In this paper we treat a discrete-time generalized semi-Markov process in which simultaneous deaths of more than one lifetime and simultaneous arrivals are permitted and service scheduling is probabilistic. Necessary and sufficient conditions for insensitivity are derived and a simple algorithmic procedure provided whereby the equilibrium probabilities can be furnished when insensitivity holds. Some particular cases of special interest are examined in detail.
"Insensitivity in Discrete-Time Generalized Semi-Markov Processes Allowing Multiple Events and Probabilistic Service Scheduling." Ann. Appl. Probab. 5 (1) 78 - 96, February, 1995. https://doi.org/10.1214/aoap/1177004829