Maintenance of a deteriorating single server system with Markovian arrivals and random shocks

► The effect of the introduction of the probabilistic rule while the server is idle. ► Relationship between effective service rate and denominator of traffic intensity. ► Role of correlation in the performance measures. ► Insensitive results for the extreme cases of the probability (0 or 1). ► Generalization of the results from Poisson process to versatile point process.