Fast simulation of discrete time queues with Markov modulated batch arrivals and batch departures

In this paper we consider a slotted queueing model with finite buffers and correlated input. Arrivals are generated by different sources and offered in batches at the end of each slot. The batch sizes depend on the states of the sources which change their states according to Markov schemes. In case that the buffer reaches its limits, the excess of the buffer is lost. At the end of a slot a random batch is removed from the buffer. We prove a large deviations result for the loss probability in this model and apply importance sampling for estimation of this probability.