A queuing network model for minimizing the total makespan of computational grids

This paper offers a mathematical solution based on queuing theory and a generalized stochastic Petri net model to minimize the total makespan of the grid computing environments. A grid manager could minimize the total makespan through cautious distribution of subtasks to the grid resources. Subtask arrival rates depend on the arrival rate of the grid tasks submitted to the grid manager, local tasks directly submitted to the grid resources and the processing speed of the resources. Modeling the grid environment using queuing network, the steady state analysis of the network will result in the mean response time of the resources. Therefore, the total makespan could be minimized by minimizing the longest mean response time of the resources. The accuracy of the values obtained for the subtasks arrival rates at each of the grid resources from solving the corresponding queuing network could be further evaluated by steady state analysis of the generalized stochastic Petri net modeling the same grid environment.

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► We model grid computing environment using queuing networks (QNs) and generalized stochastic Petri nets (GSPNs).
► The proposed models consider both grid and local tasks.
► The aim of the modeling is to find subtask arrival rates at each of the grid resources to reach minimum total makespan.
► The results obtained for subtasks arrival rates in both methods (QN and GSPN) are similar.