We construct, analyze and solve models of systems where a number of servers offer services to an incoming stream of demands. Each server goes through alternating periods of being operative and inoperative. The objective is to evaluate and optimize performance and cost metrics. A large real-life data set containing information about server breakdowns is analyzed first. The results indicate that the durations of the operative periods are not distributed exponentially. However, hyperexponential distributions are found to be a good fit for the observed data. A model based on these distributions is then formulated, and is solved exactly using the method of spectral expansion. A simple approximation which is accurate for heavily loaded systems is also proposed. The results of a number of numerical experiments are reported.