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Scheduling Parameter Sweep Applications

- Sathish Vadhiyar
- Sources/Credits Papers on survey of heuristis

and APST papers. Figures taken from the papers

Background

- Tasks of a job do not have dependencies
- A machine executes a single task at a time

space shared machines - Collection of tasks and machines are known

apriori - Matching of tasks to machines done offline
- Estimates of execution time for each task on each

machine is known

Scheduling Problem

- ETC Expected time to compute matrix
- ETC(i,j) estimated execution time of task i on

machine j - Notations
- mat(j) machine availability time for machine j,

i.e., earliest time at which j has completed all

tasks that were previously assigned to it - Completion time, ct(i,j) mat(j)ETC(i,j)
- Objective find max ct(i, j), makespan, and find

heuristic with minimum makespan

Scheduling Heuristics

- Opportunistic Load Balancing (OLB)
- Assign next task (arbitrary order) to the next

available machine - Regardless of tasks ETC on that machine
- User Directed Allocation (UDA)
- Assign next task (arbitrary order) to the machine

with lowest ETC - Regardless of machine availability
- Fast greedy
- Assign each task (arbitrary order) to the machine

with minimum ct

Scheduling Heuristics

- 4. Min-Min
- Start with a list of Unmapped tasks, U.
- Determine the set of minimum completion times for

U. - Choose the next task that has min of min

completion times and assign to the machine that

provides the min. completion time. - The new mapped task is removed from U and the

process is repeated. - Theme - Map as many tasks as possible to their

first choice of machine - Since short jobs are mapped first, the percentage

of tasks that are allocated to their first choice

is high

Scheduling Heuristics

- 5. Max-Min
- Start with a list of Unmapped tasks, U.
- Determine the set of minimum completion times for

U. - Choose the next task that has max of min

completion times and assign to the machine that

provides the min. completion time. - The new mapped task is removed from U and the

process is repeated. - Avoid starvation of long tasks
- Long tasks executed concurrently with short tasks
- Better machine-utilization
- 6. Greedy
- Combination of max-min and min-min
- Evaluates both and finds the better solution

Scheduling Heuristics

- Genetic Algorithm

GA

- Operates 200 chromosomes. A chromosome represents

a mapping of task to machines, a vector of size

t. - Initial population 200 chromosomes randomly

generated with 1 Min-Min seed - Evaluation initial population evaluated based

on fitness value (makespan) - Selection
- Roulette wheel probabilistically generate new

population, with better mappings, from previous

population - Elitism guaranteeing that the best solution

(fittest) is carried forward

GA - Roulette wheel scheme

- Chromosomes 1 2 3 4
- Score 4 10 14 2
- Probability of 0.13 0.33 0.47 0.07
- selection
- Select a random number, r, between 0 and 1.
- Progressively add the probabilities until the sum

is greater than r

GA

- Crossover
- Choose pairs of chromosomes.
- For every pair
- Choose a random point
- exchange machine assignments from that point till

the end of the chromosome - Mutation. For every chromosome
- Randomly select a task
- Randomly reassign it to new machine
- Evaluation
- Stopping criterion
- Either 1000 iterations or
- No change in elite chromosome for 150 iterations

Simulated Annealing

- Poorer solutions accepted with a probability that

depends on temperature value - Initial mapping
- Initial temperature initial makespan
- Each iteration
- Generate new mapping based on mutation of prev.

mapping. Obtain new makespan - If new makespan better, accept
- If new makespan worse, accept if a random number

z in 0,1 gt y where - Reduce temperature by 10

Genetic Simulated Annealing (GSA)

- Almost same as GA
- During selection, SA is employed to form new

population - Initial system temperature average makespan of

the population - Each iteration of GA
- Post-mutation or post-crossover, during a

comparison of chromosome with the previous

chromosome - if (new makespan) lt (old makespan

temperature), new chromosome becomes part of the

population - Temperature decreased by 10

Tabu search

- Keeps track of regions of solution space that

have already been searched - Starts with a random mapping
- Generate all possible pairs of tasks, (i,j), t in

(0, t-1) and j in (i1, t) - i and js machine assignments are exchanged

(short hop) and makespan evaluated - If makespan better (successful short hop), search

begins from i0, else search continues from

previous (i,j) - Continue until 1200 successful short hops or all

pairs have been evaluated - Add final mapping to tabu list. The list keeps

track of solution space searched - A new random mapping generated that differs from

solution space by atleast half the machine

assignments (long hop) - Search continued until fixed number of short and

long hops

A Comparison Study of Static Mapping Heuristics

for a Class of Meta-Tasks on Heterogeneous

Computing Systems Tracy D. Braun et. al

Simulation Results

- ETC matrix randomly generated using uniform

distribution - ETC matrices may be
- Consistent m/c i faster than m/c j for all

tasks. Each row is sorted across all columns. - Inconsistent not sorted
- Semi-consistent sorted across even columns.
- t512, m16
- OLB, UDA, Fast Greedy and Greedy few seconds
- SA, tabu 30 seconds
- GA, GSA 60 seconds
- A - 20 minutes

Task execution results

- Consistent cases
- UDA performs worst in consistent cases why?
- Inconsistent cases
- UDA improves because best machines are

distributed avoiding load imbalance - Fast greedy and Min-Min improve upon UDA since

they consider MCTs and MCTs are also evenly

distributed - Tabu search gave poor performance for

inconsistent cases since there are more

successful short hops than long hops. - In both cases, Min-Min performed better than

Max-Min due to the nature of the task mix - In both cases, GAs performed the best.

All tasks were assigned the same machine

AppLeS Parameter Sweep Template (APST)

APST

- For efficient deployment of parameter sweep

applications on the Grid - Distinct experiments share large input files and

produce large output files - Shared data files must be co-located with

experiments - PSA set of independent tasks
- Input set of files, a single file can be input

to more than 1 task - Output each task produces exactly one output
- Number of computational tasks in PSA orders of

magnitude greater than number of processors

Scheduling Heuristics

- Self-scheduled workqueue
- Adaptive scheduling algorithm assigns tasks to

nodes as soon as they are available in a greedy

fashion - Suitable
- If no large input files
- Large clusters interconnected with high-speed

clusters - Computation to data-movement times are high

Algorithm

Gantt Chart

Step 4

Heuristics

- Min-min
- f minimum of CTi,j
- Best minimum
- Max-min
- f minimum of CTi,j
- Best maximum
- Sufferage
- f ratio between second minimum and minimum
- Best maximum
- a host should be given to a task that would

suffer the most if not given the host - XSufferage
- Site-level
- Cluster-level MCTs and cluster-level sufferage
- Avoids deficiencies of sufferage when a tasks

input file is in a cluster and 2 hosts in the

cluster have identical performance

Sufferage and XSufferage

Host k in cluster j

Sufferage and XSufferage

Sample APST Setup

Impact of Quality of Information on Scheduling

- Random noise -p,p p 0-100 added to

accuracy of estimates

Results

Results

Robust Static Allocation of Resources for

Independent Tasks-Sugavanam et. al., JPDC 2007

- ETC numbers are just estimates and inaccurate
- Need to map tasks to maximize the robustness of

makespan against estimation errors - Robustness?
- Degradation in makespan is within acceptable

limits when estimates are perturbed - The goal is to maximize the collective allowable

error in estimation without makespan exceeding

the constraint

Problem Formulation

- Cest vector of estimated execution times on a

machine - C vector of actual times
- Performance feature, Ø that determines the

robustness of the makespan is the finish times of

machines Fj, 1ltjltM - Robustness radius for machine j and for mapping

µ minimum Euclidean distance between C and Cest

within which the finish time of machine j can

reach tolerable variation

Robustness Radius

- Within this robustness radius, the finish time of

machine j will be atmost the makespan constraint,

tau. - The above equation can be interpreted as the

perpendicular distance from cest to the

hyperplane, tau-Fj(C) 0 - Rewritten as

Robustness Metric

- Robustness metric for the mapping
- If Euclidean distance between actual and

estimated is no larger than the above metric, the

makespan will be atmost the constraint, tau - The larger the robustness metric, better the

mapping - Thus the problem is to maximize the metric such

that the makespan is within the time constraint

Heuristics Max-Max

Greedy Iterative Maximization (GIM)

Greedy Iterative Maximization (GIM)

Sum Iterative Maximization (SIM)

Robustness improvement change in the sum of

the robustness radii of the machines after task

reassignment or swapping

Sum Iterative Maximization (SIM)

Genitor

Genitor

Memetic Algorithm

- Combines global search using genetic algorithm

and local search using hill climbing

Memetic

HereBoy Evolutionary Algorithm

- Combines GA and SA

HereBoy Evolutionary Algorithm

Reduces the mutation as the current robustness

reaches upper bound

User defined maximum mutation rate

User defined maximum probability

Probability of accepting a poorer solution

UB calculation for Hereboy

- Assumes a homogeneous MET system execution time

for a task on all machines is equal to minimum

execution time on the original set of machines - The tasks are arranged in ascending order
- NT/M. The first N tasks are stored in a set S

GIM and SIM had low makespan and high robustness

References

- The AppLeS Parameter Sweep Template User-Level

Middleware for the Grid by Henri Casanova,

Graziano Obertelli, Francine Berman and Rich

wolski Proceedings of the Super Computing

Conference (SC'2000). - Heuristics for Scheduling Parameter Sweep

applications in Grid environments by Henri

Casanova, Arnaud Legrand, Dmitrii Zagorodnov and

Francine Berman in Proceedings of the 9th

Heterogeneous Computing workshop (HCW'2000),

pp349-363. - A Comparison Study of Static Mapping Heuristics

for a Class of Meta-Tasks on Heterogeneous

Computing Systems Tracy D. Braun, Howard Jay

Siegel, Noah Beck, Ladislau L. Bölóni, Albert I.

Reuther, Mitchell D. Theys, Bin Yao, Richard F.

Freund, Muthucumaru Maheswaran, James P.

Robertson, Debra Hensgen, Eighth Heterogeneous

Computing Workshop , April 12 - 12, 1999, San

Juan, Puerto Rico Page 15 - Robust static allocation of resources for

independent tasks under makespan and dollar cost

constraints. Journal of Parallel and Distributed

Computing, Volume 67, Issue 4, April 2007, Pages

400-416. Prasanna Sugavanam, H.J. Siegel, Anthony

A. Maciejewski, Mohana Oltikar, Ashish Mehta, Ron

Pichel, Aaron Horiuchi, Vladimir Shestak,

Mohammad Al-Otaibi, Yogish Krishnamurthy, et al.

Simulation Background

- ETC(i,j) B(i)xrij
- B(i) xbi xbi ? 1, ?b
- xrij ? 1, ?r
- ?r, ?b can control machine and task heterogeneity
- ETC matrix randomly generated using uniform

distribution

Models used in APST

Scheduling

- Goal
- Minimize applications makespan - time between

when 1st input file submitted and when last

output file is obtained - Sched()
- Takes into account resource performance estimates

to generate a plan for assigning file transfers

to links and tasks to hosts - Call sched repeatedly at various point of time

(called scheduling events) to make it more

adaptive - At each scheduling event, sched() knows
- Grid topology
- Number and locations of copies of input files
- List of computations and file transfers currently

underway or already completed

APST Architecture

NWS also used for forecasting ETC values