User-perceived availability of M-for-N shared spare-server systems with general repair-time distributions

In this study, we investigate the user-perceived availability of M-for-N shared spare-server systems. We assume that there are N identical working servers, each serving a single user group, and M identical shared spare servers in the system. We also assume that the time to failure of the server is subject to an exponential distribution, and the time needed to repair a failed server is subject to an arbitrary general distribution (with finite mean and variance). Under these assumptions, we derive the availability for each user group by combining the state transition analysis and the supplementary variable method.