Markov modulated fluid queues with batch fluid arrivals

In the conventional Markov modulated fluid queue, the buffer content process has a continuous sample path. This paper concerns a Markov modulated fluid queue whose buffer content process may have jumps. This model extends not only the conventional fluid queue but also the MAP/G/1 model. We give a procedure to get a Laplace–Stieltjes transform of the stationary joint distribution of the buffer content and background state. Some numerical examples are presented as well.