Insensitivity in Discrete-Time Generalized Semi-Markov Processes Allowing Multiple Events and Probabilistic Service Scheduling

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.