A mathematical model for performability of Beowulf clusters

Beowulf clusters have become very popular as an alternative to supercomputers world-wide. However, the most pressing issues of today´s cluster solutions is the need for high availability and performance. Such systems, clearly, are prone to break-downs. Even if cover is provided with some probability c, there will be reconfiguration and/or rebooting delays to resume the operation of a cluster. In this paper, the performance modelling for Beowulf multiprocessor systems is presented. For these systems, one head processor and several identical processors serving a common stream of arriving jobs is considered. To account for delays due to reconfiguration and rebooting, such systems are modelled and solved for exact performability measures, for both bounded and unbounded queuing capacities, using the spectral expansion method.