Optimal number of nodes for computation in grid environments

We show that there exists an optimal number of nodes to be assigned to jobs for execution in grid systems, which depends on the distributions of computation and communication service times. We also show that the analytical models proposed for parallel computers are not accurate for grid systems. We therefore extend to grid environment the definitions of speedup, efficiency and efficacy that are usually given for parallel systems. We also adopt a queueing network model with three different types of workload to prove that in every case an optimal number of nodes exists and that the mean value of CPU and communication service times is just a scale factor for this optimum.