Finite source blocking systems with multi-level active and idle periods

Service systems are studied with a limited capacity and an input by a finite number of sources that can have different active (service) and idle levels. The random periods of these levels are generally distributed. It is shown that the steady state distribution has a product form and is insensitive to the distributional forms of the random periods (i.e. it depends only on their means). In particular, different active and idle levels appear to ‘average out’.