A MAP/PH/1 k-out-of-n:G System with External Customer Service under Non-Preemptive Priority, Working Vacation and N-Policy

In this paper a working vacation is incorporated to analyse the reliability of a k-out-of-n: G repairable system with a single server. The server fixes broken system components and offers external customer service during idle time to create more revenue. In this model, if the server is busy with an external failed component, the server changes its service to internal components only after completing the ongoing service. The failure times of system components follow an exponential distribution, while the service time follows a phase-type distribution. A Markovian arrival process (MAP) is used to show the arrival pattern of external customers to the system. Here, the matrix-geometric method is used to obtain the system’s stability and steady-state distributions. A numerical investigation is conducted to analyse the variations in system reliability corresponding to different parameters. Also, the optimal N policy level is obtained numerically by minimizing a cost function.