This paper presents an alternative traffic model for an ATM multiplexer providing video, voice, image, and data services. The traffic model classifies the input traffic into two types: real-time and non-real-time. The input process for realtime traffic is periodic and correlated, while that for non-realtime traffic is batch Poisson and independent. This multiplexer is assumed to be a priority queueing system with synchronous servers operating on time-frame basis and with separate finite buffers for each type of traffic. State probabilities and performance measures are successfully obtained using a Markov analysis technique and an application of the residue theorem in complex variable. The results can be applied in the design of an ATM multiplexer.