This paper concerns the performance analysis of a slotted transmission system. Packets of equal size arrive at the transmission facility which can handle a certain maximum number of packets per time-unit called frame. Transmission is assumed to be gated at the start of frames. Temporary overflow is stored in a buffer with infinite capacity. The packet arrival process is described by a Markov chain with finite state space. We derive the stationary expected number of packets in the buffer and the stationary expected packet delay. We also formulate and describe the implementation of an algorithm to compute these quantities. The accuracy of the algorithm is checked by simulation. A realistic traffic model is given and specific parameters are chosen. Results and numerical aspects are evaluated.