Looking at the stochastic modelling of systems, this book examines one of the basic problems with such modelling - the existence and uniqueness of stationary (limiting) distributions of system characteristics. The book looks at topics such as the arrival instants of customers in a queue, model continuity and insensitivity of stationary distributions concerning the form of the distribution functions of certain input characteristics. These problems have been traditionally treated by means of Markov, renewal, and Markov renewal processes, which the authors claim are often not adequate for these problems.