Costdriven Scheduling of Grid Workflows Using Partial Critical

Cost-driven Scheduling of Grid Workflows Using Partial Critical Paths 28 October 2010 Saeid Abrishami and Mahmoud Naghibzadeh Ferdowsi University of Mashhad, Iran Dick Epema Delft University of Technology Delft, the Netherlands Grid 2010, Brussels, Belgium Delft University of Technology Challenge the future

Introduction • Utility Grids versus Community Grids • main difference: Qo. S 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 Qo. S attributes than execution time, e. g. , economical cost, play a role, so it is a multi-objective problem • We propose a new Qo. S-based workflow scheduling algorithm called Partial Critical Paths (PCP) Partial Critical Paths 2

The PCP Algorithm: main idea • The PCP Algorithm tries to create a schedule that 1. minimizes the total execution cost of a workflow 2. while satisfying a user-defined deadline • The PCP Algorithm 1. 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 Partial Critical Paths 3

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 {t 1, t 2, …, 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 t 1 tentry e 1, 4 texit t 3 t 2 t 5 t 6 Partial Critical Paths 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) Partial Critical Paths 5

Basic Definitions • Minumum Exection Time: • Minimum Transfer Time: used for finding the partial critical paths • 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 Partial Critical Paths 6

The PCP Scheduling Algorithm PROCEDURE Schedule. Workflow(G(T, V), deadline) 1. 2. 3. 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 • 1. 2. 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. 2. 3. Mark tentry and texit as scheduled Set AST(tentry)=0 and AST(texit) = deadline Call Schedule. Parents(texit) If this procedure was successful make advance reservations for all tasks in G according to the schedule, otherwise return failure Partial Critical Paths 7

Schedule. Parents (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 126 p 281 t 69 • 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 Partial Critical Paths 8

Schedule. Parents (2) PROCEDURE Schedule. Parents(t) 1. If t has no unscheduled parents then return success 2. Let Critical. Path be the partial critical path of t 3. Call Schedule. Path(Critical. Path) 4. If this procedure is unsuccessful, return failure and a suggested start time for the failed node (try to repair) 5. For all ti on Critical. Path /* from start to end */ Call Schedule. Parents(ti) 6. Iterate over all non-scheduled parents of t Partial Critical Paths 9

Scheduling. Path (1) • Schedule. Path tries to find the cheapest schedule for a Path without violating the actual start times of the scheduled children of the tasks on Path • Schedule. Path 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 Partial Critical Paths 10

Scheduling. Path (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 Partial Critical Paths 11

An Example (1) Start: Call Schedule. Parents(E) S 1 4 7 2 5 8 3 6 9 Partial Critical Paths E 12

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

An Example (3) Call Schedule. Path for path 2 -6 -9 Call Schedule. Parents for nodes 2, 6, and 9, respectively S 1 4 7 2 5 8 3 6 9 Partial Critical Paths E 14

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

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

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

An Example (7) Now scheduling of the path 2 -6 -9 has been finished, and Schedule. Parents is called again for node E to find its next partial critical path and to schedule that path S 1 4 7 2 5 8 3 6 9 Partial Critical Paths E 18

Performance Evaluation Experimental Setup (1): the system • Simulation Software: Grid. Sim • 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) Partial Critical Paths 19

Performance Evaluation Experimental Setup (2): the workflows • Five synthetic workflow applications that are based on real scientific workflows (see next page) • Montage • Cyber. Shake • 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 Partial Critical Paths 20

Performance Evaluation Experimental Setup (3): the workflows LIGO Montage SIPHT Epigenomics Cyber. Shake Partial Critical Paths 21

Performance Evaluation Experimental Setup (4): metrics • Three scheduling algorithms to schedule each workflow: • HEFT: • Fastest: • Cheapest: a well-known makespan minimization algorithm submits all tasks to the fastest cluster 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 Partial Critical Paths 22

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

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 Partial Critical Paths 24

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

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

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 subdeadline constraints Partial Critical Paths 27

Performance Evaluation Comparison to Other Algorithms (2): Cost Cyber. Shake Epigenomics us LIGO Partial Critical Paths them 28

Performance Evaluation Comparison to Other Algorithms (3): Cost Montage SIPHT Partial Critical Paths 29

Related Work • Sakellariou et al. proposed two scheduling algorithms for minimizing the execution time under budget constraints: 1. Initially schedule a workflow with minimum execution time, and then refine the schedule until its budget constraint is satisfied 2. Initially assign each task to the cheapest resource, and then refine the schedule to shorten the execution time under budget constraints Partial Critical Paths 30

Conclusions • PCP: a new algorithm for workflow scheduling in utility grids that minimizes the total execution cost while meeting a userdefined 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 Partial Critical Paths 31

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 Partial Critical Paths 32