Analysis of machine-repairing systems with server breakdown and delayed repairs

This paper considers a machine-repairing system with a partial breakdown and delay-repairs. When the servers fail, the service continues at a slower rate instead of stopping completely. We utilise a matrix-analytic method to obtain steady-state probabilities. We then develop system performance measures. A cost model is developed to simultaneously determine the optimal value of the number of servers, the number of standby servers, the two service rates, and the cost of maintaining system availability at an acceptable level. We employ the probabilistic global search Lausanne method to deal with the optimisation problem. Sensitivity analysis is also conducted in which various system parameters are evaluated under optimal operating conditions. Finally, an application example is provided to demonstrate how the presented model could be used in real-life situations.