In this paper, we present a discrete-time finite queueing model with deterministic service times and an MMBBP (Markov Modulated Batch Bernoulli Process) as a bursty input traffic model of IP packets in order to investigate the performance of a DBAS (Dynamic Bandwidth Allocation Scheme) in an ATM/IWU (interworking unit). We assume that the segmentation processing time devoted to each cell requires several slot times in the ATM/IWU. In an MMBBP process, the arrivals during a slot time occur as batch Bernoulli processes with the batch size distributions varying according to the phases of a Markov chain. As performance measures, we obtain the packet loss probability and the mean packet delay of an arbitrary packet. We present some numerical results to show the effects of the service time and burstiness of input traffic on the performance of the presented DBAS.