Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths

28 October 2010

Challenge the future

DelftUniversity ofTechnology

Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths

Dick EpemaDelft University of TechnologyDelft, the Netherlands

Saeid Abrishami and Mahmoud NaghibzadehFerdowsi University of MashhadMashhad, Iran

Grid 2010, Brussels, Belgium

2Partial Critical Paths

Introduction• Utility Grids versus Community Grids

• main difference: QoS and SLAs• Workflows: a common application type in distributed systems• The Workflow Scheduling Problem

• community grids: many heuristics try to minimize the makespan of the workflow

• utility grids: other QoS attributes than execution time, e.g., economical cost, play a role, so it is a multi-objective problem

• We propose a new QoS-based workflow scheduling algorithm called Partial Critical Paths (PCP)


The PCP Algorithm: main idea• The PCP Algorithm tries to create a schedule that

1. minimizes the total execution cost of a workflow2. while satisfying a user-defined deadline

• The PCP Algorithm• first schedules the (overall) critical path of the workflow such that

• its execution cost is minimized • it completes before the user’s deadline

1. finds the partial critical path to each scheduled task on the critical path and executes the same procedure in a recursive manner

overall critical pathpartial critical path


Scheduling System Model (1)• Workflow Model

• an application is modeled by a directed acyclic graph G(T,E)• T is a set of n tasks {t1, t2, …, tn}• E is a set of arcs between two tasks

• each arc ei,j = (ti, tj) represents a precedence constraint• dummy tasks: tentry and texit

tentry

t2

texit

t1

t3

t4

t5 t6

e1,4


Scheduling System Model (2)• Utility Grid Model

• Grid Service Providers (GSPs)• Each task can be processed by a number of services on different

GSPs• ET(ti,s) and EC(ti,s)

• estimated execution time and execution cost for processing task ti on service s

• TT(ei,j,r s) and TC(ei,j,r,s)• estimated transfer time and transfer cost of sending the required

data along ei,j from service s (processing task ti) to service r (processing task tj)

• Grid Market Directory (GMD)


Basic Definitions• Minumum Exection Time:

• Minimum Transfer Time:

• Earliest Start Time:

• SS(ti): the selected service for processing the scheduled task ti• AST(ti): the actual start time of ti on its selected service

),(min)( stETtMET iSsii

),,(min)( ,,, rseTTeMTT jiSrSsjiji

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EST(tentry ) = 0

EST(ti) = maxt p ∈parents( ti )

EST(t p ) + MET(t p ) + MTT(ep,i)

used for finding thepartial critical paths


The PCP Scheduling AlgorithmPROCEDURE ScheduleWorkflow(G(T,V), deadline)

• Request available services for each task in T from GMD• Query available time slots for each service from related GSPs• Add tentry and texit and their corresponding edges to G • Compute MET(ti) for each task in G• Compute MTT(ei,j) for each edge in G• Compute EST(ti) for each task in G

1. Mark tentry and texit as scheduled 2. Set AST(tentry)=0 and AST(texit) = deadline3. Call ScheduleParents(texit) 4. If this procedure was successful make advance reservations

for all tasks in G according to the schedule, otherwise return failure


ScheduleParents (1)• The Critical Parent of a node t is the unscheduled parent

p of t for which EST(p)+MET(p)+MTT(ep,t) is maximal

• The Partial Critical Path of node t is:• empty if t does not have unscheduled parents • consists of the Critical Parent p of t and the Partial

Critical Path of p if t has unscheduled parents• Critical parent and partial critical path change over time

p t

126

69

281


ScheduleParents (2)PROCEDURE ScheduleParents(t)

• If t has no unscheduled parents then return success• Let CriticalPath be the partial critical path of t• Call SchedulePath(CriticalPath)• If this procedure is unsuccessful, return failure and a

suggested start time for the failed node (try to repair)• For all ti on CriticalPath /* from start to end */

Call ScheduleParents(ti) 1. Iterate over all non-scheduled parents of t


SchedulingPath (1)• SchedulePath tries to find the cheapest schedule for

a Path without violating the actual start times of the scheduled children of the tasks on Path

• SchedulePath is based on a backtracking strategy• A selected service for a task is admissible if the

actual start times of the scheduled children of that task can be met


SchedulingPath (2)• Moves from the first task in Path to the last task

• For each task, it selects an untried available service

• If the selected service creates an admissible (partial) schedule, then it moves forward to the next task, otherwise it selects another untried service for that task

• If there is no available untried service for that task left, then it backtracks to the previous task on the path and selects another service for it

• This may lead to failure


An Example (1)

S

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E

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Start: Call ScheduleParents(E)


An Example (2)

S

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E

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find the Partial Critical Path for node E(this is the overall critical path of the workflow)


An Example (3)

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Call SchedulePath for path 2-6-9Call ScheduleParents for nodes 2, 6, and 9, respectively


An Example (4)

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Node 2 has no unscheduled parents,so its partial critical path is empty


An Example (5)

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Node 6: find its partial critical path and then call SchedulePathScheduleParents is called for node 3 but it has no

unscheduled parentsIf SchedulePath cannot schedule this path, then it returns failure, which causes the path 2-6-9 to be rescheduled.


An Example (6)

S

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E

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Node 9: find its partial critical path and then call SchedulePathScheduleParents is called for the nodes 5 and 8 but they have no

unscheduled parentsIf SchedulePath cannot schedule this path, then it returns failure, which causes the path 2-6-9 to be rescheduled.


An Example (7)

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Now scheduling of the path 2-6-9 has been finished, and ScheduleParents is called again for node E to find its next partial critical path and to schedule that path


Performance Evaluation

• Simulation Software: GridSim• Grid Environment: DAS-3, a multicluster grid in the

Netherlands • 5 clusters (32-85 nodes)• Average inter-cluster bandwidth: between 10 to 512 MB/s• Processor speed: have been changed to make a 10 times

difference between the fastest and the slowest cluster • Processor price: fictitious prices have been assigned to each

cluster (faster cluster has a higher price)

Experimental Setup (1): the system


• Five synthetic workflow applications that are based on real scientific workflows (see next page)

• Montage• CyberShake• Epigenomics• LIGO • SIPHT

• Three sizes for each workflow: • small (about 30 tasks)• medium (about 100 tasks) • large (about 1000 tasks)

• Each task can be executed on every cluster

Performance EvaluationExperimental Setup (2): the workflows


MontageLIGO

SIPHT

CyberShake Epigenomics

Performance EvaluationExperimental Setup (3): the workflows


• Three scheduling algorithms to schedule each workflow:• HEFT: a well-known makespan minimization algorithm• Fastest: submits all tasks to the fastest cluster• Cheapest: submits all tasks to the cheapest (and

slowest) cluster

• The Normalized Cost and the Normalized Makespan of a workflow:

• CC : the cost of executing that workflow with Cheapest• MH : the makespan of executing that workflow with HEFT€

NC = total schedulecos tCC HM

makespanscheduleNM

Performance EvaluationExperimental Setup (4): metrics


Performance EvaluationExperimental Results (1)

Normalized Makespan (left) and Normalized Cost (right) of scheduling workflows with HEFT, Fastest and Cheapest



Normalized Makespan (left) and Normalized Cost (right) of scheduling small workflows with the Partial Critical Paths algorithm

deadline=deadline-factor x MH



Normalized Makespan (left) and Normalized Cost (right) of scheduling medium workflows with the Partial Critical Paths algorithm



Normalized Makespan (left) and Normalized Cost (right) of scheduling large workflows with the Partial Critical Paths algorithm


• One of the most cited algorithms in this area has been proposed by Yu et al.:• divide the workflow into partitions • assign each partition a sub-deadline according to the minimum

execution time of each task and the overall deadline of the workflow• try to minimize the cost of execution of each partition under the

sub-deadline constraints

Performance EvaluationComparison to Other Algorithms (1)


Performance EvaluationComparison to Other Algorithms (2): Cost

CyberShake Epigenomics

LIGO them

us


Performance EvaluationComparison to Other Algorithms (3): Cost

Montage SIPHT


Related Work• Sakellariou et al. proposed two scheduling algorithms

for minimizing the execution time under budget constraints:

• Initially schedule a workflow with minimum execution time, and then refine the schedule until its budget constraint is satisfied

• Initially assign each task to the cheapest resource, and then refine the schedule to shorten the execution time under budget constraints


Conclusions• PCP: a new algorithm for workflow scheduling in utility

grids that minimizes the total execution cost while meeting a user-defined deadline

• Simulation results: • PCP has a promising performance in small and medium

workflows• PCP’s performance in large workflows is variable and depends

on the structure of the workflow

• Future work:• To extend our algorithm to support other economic grid models • Try to enhance it for the cloud computing model


Information

• PDS group home page and publications database: www.pds.ewi.tudelft.nl

• KOALA web site: www.st.ewi.tudelft.nl/koala

• Grid Workloads Archive (GWA): gwa.ewi.tudelft.nl

• Failure Trace Archive (FTA): fta.inria.fr

http://www.pds.ewi.tudelft.nl/

http://www.st.ewi.tudelft.nl/koala

Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths

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