LOSS and GAIN approaches

Presented by: Elaheh Barati

elaheh@wayne.edu

Wayne State University

"Scheduling Workflows
With Budget Constraints"

Subtitle

 Rizos Sakellariou, Henan Zhao, Eleni AND Tsiakkouri, Marios D. Dikaiakos

School of Computer Science, University of Manchester

Department of Computer Science, University of Cyprus

In Integrated research in GRID computing, pp. 189-202. Springer US, 2007.

Content

• Introduction
• Background
• Proposed algorithm
• Experimental results
• Conclusions

In the context of Grid computing, applications can be represented as workflows modeled as Directed Acyclic Graphs (DAGs)

A DAG represents a model that helps build a schedule
of the tasks onto resources in a way that precedence constraints are respected and the schedule is optimized

Minimization of an application's execution time might be an important user requirement

Minimization of an application's execution time might be an important user requirement

Managing a Grid environment is a more complex task

Aim is to find the schedule that gives the shortest makespan for a given DAG and a given set of resources without exceeding the budget available.

Objective

To solve the problem of scheduling optimally under a budget constraint :

LOSS

GAIN

Families of Heuristics

LOSS Approach

1.  Starts with an assignment of tasks onto machines that is optimized for makespan
2.  Swaps tasks between machines by choosing first those tasks where the largest savings in terms of money will result in the smallest loss in terms of schedule length.

GAIN Approach

1. starts with the cheapest assignment of tasks onto resources
2.  Swaps tasks between machines by choosing first those tasks where the largest benefits in terms of minimizing the makespan will be obtained for the smallest expense.

(a) an example graph

(b) the computation cost of nodes on three different machines

 (c) communication cost between the machines

(e) the start time and finish time of
each node in (d)

(d) the schedule derived using the HEFT algorithm

(b) the computation cost of nodes on three different machines

Contribution of this paper

Extension of the traditional DAG models:  

The overall financial cost of the schedule does not exceed a certain budget

Proposed Algorithm

The key idea:                                                              

 satisfy the budget constraint by
finding the best affordable assignment possible

Algorithm definitions

best assignment 

the assignment whose execution time is the minimum possible. 

affordable assignment

the assignment whose cost does not exceed the budget available.​

 cost of the cheapest assignment

available budget 

Algorithm Assumptions

• LOSS1 and GAIN1: the weights are computed exactly as
  described before.
• LOSS2 and GAIN2: the values of Told , Tnew , and Cnew , Cold
  refer to the benefit in terms of the overall makespan
  and the overall cost for the schedule and not the benefit associated with the individual tasks being considered for reassignment.
• LOSS3 and GAIN3: the weights are recomputed each time a reassignment is made by the algorithm.

Variants

• Run the proposed algorithm with four different types
  of DAGs used​ in: 
  • FFT
  • Fork-Join (denoted by FRJ)
  • Laplace (denoted by LPL)
  • Random DAGs​

Experiment Setup

All DAGs contain about 100 nodes scheduled on 3 different machines.

Experimental results

value of k varies between 0.1 and 0.9

values of budget that lie in ten equally distanced points
between the money cost for the cheapest assignment and the money cost for the schedule generated by HEFT or HBMCT

total cost of the assignment

the cost of the cheapest assignment

Experimental results

makespan returned by algorithm

the makespan
of the cheapest assignment

Normalized Schedule Length:

the makespan of HEFT or HBMCT

between 0 and 1 indicating how close the algorithm was to each of the two bounds

Experimental results

Average Normalized Difference metric:

Experimental results

Average normalized difference for the three variants of loss when HEFT is used to generate the initial schedule

Average normalized difference for the three variants of gain

Average running time for each variant of the algorithm, using FFT DAGs.

Conclusion

•  An algorithm was implemented to schedule DAGs onto heterogeneous machines under budget constraints.
• Different variants of the algorithm were
  modelled and evaluated.
• Starting from an optimized schedule, in terms of its makespan, pays off when trying to satisfy the budget
  constraint. 

Future work

• Other types of DAGs that correspond to workflows of interest in the Grid community could be considered
•  More sophisticated models to charge for machine time could be incorporated
• More dynamic scenarios and environments for the execution of the DAGs and the modelling of the machine time could be considered