On discrete-time single-server queues with Markov modulated batch Bernoulli input and finite capacity

This paper investigates a discrete-time system with Markov modulated batch Bernoulli process inputs, general service times, and a finite capacity waiting room (queue). The FIFO and space priority service rules are considered. The main motivation for studying this type of queue is its potential applicability to time-slotted communication systems in broadband ISDN. Applying the supplementary variable technique and the matrix analysis approach, the authors obtain the steady-state distributions of the number of customers in the system as well as loss probabilities under individual service rules.