A Mathematical Model for Cluster Applications

Abstract

In this paper, we use probabilistic modeling and techniques to derive formulas in order to determine the number of computer nodes needed to execute applications on a cluster of computers so that application response time can be satisfied. Our probabilistic model is basically an M/G/1/K queueing system.  In this model, we account for the workload conditions (in terms of the number of applications or jobs being received per unit time) as well as the processing power of each node.  Finally, We use simulations to present a numerical example showing how our probabilistic model can be used.