Multi-server machine repair model with standbys and synchronous multiple vacation

This paper investigates a machine repair problem with homogeneous machines and standbys available, in which multiple technicians are responsible for supervising these machines and operate a (R, V, K) synchronous vacation policy. With such a policy, if any V idle technicians exist in the system, these V (V < R) technicians would take a synchronous vacation. Upon returning from vacation, they would take another vacation if there is no broken machine waiting in the queue. This pattern continues until at least one failed machine arrives. It is assumed that the number of teams/groups on vacation is less than or equal to K (0 ≦ KV < R). The matrix analytical method is employed to obtain a steady-state probability and the closed-form expression of the system performance measures. Efficient approaches are performed to deal with the optimization problem of the discrete/continuous variables while maintaining the system availability at a specified acceptable level.