Performability Evaluation of Grid Environments Using Stochastic Reward Nets

In this paper, performance of grid computing environment is studied in the presence of failure-repair of the resources. To achieve this, in the first step, each of the grid resource is individually modeled using Stochastic Reward Nets (SRNs), and mean response time of the resource for grid tasks is computed as a performance measure. In individual models, three different scheduling schemes called random selection, non-preemptive priority, and preemptive priority are considered to simultaneously schedule local and grid tasks to the processors of a single resource. In the next step, single resource models are combined to shape an entire grid environment. Since the number of the resources in a large-scale grid environment is more than can be handled using such a monolithic SRN, two approximate SRN models using folding and fixed-point techniques are proposed to evaluate the performance of the whole grid environment. Brouwer's fixed-point theorem is used to theoretically prove the existence of a solution to the fixed-point approximate model. Numerical results indicate an improvement of several orders of magnitude in the model state space reduction without a significant loss of accuracy.