3D Analytical Modelling and Iterative Solution for High Performance Computing Clusters

Mobile Cloud Computing enables the migration of services to the edge of Internet. Therefore, high performance computing clusters are widely deployed to improve computational capabilities of such environments. However, they are prone to failures and need analytical models to predict their behaviour in order to deliver desired quality-of-service and quality-of-experience to mobile users. This paper proposes a 3D analytical model and a problem-solving approach for sustainability evaluation of high-performance computing clusters. The proposed solution uses an iterative approach to obtain performance measurements to overcome the state space explosion problem. The availability modelling and evaluation of master and computing nodes are performed using a multi-repairman approach. The optimum number of repairmen is also obtained to get realistic results and reduce the overall cost. The proposed model is validated using discrete event simulation. The analytical approach is much faster and in good agreement with the simulations. The analysis focuses on mean queue length, throughput and mean response time outputs. The maximum differences between analytical and simulation results in the considered scenarios of up to a billion states are less than 1.149%, 3.82%, and 3.76%, respectively. These differences are well within the 5% of confidence interval of the simulation and the proposed model.