Task dispatching approach to reduce the number of waiting tasks in grid environments

In this paper, a mathematical solution for reducing the mean number of the tasks waiting to be processed in a grid environment is proposed. The approach uses queuing theory and models the grid environment in the form of an open queuing network (QN). Applying the steady state analysis to the proposed QN and minimizing the mean number of waiting tasks within the grid environment, an equality and inequality system is obtained. Solving the equality and inequality system, subtasks arrival rates at each of the resources within the grid environment can be estimated. Applying the obtained subtasks arrival rates at each of the grid resources, the mean number of the waiting tasks in the grid environment could be minimized. To evaluate the results obtained from the proposed QN and provide a graphical representation of the grid environment a formal description of the environment in terms of generalized stochastic Petri nets (GSPNs) is presented. Steady state analyzing of the GSPN model and finding the subtask dispatching weights at each of the grid resources, subtask arrival rates can be estimated. Comparing the results obtained from two proposed approaches shows that the subtasks arrival rates achieved from QNs and GSPNs are the same.