
of processor numbers.
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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 lt 3 in the offline case
• Cmax(LIST)/Cmax lt 5 in the online case
• U.Schwiegelshohn, A.Tchernykh, R.Yahyapour
• Online Scheduling in Grids. IEEE, IPDPS08, 2008

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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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Adaptive Admissible Allocation
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Two Level Grid Model
We regard MPS as two stage (two layer) scheduling
MPS  MPS_Allocation  PS.
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Allocation
For each job first be the minimum i such that
node is able to execute a job . last is the
maximum i set of nodes first, first1, . . . ,
last is a set M-available.
m1
m2
m3
m4
m5
mm

first(Jj) 2
last(Jj) m
M-available
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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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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
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Competitive factor
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Competitive factor
A.Tchernykh, U.Schwiegelshohn, R.Yahyapour,
N.Kuzurin. Online Hierarchical Job Scheduling in
Grids. IEEE, CoreGrid08, EuroPar, 2008
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Thank you