In a number of well-known applied probability models certain steady-state probabilities display an insensitivity property: they depend only on the means of certain lifetime distributions entering the definition of the model, not on their exact shapes. This phenomenon has been studied by Matthes and co-workers in a general framework. New and simple proofs are given for their essential results.
"Insensitivity of Steady-state Distributions of Generalized Semi-Markov Processes. Part II." Ann. Probab. 6 (1) 85 - 93, February, 1978. https://doi.org/10.1214/aop/1176995612