Reliability of a controllable M/M/2 system with warm standbys operating under the triadic (0, Q, N, M) policy

We consider an M/M/2 queueing system with m operating machines, w warn stand-bys, and two removable servers. We assume that the number of working servers can be adjusted one at a time at any failure or repair completion epochs depending on the number of failed machines in the system. The reliability characteristics, such as the system reliability and the mean time to system failure (MTTF) in a controllable system operating under the triadic (0, Q, N, M) policy are derived. Numeraical results of the system reliability and the MTTF for various values of system parameters are provided.