On Discrete Buffers in a Two-State Environment

A discrete buffered system with infinite buffer size, one single output channel, and periodic opportunities for service (synchronous transmission) is considered in a two-state environment. The output channel is subjected to a random interruption process, which is characterized by a Bernoulli sequence of independent random variables, with probabilities dependent on the environment state. The environment states have random sojourn times with "mixture of geometrics"-type distributions. The arrival process is dependent on the environment state, but arbitrary. For this system, expressions are derived for the probability generating functions of the number of messages in the buffer at various time instants. A number of special cases and possible applications of the model are discussed, and an extended example is given as an illustration of the study.