Analytical Modelling of Large Scale Multi-Server Systems with Deferred Repairs: A Reward Rate Approach

Fault-tolerant systems with repair-upon-failure strategy can become expensive in terms of labour and time. Postponing non essential repairs can reduce these costs. Of course, 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. In this paper, analytical modelling of large scale multi-server systems, with identical servers, serving a stream of arriving jobs is considered. A hierarchical approach which uses Markov reward rates has been employed. Simulation results are also presented in order to confirm the accuracy of the analytical model.