Bounds for the tail distribution in a queue with the superposition of general periodic Markov sources

For ATM networks we derive the bounds formulas for the asymptotic tail distribution in a queue whose arrival process is a superposition of general periodic Markov sources. Note that we make no assumption for the structure of the general periodic Markov sources except that the underlying Markov chains are irreducible. The periodic source model in this paper is thus rather general. Taking initial state conditions of the periodic sources into account, we construct a superposed arrival process. Contrary to the previous works, this implies that the periodic sources are not independent. We also provide examples to investigate the efficiency and the accuracy of our bound formulas