Mathematical modelling for performability analysis of homogeneous multi-server systems with deferred repairs.

Fault-tolerant systems with repair-upon-failure strategy can become expensive in terms of labour and time. Especially for homogeneous multi-server systems, if no control hierarchy exists, postponing non essential repairs can reduce these costs without affecting the availability of the whole system significantly. 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. Performability evaluation of such systems is very important. In this paper, the performance modelling of a homogeneous, multi-server system, serving a stream of arriving jobs is considered. To analyse the effects of various deferred repair strategies, such systems are modelled and solved for exact performability measures for both bounded and unbounded queuing systems.