A mathematical model for highly available clusters with one head and several identical computing nodes.

Fault-tolerant systems with repair-upon-failure strategy can become expensive in terms of labour and time. While postponing these repairs, it is essential to keep the whole system capable to deal with user requests. For this purpose, usually, a threshold value is defined which represents the minimum number of servers the system administrator should keep operative. Highly available multiprocessor systems with one head and several computation nodes is a common configuration in various cluster systems used as a low-cost alternative to supercomputers. It is typical to introduce a redundant head for such systems to improve availability. Deferred repairs can be used for such systems for reducing repair costs when no permanent repair facility exists on premises. Performability evaluation of such systems is very important since the systems are fault tolerant. In this paper, the performance modelling for highly available multiprocessor systems is presented. For these systems, one main and several identical computing nodes serving the same stream of arriving jobs is considered. To improve the availability of the system, the head node is backed-up. To account for delays due to switching of head node, such systems are modelled and solved for exact performability measures for both bounded and unbounded queuing systems assuming a deferred repair strategy