ON DISCRETE-TIME SINGLE-SERVER QUEUES WITH MARKOV MODULATED BATCH BERNOULLI INPUT AND FINITE CAPACITY

Abstract

This paper investigates a discrete-time system with Markov modulated batch Bernoulli process (MMBP) 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 (B-ISDN). Applying the supplementary variable technique and the matrix analysis approach, we obtain the steady-state distributions of the number of customers in the system as well as loss probabilities under individual service rules.

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