A central limit theorem for a class of Markovian packet streams under heavy traffic conditions

An earlier article by the authors treats a general class of Markovian packet streams which can be indexed by Markov chains. The limiting process formed by superposing an increasing number of thin packet streams is a sequence of dependent Poisson random variables and was given special attention. Here the authors show that, under heavy traffic conditions, , suitably scaled, possesses a multivariate-normal limiting distribution.