Minimum cost design of a parallel computing cluster

In this paper, we address the problem of determining the minimal cost network size of a parallel computing cluster. The paper illustrates how a complex network planning problem can be simplified using approximation methods. Thus, the approximations assist the network planners to estimate the minimal cost parallel computing networks. We assume all nodes in the network are identical and independent. Equipment cost, cost of time to process the task and cost of system failure are used as components in the cost function. Golden section search is used to locate the minima of the cost function. These minima are used as sampling points to determine the approximation function. Linear and non-linear approximations are used to represent the optimal network size. Results indicate that non-linear approximation is a much better representation of the system with a very low percentage error.