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Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths

Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths. Saeid Abrishami and Mahmoud Naghibzadeh Ferdowsi University of Mashhad Mashhad, Iran. Dick Epema Delft University of Technology Delft, the Netherlands. Grid 2010, Brussels, Belgium. Introduction.

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Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths

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  1. Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths Saeid Abrishami and Mahmoud Naghibzadeh Ferdowsi University of Mashhad Mashhad, Iran Dick Epema Delft University of Technology Delft, the Netherlands Grid 2010, Brussels, Belgium

  2. Introduction • Utility Grids versus Community Grids • main difference: QoS and SLAs • Workflows: a common application type in distributed systems • The Workflow SchedulingProblem • 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)

  3. The PCP Algorithm: main idea • The PCP Algorithm tries to create a schedule that • minimizes the total execution cost of a workflow • 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 • finds the partial critical path to each scheduled task on the critical path and executes the same procedure in a recursive manner overall critical path partial critical path

  4. 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 e1,4 t1 t4 tentry texit t3 t2 t5 t6

  5. 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)

  6. 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 used for finding the partial critical paths

  7. The PCP Scheduling Algorithm PROCEDURE 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 • Mark tentry and texit as scheduled • Set AST(tentry)=0 and AST(texit) = deadline • Call ScheduleParents(texit) • If this procedure was successful make advance reservations for all tasks in G according to the schedule, otherwise return failure

  8. 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 126 281 p t 69

  9. 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) • Iterate over all non-scheduled parents of t

  10. 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

  11. 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

  12. An Example (1) Start: Call ScheduleParents(E) 1 4 7 S 2 5 8 E 3 6 9

  13. An Example (2) find the Partial Critical Path for node E (this is the overall critical path of the workflow) 1 4 7 S 2 5 8 E 3 6 9

  14. An Example (3) Call SchedulePath for path 2-6-9 Call ScheduleParents for nodes 2, 6, and 9, respectively 1 4 7 S 2 5 8 E 3 6 9

  15. An Example (4) Node 2 has no unscheduled parents, so its partial critical path is empty 1 4 7 S 2 5 8 E 3 6 9

  16. An Example (5) Node 6: find its partial critical path and then call SchedulePath ScheduleParents is called for node 3 but it has no unscheduled parents If SchedulePath cannot schedule this path, then it returns failure, which causes the path 2-6-9 to be rescheduled. 1 4 7 S 2 5 8 E 3 6 9

  17. An Example (6) Node 9: find its partial critical path and then call SchedulePath ScheduleParents is called for the nodes 5 and 8 but they have no unscheduled parents 1 4 7 If SchedulePath cannot schedule this path, then it returns failure, which causes the path 2-6-9 to be rescheduled. S 2 5 8 E 3 6 9

  18. An Example (7) 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 1 4 7 S 2 5 8 E 3 6 9

  19. Performance Evaluation Experimental Setup (1): the system • 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)

  20. Performance Evaluation Experimental Setup (2): the workflows • 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

  21. Performance Evaluation Experimental Setup (3): the workflows LIGO Montage SIPHT Epigenomics CyberShake

  22. Performance Evaluation Experimental Setup (4): metrics • 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

  23. Performance Evaluation Experimental Results (1) Normalized Makespan (left) and Normalized Cost (right) of scheduling workflows with HEFT, Fastest and Cheapest

  24. Performance Evaluation Experimental Results (2) deadline=deadline-factor x MH Normalized Makespan (left) and Normalized Cost (right) of scheduling small workflows with the Partial Critical Paths algorithm

  25. Performance Evaluation Experimental Results (3) Normalized Makespan (left) and Normalized Cost (right) of scheduling medium workflows with the Partial Critical Paths algorithm

  26. Performance Evaluation Experimental Results (4) Normalized Makespan (left) and Normalized Cost (right) of scheduling large workflows with the Partial Critical Paths algorithm

  27. Performance Evaluation Comparison to Other Algorithms (1) • 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

  28. Performance Evaluation Comparison to Other Algorithms (2): Cost CyberShake Epigenomics us LIGO them

  29. Performance Evaluation Comparison to Other Algorithms (3): Cost Montage SIPHT

  30. 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

  31. 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

  32. 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

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