Transmitting telephone calls over the Internet causes problems not present in current telephone technology such as packet loss and delay due to queueing in routers. In this undergraduate thesis we study how a Markov modulated Poisson process is applied as an arrival process to a multiplexer and we study the performance in terms of loss probability. The input consists of the superposition of independent voice sources. The predictions of the model is compared with results obtained with simulations of the multiplexer made with a network simulator. The buffer occupancy distribution is also studied and we see how this distribution changes as the load increases.