Busy time of a nonstationary single-channel service system and related matters

A method is described for computing the busy time probability distribution density in a nonstationary single channel service system. This computer-aided method reduces the probability density computation to solution of a two dimensional integral Volterra type equation and, in a simpler case where the duration of customer service and the time intervals between arrivals of customers are described by nonstationary exponential formulae, to a single dimensional Volterra type equation. A method is described for design of nonstationary system where explicit expression of an accurate solution is possible. Some related matters are considered.