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A probabilistic task scheduling method for grid environments

Entezari Maleki, R ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.future.2011.09.005
  3. Abstract:
  4. This paper presents a probabilistic task scheduling method to minimize the overall mean response time of the tasks submitted to the grid computing environments. Minimum mean response time of a given task can be obtained by finding a subset of appropriate computational resources to service the task. To achieve this, a discrete time Markov chain (DTMC) representing the task scheduling process within the grid environment is constructed. The connection probabilities between the nodes representing the grid managers and resources can be considered as transition probabilities of the obtained DTMC. Knowing the mean response times of the managers and resources, and finding fundamental matrix of the DTMC, the mean response time related to each of the absorbing DTMCs existing inside the overall DTMC can be computed. Minimizing the obtained mean response times and taking into account the probability constraints in each of the absorbing DTMCs, a nonlinear programming (NLP) problem is defined. Solving the NLP problem, the connection probabilities between the managers and resources are obtained. Finally, using the connection probabilities, the best scheduling path within the environment and the minimum mean response time of a particular task can be achieved. In a case in which there is only one optimal scheduling choice within the environment, the proposed method can deterministically find such scheduling by assigning zero or one to the connection probabilities. Results obtained from evaluating the proposed method on the hypothesis and real grid environments show the preference of the proposed method compared to the other methods in minimizing both the overall mean response time of the tasks and total makespan of the environment
  5. Keywords:
  6. Discrete time Markov chain ; Grid environment ; Computational resources ; Connection probability ; Discrete time Markov chains ; Fundamental matrix ; Grid computing environment ; Grid environments ; Makespan ; Mean response time ; Optimal scheduling ; Probabilistic scheduling ; Probability constraints ; Task-scheduling ; Transition probabilities ; Management ; Managers ; Markov processes ; Multitasking ; Optimization ; Probability ; Queueing networks ; Scheduling ; Scheduling algorithms ; Grid computing
  7. Source: Future Generation Computer Systems ; Volume 28, Issue 3 , 2012 , Pages 513-524 ; 0167739X (ISSN)
  8. URL: http://www.sciencedirect.com/science/article/pii/S0167739X11001713