December15,2009 PeterN.NyumuProfessor:AlfredoGoldman SchedulinginGridComputingusingMaster-SlaveSchedulingModel

(1)

Outline Introduction Single-Master Master-Slave Systems Final

Scheduling in Grid Computing using Master-Slave Scheduling Model

Peter N. Nyumu Professor: Alfredo Goldman

Mac0461

December 15, 2009

(2)

Introduction

Brief Description and Applications Scheduling

Single-Master Master-Slave Systems No-Wait in Process

Final

(3)

Motivation

I Research in my undergraduate work

(4)

Brief Description

I Master-Slave scheduling model, involves two sets of processors

I Master process and Slave processor

I The slave processors are responsible for the actual execution of the orders

(5)

Brief Description

I Master-Slave scheduling model, involves two sets of processors

I Master process and Slave processor

I The master processors are responsible of preprocessing and postprecessing of work orders

I The slave processors are responsible for the actual execution of the orders

(6)

Master-Slave Model

(7)

Two different schedule

I 1. No-wait-in schedule

I Each slave task must be scheduled immediately after the corresponding preprocessing task finishes

I Each postprocessing task must be scheduled immediately after the corresponding slave task finishes.

(8)

Two different schedule

I 1. No-wait-in schedule

I Each slave task must be scheduled immediately after the corresponding preprocessing task finishes

I Each postprocessing task must be scheduled immediately after the corresponding slave task finishes.

(9)

Two different schedules

I 2. Canonical schedule

I Satisfies the following properties:

I No preemptions

I The preprocessing tasks begin on the master machine at time 0 and complete at time P

a_i

I Slave tasks begin as soon as their corresponding preprocessing tasks complete.

I Postprocessing tasks are done in the same order as the slave tasks complete and as soon as possible.

(10)

Two different schedules

I 2. Canonical schedule

I Satisfies the following properties:

I No preemptions

I The preprocessing tasks begin on the master machine at time 0 and complete at time P

a_i

I Slave tasks begin as soon as their corresponding preprocessing tasks complete.

I Postprocessing tasks are done in the same order as the slave tasks complete and as soon as possible.

(11)

Application of Master-Slave model

I parallel computing

I semiconductor testing

I industrial applications

(12)

Unconstrained Minimum Finish Time Problem (UMFT)

I UMFT problem is NP-hard.

I Apply the canonical schedule.

I Can rearrange the master tasks so that all preprocessing tasks complete before any postprocessing task starts.

I For any canonical schedule S, ^C_C^S∗ ≤2 and the bound is tight.

(13)

No-Wait in Process

Applying Heurisitic in UMFT

I A better bound is achieved by applying the following heuristic:

I Let S₁={i :a_i ≤c_i} andS₂ ={i :a_i >c_i}

I Reorder the jobs in S₁ according to nondecreasing order of b_i.

I Reorder the jobs in S₂ according to nonincreasing order of b_i.

I Generate the canonical schedule in which thea tasks ofS1

precede those of S₂.

I C^H

C^∗ ≤ ³₂ and bound is tight.

(14)

Applying Heurisitic in UMFT

I A better bound is achieved by applying the following heuristic:

I Let S₁={i :a_i ≤c_i} andS₂ ={i :a_i >c_i}

I Reorder the jobs in S₁ according to nondecreasing order of b_i.

I Reorder the jobs in S₂ according to nonincreasing order of b_i.

I Generate the canonical schedule in which thea tasks ofS1

precede those of S₂.

I C^H

C^∗ ≤ ³₂ and bound is tight.

(15)

No-Wait in Process

Order Preserving Minimum Finish Time (OPMFT)

I We have same order of preprocessing and postprocessing

I Apply canonical schedule

I Its possible to construct an O(nlogn) algorithm, by defining a canonical order preserving schedule (COPS)

I There is an OPMFT schedule which is a COPS in which the preprocessing order satifies that, jobs with c_j >a_j come first, jobs with cj =aj come next, and thejobs with cj <aj come last.

(16)

Order Preserving Minimum Finish Time (OPMFT)

I We have same order of preprocessing and postprocessing

I Apply canonical schedule

I Its possible to construct an O(nlogn) algorithm, by defining a canonical order preserving schedule (COPS)

I There is an OPMFT schedule which is a COPS in which the preprocessing order satifies that, jobs with c_j >a_j come first, jobs with cj =aj come next, and thejobs with cj <aj come last.

(17)

No-Wait in Process

Canonical Reverse Order Schedules (CROS)

I construction of reverse order processing

I It works as follows:

I the master preprocesses the n jobs in the order σ

I slave i begins the slave processing of jobi as soon as the master completes its preprocessing.

I the master begins the postprocessing of the last job inσ as soon as its slave task is complete

I the master begins the postprocessing of job j 6=k at the later of the two times (a) when it has finished the postprocessing of the succesor of j in σ, and (b) when slavej has finished bj.

(18)

No-Wait in Process

Canonical Reverse Order Schedules (CROS)

master completes its preprocessing.

I the master begins the postprocessing of job j 6=k at the later of the two times (a) when it has finished the postprocessing of the succesor of j in σ, and (b) when slavej has finished bj.

(19)

No-Wait in Process

Canonical Reverse Order Schedules (CROS)

I the master preprocesses the n jobs in the order σ

I slave i begins the slave processing of jobi as soon as the master completes its preprocessing.

I the master begins the postprocessing of job j 6=k at the later

(20)

No-Wait in Process

I The Minimize Finish Time (MFTNW), subject to the no-wait-in-process constraint.

(21)

No-Wait in Process

I The Order-Preserving version of MFTNW.

I The Reverse-Order version of MFTNW.

(22)

No-Wait in Process

I The Order-Preserving version of MFTNW.

I The Reverse-Order version of MFTNW.

(23)

December15,2009 PeterN.NyumuProfessor:AlfredoGoldman SchedulinginGridComputingusingMaster-SlaveSchedulingModel

Scheduling in Grid Computing using Master-Slave Scheduling Model

Motivation

Brief Description

Brief Description

Master-Slave Model

Two different schedule

Two different schedule

Two different schedules

Two different schedules

Application of Master-Slave model

Unconstrained Minimum Finish Time Problem (UMFT)

Applying Heurisitic in UMFT

Applying Heurisitic in UMFT

Order Preserving Minimum Finish Time (OPMFT)

Order Preserving Minimum Finish Time (OPMFT)

Canonical Reverse Order Schedules (CROS)

Canonical Reverse Order Schedules (CROS)

Canonical Reverse Order Schedules (CROS)

No-Wait in Process

No-Wait in Process

No-Wait in Process

Questions